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On Size and Scale in Ceomorphology
Abstract
Examines some of the formal relations between landform parameters themselves, or between them and supposed governing processes in terms of the information required in geomorphological theories and the constraints imposed by sound mechanical theories. It is principally concerned with empirical proportional relations and the sections include: allometric analysis; the form of alluvial fans; functionally; determined allometry: total stream length and drainage area; allometry as a test of formal assumptions; hydromorphological equations; dimensional analysis and similitude. -Keith Clayton
... Geomorphic scaling laws derived from feature dimensions demonstrate allometry: a general physical principle in 25 which geometric (and/or metabolic) characteristics of an object or organism are correlated to its size. Allometric patterns in geomorphology are a quantitative signature of intrinsic structure, organisation, or regularity (Church and Mark, 1980;Dodds and Rothman, 2000;Moscardelli and Wood, 2006;Straub et al., 2007;Paola et al., 2009;Wolinsky et al., 2010; https://doi.org/10.5194/esurf-2019-39 Preprint. ...
... Although a test of drainage-network evolution in an experimental basin by Mosley and Parker (1972) did not confirm Woldenberg's (1966) argument for allometric growth, neither did their exercise disparage geomorphic allometry as a subject for further research. Rather, Mosley and Parker (1972) 45 describe their null result with a generosity that further opened the problem, encouraging geomorphologists to consider the inductive challenges posed by "static" versus "dynamic" allometry (Mosley and Parker, 1972;Bull, 1975Bull, , 1977Church and Mark, 1980). The majority of geomorphic scaling laws exemplify static allometry: snapshots of landform examples sampled from a 50 collection of different sites, or from a "population" of many examples at a single site. ...
... Opportunities to record stages of dynamic allometry in a landscape, from initial to "final" morphology, 240 are rare -not only for individual landforms, but also for a collective "population" of spatially related landforms. As Church and Mark (1980) advised: "The most appealing avenue for resolution of the problem, in general, appears to lie in recourse to physical models. Empirical proportional relations take on a crucial role in this strategy, for they will tell us whether or not scale distortion (allometry) occurs between various combinations of the extensive properties of the prototype and model." ...
Allometry refers to a physical principle in which geometric (and/or metabolic) characteristics of an object or organism are correlated to its size. Allometric scaling relationships typically manifest as power laws. In geomorphic contexts, scaling relationships are a quantitative signature of organisation, structure, or regularity in a landscape, even if the mechanistic processes responsible for creating such a pattern are unclear. Despite the ubiquity and variety of scaling relationships in physical landscapes, the emergence and development of these relationships tend to be difficult to observe – either because the spatial and/or temporal scales over which they evolve are so great, or because the conditions that drive them are so dangerous (e.g., an extreme hazard event). Here, we use a physical experiment to examine dynamic allometry in overwash morphology along a model coastal barrier. We document the emergence of a canonical scaling law for deposit (washover) length versus area. Comparing the experimental features, formed during a single forcing event, to four decades of change in real washover morphology from the Ria Formosa barrier system, in southern Portugal, we show that features forming at the event scale might exhibit a different pattern of change over longer time scales. This work reinforces the potential importance of initial conditions in landscape evolution, such that a landscape may reflect characteristics associated with an equilibrium or steady-state condition even when features within that landscape do not.
... Researchers showed that geomorphic parameters can be used to identify the catchment types. Terrain analysis explores the catchment formation mechanisms of different disaster types by revealing the relationship between the river basin size and its contribution to the basin [12][13][14][15]. Melton's ruggedness number has been used to obtain a rapid first approximation of the potential debris flow disaster [16][17][18][19]. ...
... Secondly, 80% of all debris flow events in a catchment that belong to the same type were selected. As a result, we obtained a total of 90 catchment samples, including 13 The precision of the debris flow inventory greatly affects the reliability of the analysis results [46]. In this study, the debris flow inventory of the Beijing mountainous area was obtained from the list in the document, named Debris Flow in Beijing Mountain Area [42]. ...
... The Mr, which is a dimensionless parameter, is used for measuring the roughness and average slope of the catchments [13,56]. It effectively characterizes the geological disaster process type of the river basin [18]. ...
The distinguishable sediment concentration, density, and transport mechanisms characterize the different magnitudes of destruction due to debris flow process (DFP). Identifying the dominating DFP type within a catchment is of paramount importance in determining the efficient delineation and mitigation strategies. However, few studies have focused on the identification of the DFP types (including water-flood, debris-flood, and debris-flow) based on machine learning methods. Therefore, while taking Beijing as the study area, this paper aims to establish an integrated framework for the identification of the DFP types, which consists of an indicator calculation system, imbalance dataset learning (borderline-Synthetic Minority Oversampling Technique (borderline-SMOTE)), and classification model selection (Random Forest (RF), AdaBoost, Gradient Boosting (GBDT)). The classification accuracies of the models were compared and the significance of parameters was then assessed. The results indicate that Random Forest has the highest accuracy (0.752), together with the highest area under the receiver operating characteristic curve (AUROC = 0.73), and the lowest root-mean-square error (RMSE = 0.544). This study confirms that the catchment shape and the relief gradient features benefit the identification of the DFP types. Whereby, the roughness index (RI) and the Relief ratio (Rr) can be used to effectively describe the DFP types. The spatial distribution of the DFP types is analyzed in this paper to provide a reference for diverse practical measures, which are suitable for the particularity of highly destructive catchments.
... Fan catchment relationships became a fundamental concern and empirical models were utilized to understand the links between certain characteristics of fans and their corresponding catchments. Several studies explored the relation between the size of fans and their contributing catchments to understand the mechanisms of fan development (Bull 1962;Hooke 1968;Church & Mark 1980;Mills 1982Mills , 1983Lecce 1990;Viseras et al. 2003). Depositional processes usually have a considerable impact on fan catchment relationships Therefore the study of the relationships between some of the distinctive morphometric variables of alluvial fans and their catchments is important in the classification of fan catchment systems according to the dominant depositional process. ...
... The full list of morphometric variables, used to describe the fans and corresponding catchments, is given in Table 1. The morphometric variables that led to the classification of alluvial fan catchment systems into groups according to the dominant primary depositional process (fluvial and/or debris flow) controlling fan formation and recent evolution were the catchment area, (Melton 1965;Church & Mark 1980) calculated by the formula ...
... Melton's ruggedness number is basically a slope index for the catchment area. It is a dimensionless measure of catchment relief providing an effective measure of gradient down which material moves towards the fan (Church & Mark 1980;Kostaschuk et al. 1986). A valuable characteristic of the ruggedness number is its capability of discriminating catchments dominated by debris flow processes from catchments dominated by fluvial processes Table 3. Maximum, minimum and mean values of the characteristic parameters for the groups of fans and catchment areas (Marchi & Dalla Fontana 2005;Karymbalis 2007). ...
We applied a computational method to aid in clustering 41 alluvial fans along the southern coast of the Gulf of Corinth, Greece. The morphology of the fans and their catchments was quantitatively expressed through 12 morphometric parameters estimated using geographical information system techniques and the relationships among the geomorphometric features of the fans and their catchments were examined. Self-organizing maps were used to investigate the clustering tendency of fans based on morphometric variables describing both the fans and their corresponding catchments. The results of unsupervised classification through the self-organizing maps method revealed correlations among the morphometric parameters and five groups of alluvial fans were identified. These groups had a clear physical explanation, showed a preferred geographical distribution and reflected the processes related to the development of the fans. The geographical distribution of the fan catchment groups was partially controlled by variations in the relative tectonic uplift rate, which was the main control on the accommodation space for the development and accretion of the fans. The smaller fans were located in the central part of the study area, where the uplift rates were higher, whereas larger fluvial-dominated fan deltas formed to the east and west of the central group, where the uplift rates were lower.
... It has been claimed that the range of Hack's (1957) law exponents relating river length to drainage basin area is 0.57 -0.6 (Maritan et al., 1996). Because it is known that the Euclidean length across drainage basins is proportional to the drainage basin area to the power of 0.5 (Church and Mark, 1980;Montgomery and Dietrich, 1992). It is logical to relate river sinuosity to optimal 2D percolation, so that the exponent in Hack's law becomes simply half the sinuosity exponent. ...
... where 1.21 is the percolation theoretical value for the optimal path exponent in 2D (Porto et al., 1997), and C 1 is an unknown (Montgomery and Dietrich, 1992; proportional to A 1/2 , Church and Mark, 1980), Eq. (1) (Hunt, 2016a) also yields the Hack-type relationship given by ...
Predicting the temporal and spatial evolution of the river network is part of the Earth's critical zone investigations, which has become an important endeavor. However, modeling integration of the river network and critical zone over millions of years is rare. We address the problem of how to predict integrated river length development as a function of time within a framework of addressing the critical zone depth as a function of time. In case of groundwater-river interaction, we find a non-linear spatio-temporal scaling relationship between time, t , and total river length L , given by t ≈ L p with power p being near 1.2. The basis of our model is the presumption that groundwater flow paths are relevant to river integration. As river integration may proceed over disconnected basins with irregular relief, the relevant optimal subsurface flow paths are proposed to be defined within a 3D network, with optimal path exponent 1.43. Because the 2D model of the river length has already been shown to relate to a power of the Euclidean distance across a drainage basin with the predicted universal optimal path exponent from percolation theory, D opt = 1.21, the optimal groundwater paths should relate to the surface river length with an exponent equaling the ratio 1.43/1.21 = 1.18. To define a predictive relationship for the river length, we need to use specific length and time scales. We assume that the fundamental specific length scale is a characteristic particle size (which is commonly used to define the pore scale flow network), and the fundamental time scale is the ratio of the particle size to the regional groundwater flow rate. In this paper, we consider cases of predicting spatio-temporal scaling of drainage organization in the southwestern USA–the Amargosa, Mojave, Gila (and its tributaries) and the Rio Grande, and Pecos Rivers. For the Mojave and Gila Rivers, theoretical results for time scales of river integration since ca. 10 Ma are quite predictive, though the predicted time scales exceed observation for the Rio Grande and Pecos.
... This rigour is commendable, but it sweeps across many equally interesting aspects of a field which often seeks answers across least twelve orders of magnitude, from one-day considering flows in porous media (~10 -6 m), next the distribution of water resources at the planetary scale (~10 6 m). It is quite fitting that not only should our sense of the rightful method of scientific enquiry change from one scale to the next (Schumm and Lichty, 1965), but so too should the nature of our theoretical postulates and the observations that support them (Church and Mark, 1980). An enduring truism in the move towards a global environmental science is that we must think globally, but often must act locally. ...
... An enduring truism in the move towards a global environmental science is that we must think globally, but often must act locally. Whilst the laws of physics operate similarly in all locations, the specifically-configured geographic circumstances in which they apply do not (Church, 1998). Moreover, the socially-contingent factors that skew scientists' theory choice are even less universal. ...
This chapter surveys the history of geomorphology and Earth system science 1965-2000. With roots in Enlightenment thought from Hutton, Somerville, Humboldt and Darwin we see a preoccupation with a holistic form of Earth system science develop through the reductionist, mechanistic ideas of the 19th and 20th century to be re-awoken in the 1960 and 1970s environmental movements and the space age, culminating in the major research programmes set by NASA and others subsequently. At the same time the chapter charts the evolution in geomorphology to consider plate tectonics and the origins of mountain ranges, geochemistry and its links between surfaces systems and the atmosphere, to later ideas emphasising the interplay between landforms and life. This chapter surveys changing interconnected ideas within this field and draws parallels and contrasts between the holistic depictions of Earth system science in the early part of the subject's history and the fundamental challenges facing us today as we grapple to find science-led solutions to global environmental change.
... 简介 ( (Melton, 1957a). Mr is used as a measure of the roughness and average slope of the a basin (Church and Mark, 1980;Melton, 1965). It reflects the dynamics and the susceptibility of the catchment to debris flows, and is widely used in the study of debris flows (Bovis and Jakob, 1999;Carabella et al., 2019;Jackson et al., 1987;Melton, 1957b;Wilford et al., 2004). ...
... A is the surface area, Ap is the projected area. drainage density (Dd) (Strahler, 1952), meaning that the Rn is influenced positively by the structural terrain complexity (Church and Mark, 1980). High Rn occurs in mountain catchments with a debris flow response, and low values indicate the type of fluvial process (Slaymaker, 2010). ...
Basin area, Basin perimeter, Relative perimeter, Main channel length, Curvature of the main stream, Basin length, Total length of stream channels, Average slope, Extent of terrain greater than 30°, Extent of terrain greater than 35°, Extent of terrain greater than 40°, Extent of terrain between 30°and 40°, Average aspect, Basin relief, Relief ratio, Relative relief ratio, Stream order, Stream number, Stream length ratio, Drainage density, Stream frequency, Drainage intensity, Circularity ration, Form factor, Shape factor ratio, Elongation ratio, Compactness index, Bifurcation ratio, Hypsometric Integral (HI), Melton ratio (Mr), Plane curvature, Profile curvature, Roughness, Roughness index, Ruggedness number, Terrain Ruggedness Index (TRI), Topographic Position Index (TPI), Topographic Wetness Index (TWI), Stream Power Index (SPI), Sediment Transport Index (STI), Sediment Connectivity Index (SCI), Slope Length Index (SLI), Fan mean gradient, Fitness ratio, Infiltration number.
... In organismal biology the relationship is often between body mass and another variable, such as metabolic rate, growth rate, swimming, running, or flying speed, and home range size (e.g., Schmidt-Nielsen, 1984). However, allometry has also been applied to the study of landforms, such as river basins, channels, deltas, dolines, glacial cirques, and drumlins (Woldenberg, 1966;Bull, 1975;Kemmerly, 1976;Church and Mark, 1980;Evans, 2010;Wolinsky et al., 2010). ...
... In organismal biology the relationship is often between body mass and another variable, such as metabolic rate, growth rate, swimming, running, or flying speed, and home range size (e.g., Schmidt-Nielsen, 1984). However, allometry has also been applied to the study of landforms, such as river basins, channels, deltas, dolines, glacial cirques, and drumlins (Woldenberg, 1966;Bull, 1975;Kemmerly, 1976;Church and Mark, 1980;Evans, 2010;Wolinsky et al., 2010). ...
Tidal channels are structurally and functionally prominent features in tidal marshes, so their restoration is central to marsh restoration. Prominent design questions in tidal marsh restoration include: How many tidal channels can a restoration site support, and thus, how many dike breaches should be made to restore tidal inundation and tidal channels? How much total channel surface area will be supported by a restored marsh, and thus, how many fish, shrimp, or other organisms can be supported by restored channel habitat? These basic design questions can be addressed by landscape allometry, which describes the proportional relative rates of change in a system between two entities of particular interest—in the case of marsh restoration, between the amount of marsh area to be restored and a wide variety of measures of tidal channel network geometry. This paper briefly reviews the development of landscape allometry, insights that it provides into landforms and related ecological patterns, and its utility and application to marsh restoration planning, design and monitoring. Its practical application is illustrated in a conceptual restoration design that is the basis for a current restoration project.
... Fan-basin relationships became a fundamental concern and empirical models were utilized to describe the rates of change between certain characteristics of an alluvial fan and its drainage basin. Several studies explore the relation between the size of fans and their contributing basins to understand the mechanisms of fan construction (Bull, 1962;Hooke, 1968;Church and Mark, 1980). Later studies of fan-basin morphometric relations focus on differentiation between debris flow and fluvially dominated fans (Kostaschuk et al., 1986;de Scally and Owens, 2004). ...
... An index of basin ruggedness (Melton, 1965;Church and Mark, 1980) calculated by the formula: ...
This study deals with the morphometric analysis of seventeen, Late Holocene, coastal alluvial fans (fan deltas) formed by mountainous streams that discharge along the southwestern coast of the Gulf of Corinth in Northern Peloponnese, Greece. Selected morphometric parameters of the drainage basins were measured and/or estimated using topographic maps at the scale of 1:50,000 while those of the fan deltas were derived from detailed topographic diagrams at the scale of 1:5,000 utilizing GIS techniques. In the current paper Self Organizing Maps (SOM) were used in order to classify the coastal alluvial fans, according to the primary dynamic factors (fluvial sediment supply and/or debris flow processes) controlling their formation and recent evolution. They were also used, to investigate the nonlinear relationships between geomorphic features (expressed by morphometric parameters) of the drainage basins and features of their fans. Furthermore, the SOM approach allowed the study of the clustering tendency of both qualitative data and morphometric variables of the fans and their basins. The coupling of quantitative morphometric analysis and artificial intelligence methods lead to the classification of the fans into two types: Large stream basins have produced relatively extensive gently sloping fans dominated by fluvial processes while torrents with small rough drainage basins have formed steep debris-flow dominated fans.
... This is the basis of hydraulic geometry analysis (Hey 1978, Ferguson 1986 or allometric studies, which are based on empirical power functions, relating basin size, usually basin area, to channel geometry (e.g. width, depth, cross-sectional area, channel length, area of alluvial fans) (Church and Mark 1980). Comparative studies can also consider the temporal trend of each spatial component to consider differences in adjustment rather than differences in structure. ...
... This can be done with comparative studies to identify thresholds or correlations between attributes of components in similarity or connectivity approaches. Allometric analysis is a well-known quantitative approach based on the fluvial systemic, which facilitated major developments in geomorphology (Church and Mark 1980). The fluvial system concept also underlined efforts to establish discriminate models of fluvial pattern (Bridge 1993) and regression models linking discharge and channel forms (Hey and Thorne 1986). ...
... This is the basis of hydraulic geometry analysis (Hey 1978, Ferguson 1986 or allometric studies, which are based on empirical power functions, relating basin size, usually basin area, to channel geometry (e.g. width, depth, cross-sectional area, channel length, area of alluvial fans) (Church and Mark 1980). Comparative studies can also consider the temporal trend of each spatial component to consider differences in adjustment rather than differences in structure. ...
... This can be done with comparative studies to identify thresholds or correlations between attributes of components in similarity or connectivity approaches. Allometric analysis is a well-known quantitative approach based on the fluvial systemic, which facilitated major developments in geomorphology (Church and Mark 1980). The fluvial system concept also underlined efforts to establish discriminate models of fluvial pattern (Bridge 1993) and regression models linking discharge and channel forms (Hey and Thorne 1986). ...
The fluvial system is a complex adaptive process-response system with two main physical components, the morphological system and the cascading system. The fluvial system changes progressively through geological time, as a result of normal erosional and depositional processes. The hydrosystem integrity depends on the dynamic interactions of hydrological, geomorphological and biological processes acting in these three dimensions over a range of time-scales. The fluvial anthroposystem theory, with human pressures ubiquitous for many centuries, rivers are reacting to multiple human pressures acting at different time-scales and different locations within the basin. Similarity analysis and connectivity analysis are ways to study the fluvial system in a comparative manner, one focusing on single temporal and spatial-scale components, the other on the links between components of different scales. This chapter talks about research on the Drome, the Roubion, the Eygues and the Bega river to understand the system evolution and to inform management decisions.
... In fact, they occur where there is a significant decrease in slope (from that of the channel upstream), limiting the transport capacity of the river and inducing deposits of sediment provided by its upstream steep tributaries. Some authors have included normalized or dimensionless data to produce better fits or better agreements with theoretical statements (Church and Mark 1980). Most of the relations follow a log–log or semi-logarithmic form (Table 21 .1). ...
... Further, establishing causality and correlations is particularly difficult when dealing with a process that is not at an equilibrium (Ebisemiju 1988). Mass equilibrium is more rapidly attained in small watersheds (Church and Mark 1980) , which implies that catchment comparisons should consider size effects. Strong correlations could be interpreted as evidence of such an equilibrium. ...
This chapter reviews statistical tools and illustrates their use to answer geomorphological questions, and also overviews their advantages and limits. Application of statistical tools in fluvial geomorphology has the advantages of reducing subjectivity, eliminating assumptions, facilitating comparison between different spatial and temporal datasets of large sizes and refining data collection. Bivariate statistics, and regressions in particular, have been one of the most popular statistical tools in geomorphology. They focus on the relationship, or correlation, between two variables. Probabilities are useful to generate models in which the variables of interest are categorical, such as indicator variables of events (e.g. occurrence of peak flows). One of the most basic tools dealing with probabilities is the logistic or multinomial models. To develop more realistic descriptions of fluvial morphological systems, process-response systems, time and space trends and size effects, requires the collection of sufficient data and more thought about their relevance.
... Schumm and Lichty [84] indicated the dependent and independent processes of landform evolution at various spatial scales. Church and Mark [85] explained the proportional characteristics of landforms and their behaviors at different scales. Gomi et al. [86] reviewed that hydrologic and geomorphic processes differed by headwaters (≤1 km 2 in catchment area) and network systems (>1 km 2 in catchment area). ...
Accurate modeling of flood flow hydrographs for small forested catchments in steep mountainous terrain is challenging because of large errors in the estimation of response time using existing empirical equations. The time of concentration (TC) for a catchment is a widely used time parameter for estimating peak discharges in hydrological designs. In this study, we developed an estimated TC using readily available mountain catchment variables, a small catchment, steep slope, and narrow valley, using empirical equations. For our approach, we used directly measured data from 39 forested catchments (area: 0.02–9.69 km2) during 3648 observed rainfall events over a 10-year observation period. Based on the uncertainties inherent in the empirical equation, the estimated TC values were compared and analyzed through multiple regression and two different modified empirical modelling equations using our observed catchment parameters. The mean TC was significantly correlated with catchment size and stream length but negatively correlated with stream slope (p < 0.01). As a result, the mean TC estimated using the three modelling equations with catchment variables was qualitatively similar and had relative differences ranging from −12.5 to 15.5 min (−49 to 56%). Therefore, the models (particularly modeling equations with multiple regression, a modified empirical formula, and modified SCS Lag) can efficiently determine the TC and can be used in any small forested catchment in steep mountainous terrain.
... This is significantly slower than the~13 km 2 /yr estimated for ridges associated with historical channel changes, or~16 km 2 /yr deduced from the mapped modern splay dynamics ( Fig. 7.9). Difficulties in comparing rates across spatial and temporal scales are common (Church and Mark 1980), and may reflect the existence of periods of reduced or absent ridge construction, or show that not all splays effectively contribute to the topographic construction of the ridges. Splays not followed by successful avulsion (e.g., 2005, 2006, 2008) are particularly likely to create local sand bodies without significant topographic expression. ...
Megafans are partial cones of river sediment that reach unexpectedly large dimensions, with the largest on Earth being 700 km long. Due to recent developments in space-based observations, global mapping efforts have shown that modern megafan features cover vast landscapes on most continents. This book provides a new inventory of nearly 300 megafans across five continents. Chapters focus on regional studies of megafans from all continents barring North America and Antarctica. The major morphological attributes of megafans and multi-megafan landscapes are discussed, and the principal controls on megafan development are examined. The book also compares megafans with alluvial fans, deltas, floodplains and the recently recognised 'major avulsive fluvial system' (MAFS). The final part of the book discusses the application of megafan research to economic geology, aquifers and planetary geology including layered deposits on Mars. This is an invaluable reference for researchers in geomorphology, sedimentology and physical geography.
... With this sample size we can compare the velocities averaged over decadal and millennial time-scales. The difficulty of measuring a process over different time scales has been a significant issue in assessing contemporary rates of geomorphic processes (Church and Mark 1980;Thorn 1982). When focusing on short time-scales such as years, decades or centuries, we may adopt uniformitarian assumptions and ignore large variations in geomorphic rates associated with changing climatic and geomorphic conditions of the late Quaternary and Holocene (Luckman and Fiske 1995). ...
We compare surface velocities of nine rock glaciers over decadal and millennial time scales using independently derived velocities. We surveyed 15 rock glaciers in the Selwyn Mountains in 1983 and again in 1995, thereby obtaining 12-year average velocities. We also determined millennial scale velocities using lichenometric ages and rock glacier length on nine of the 15 rock glaciers for which lichenometric ages were available. The mean surveyed velocity of the nine rock glaciers was 0.20± 0.11 m/yr, and the mean age-length velocity was 0.20 ± 0.13 m/yr. A paired t-test of the two independently derived data sets shows no difference at the 0.01 level of significance. Given that both measures have inherent errors, the decadal and millennial velocities should be considered as being the same order of magnitude. The similarity of results of these two independent methods suggests that (1) decadal scale velocities of rock glaciers are comparable to millennial scale velocities in this area, and (2) either method can resolve long-term velocities. We examined surveyed velocities in relation to rock glacier characteristics in order to identify controls on velocities. Surface velocity is expected to vary with density, the sine of surface slope, thickness and temperature. Rock glaciers facing NE were significantly longer and moved faster than rock glaciers facing other directions. This may be due to greater snow, ice and debris accumulation causing increased mass. Maximum surveyed velocity was significantly correlated with rock glacier thickness (r 2 = 0.88) and with the sine of surface slope (r 2 = 0.50), when one and two outliers were excluded from analyses, respectively. Future work focusing on the systematic measurement of the dimensions, age, and velocities of rock glaciers should help to improve our understanding of controls on velocities of rock glaciers.
... Plusieurs travaux ont démontré la corrélation positive entre la pente du cône et la dénivelée spécifique du bassin versant (Church et Mark, 1980 ;Marchi et Brochot, 2000) d'une part ; et d'autre part la corrélation négative forte avec la superficie du bassin versant. ...
Les fonds de vallées sont des espaces inédits pour étudier les changements environnementaux et sociauxdepuis la fin du Petit Âge Glaciaire. Le cas de la vallée de Maurienne dans les Alpes du Nord est exemplaire.La pression humaine est très contrastée. On observe une concentration inégale du peuplement, uneextension des grandes infrastructures de transport le long du thalweg de l’Arc inférieur et l’artificialisationdes cours d’eau. Les cônes de déjection torrentiels se distinguent dans ce paysage fortement anthropisépar la concentration des enjeux humains. L’évolution historique du peuplement sur les cônes soulève desquestionnements sur les facteurs de changements à l’origine de la transformation profonde des paysagesen vallée de Maurienne. Les principaux jalons historiques à l’origine de ces questionnements sont la crisetorrentielle de la fin du Petit Âge Glaciaire et l’atténuation de l’activité torrentielle post-1950. L’objectifde ce travail de thèse est de restituer les trajectoires socio-environnementales des cônes de déjection torrentielspar une approche géohistorique. Ce travail se focalise sur quatre cônes de déjection sélectionnésd’après des caractères paysagers distinctifs (boisement, urbanisation, infrastructure routière, agriculture).L’étude comparée des changements environnementaux et paysagers impose un double niveau de lecture.Le premier niveau permet d’étudier les évolutions historiques de l’environnement à l’échelle desbassins versants torrentiels et de la vallée par une lecture des sources écrites. Il cible en particulier lesactivités humaines, les dynamiques de peuplement et l’activité torrentielle depuis le premier tiers du 18èmesiècle. Ce premier niveau montre une diminution des crues dommageables au début du 20ème siècle en lienavec les travaux de correction torrentielle de la Restauration des Terrains de Montagne. La recrudescencedes enjeux impactés par les crues entre 1940 et la fin des années 1990 met en relief l’accroissement de lapression humaine à proximité des berges torrentielles. Le second niveau de lecture concerne l’étude destrajectoires paysagères par la comparaison diachronique des sources iconographiques. L’exploration desfonds d’archives a permis de rassembler un corpus de cadastres et de cartes anciennes. L’identification etl’interprétation de photographies anciennes par la mise en place d’une démarche participante de collecteconstituent la part la plus exploratoire de cette recherche. L’interprétation de ces données géohistoriquesdans un SIG-Historique a pour objectif la quantification de l’occupation des sols et de l’emprise torrentielle.Le résultat de la quantification est présenté par des modèles paysagers (transects, diagrammes de transition,etc..). Ce second niveau de lecture aboutit à la proposition d’un diagramme de synthèse...
... The ruggedness number [64] is influenced positively by the structural terrain complexity [66]. The Terrain Ruggedness Index and Topographic Position Index reflect the difference between a central pixel and its surrounding cells [67]. ...
Debris flows are a major geological hazard in mountainous regions. For improving mitigation, it is important to study the spatial distribution and factors controlling debris flows. In the Bailong River Basin, central China, landslides and debris flows are very well developed due to the large differences in terrain, the complex geological environment, and concentrated rainfall. For analysis, 52 influencing factors, statistical, machine learning, remote sensing and GIS methods were used to analyze the spatial distribution and controlling factors of 652 debris flow catchments with different frequencies. The spatial distribution of these catchments was divided into three zones according to their differences in debris flow frequencies. A comprehensive analysis of the relationship between various factors and debris flows was made. Through parameter optimization and feature selection, the Extra Trees classifier performed the best, with an accuracy of 95.6%. The results show that lithology was the most important factor controlling debris flows in the study area (with a contribution of 26%), followed by landslide density and factors affecting slope stability (road density, fault density and peak ground acceleration, with a total contribution of 30%). The average annual frequency of daily rainfall > 20 mm was the most important triggering factor (with a contribution of 7%). Forest area and vegetation cover were also important controlling factors (with a total contribution of 9%), and they should be regarded as an important component of debris flow mitigation measures. The results are helpful to improve the understanding of factors influencing debris flows and provide a reference for the formulation of mitigation measures.
... Spatial allometry is the special case of allometric rescaling in which form or function is rescaled according to spatial resolution or extent (Schneider 1998); the traditional allometric relationship between body size and shape becomes a relationship between size (spatial scale) and a geometric measurement (Schneider 2001b), as represented by a scalogram (Fig. 2). Certain landform features have been found to exhibit allometric behavior (Woldenberg 1969;Bull 1975;Church and Mark 1980;Wu and Li 2006b), so it is possible that land covers might also exhibit similar behavior. However, making the jump from the suggestive findings here to a more concrete understanding of spatial allometry for land covers will require testing relationships on realworld landscapes, establishing the full range of scales over which relationships hold, and identifying the physical mechanisms that constrain each relationship. ...
Context
Reliable scaling relationships allow prediction of unknown quantities at scales not directly observed. Scaling relationships for landscape patterns are commonly estimated following a process of coarse graining, in which pixels are aggregated and a mathematical function is then fit across the multiple resolutions. However, few studies have investigated how aggregation changes the landscape composition and configuration, which in turn alters the fitted scaling function and any predictions made using that function.
Objective
Evaluate how changes in composition/configuration produced by coarse graining affect scaling function fit and the accuracy of that function for predicting patterns at finer resolutions than observed.
Methods
Neutral model landscapes with controlled composition/configuration were generated in QRule. Each raster was aggregated to seven coarser resolutions, and landscape metrics computed. Five scaling functions were fit to the seven-value set for each landscape and metric. The best-performing function for each landscape/metric was downscaled to predict the metric at a fine resolution not used in the scale-fitting process. Downscaling accuracy was measured through relative error.
Results
(1) The power law is the only function that consistently fit scalograms across all compositions/configurations. (2) Downscaling accuracy is more sensitive to configuration than composition. (3) Majority rules aggregation preserves information better with dispersed land covers. (4) Downscaling accuracies were highest around power law exponents of − 0.5 suggesting the structure of the power law may affect results.
Conclusions
Aggregation impacts the fit and use of scaling functions for downscaling/prediction. Research to differentiate aggregation effects from physical processes in complex, real-world landscapes is needed.
... Given the distance involved, a spatial analysis was undertaken to estimate drainage basin size and likely fan sizes of the local rivers based on the correlation between alluvial fan area and drainage basin size (Guzzetti et al., 1997;Leeder, 1999;Stock et al., 2008). Other variables can affect the correlation such as basin slope, sediment yield (Oguchi and Ohmori, 1994), length of the mainstream, and drainage density (Church and Mark, 1980;Prabhakaran and Jawahar Raj, 2018), but in this study it is only feasible to estimate the current drainage basin size of tributaries. We used tables from Guzzetti et al. (1997) and Leeder (1999) (Table 2), and on the northwest and southeast sides of the Luangwa gravels cover approximately 22 km 2 and 14.4 km 2 respectively. ...
This is the first systematic investigation of two distinctive geomorphological features recorded in the central Luangwa River valley, Zambia. A series of low hills was found to be capped by thin (~1 m) gravel deposits containing stratified Stone Age artefacts. More widespread gravels occur on the margins of the Luangwa River floodplain lacking stratified artefacts. The previously unreported hilltop deposits are interpreted as remnants of a dissected land-surface, and the valley floor gravels as redeposited clasts from c. 20 m of down-cutting. Clast analysis and drainage basin size analysis support a hypothesis of gravel deposition by unconstrained debris flows from the distant Muchinga escarpment, or from an intermediate zone. Excavation of a perched deposit revealed a coarsely stratified Stone Age record indicating periodic emplacement of artefact-bearing gravels over an extended period. Deposition of these perched gravels continued into the Late Pleistocene (~77 ka), based on OSL dating, after which the current dissected landscape formed. We hypothesize further, based on a regional record of landscape instability and core data from Lake Malawi, that fan formation in the valley was linked to periods of extended aridity and reduced vegetation cover followed by episodic erosional events on the return to wetter conditions. We argue that the subsequent dissection of the land-surface is the end state of a sequence of responses to base-level changes and climate change.
... 3). Accordingly, the common denominator of political, development-oriented, scientific, and economic applications of the nexus approach appears to be a deductive reasoning that "leads to necessary statements embodied in theories" [13] (p. 342), or, in other words, to biased understandings of both the causes and origins of the problems addressed and the possible solutions. ...
This paper proposes a bottom-up "nexus medium" perspective to examine and understand social organization and how socio-ecological challenges in remote rural regions are dealt with in communities that receive only limited external support. While "nexus mediums" constitute substances, matter, or objects that combine manifold vital meanings and can be seen as socially constructed and materialized arenas of social interaction, autonomous resource management is seen as a means of local social organization. Taking water as the nexus medium of choice allows us to generate locally informed insights about the role of this scarce resource for the everyday life and social organization of communities inhabiting arid rural areas. This reasoning will be exemplified by three local case studies conducted during empirical research in the Pamirs of Tajikistan utilizing a mix of qualitative methods. The findings reveal how many fundamental everyday-life-related aspects and activities of the studied communities are related to water, and how these communities are organized around common water use and management arrangements that are based on joint decision-making, shared benefits and responsibilities, and collaborative action. The "nexus medium" concept appears to be an appropriate approach for research that seeks to understand from a local perspective how communal living is organized and how socio-ecological challenges are addressed.
... Morphometric relationships between alluvial fans and relative feeder basins are different in the two considered groups, with much stronger correlation coefficients in fans not reached by debris flows (Tables 3, 4), supporting the hypothesis that fan morphology results from the dynamics of sedimentary environments in the feeder basin. The positive correlation between the Melton's number (or relief ratio) and fan gradient recognized by several authors (Melton 1965;Church and Mark 1980;Kostaschuk et al. 1986) is strong (ρ > 0.75) for F0 fans whereas it is not significant for F1 fans. This is in agreement with Kostaschuk et al. (1986) according to which river processes reflect basin parameters better than debris flows. ...
At the outlet of steep catchments, depositional processes ranging from stream flow to debris flow usually lead to alluvial fan development. Apart from geological and tectonic factors controlling basin sediment availability, several authors highlighted the control role of basin/fan morphometry on fan sedimentary processes. In this framework, the paper was aimed to identify the feeder basin variables that can best differentiate fan processes in Southern Italy. To evaluate the effect of the statistical method on variable selection, we compared logistic regression (LR) and artificial neural network (ANN), the latter not commonly used in fan studies. Alluvial fans were mapped at the mouth of steep V-shaped valleys dissecting the Tyrrhenian coast of northern Calabria, where crystalline-metamorphic and subordinate carbonate rocks crop out. Fans were classified through field survey into two groups: those with (F1), and those without (F0) any debris-flow evidence. Morphometric variables were derived for each basin/fan system. Percentage of lithological units cropping out in the catchments was also considered. Non-parametric statistics revealed that F0 and F1 significantly differ in fan size (area, perimeter and length), main channel slope, lowermost valley width, Melton’s number and geologic index. The relationships between morphometric variables were stronger for F0 than F1. The LR and ANN highlighted the primary control of basin lithology on fan dynamics, followed by basin mean slope. Although ANN outperformed LR in model calibration, both the approaches correctly classified most of the validation samples (> 87%). Alluvial fans with unknown depositional process were classified as belonging to the same group.
... The exponent for the 50th percentile in Table 2 (0.67 ± 0.02) indicates negative allometry (Church and Mark, 1980), meaning that basin area grows out of proportion to debris-flow volume. This result for debris flows is consistent with common findings in the inverse relationships between drainage basin size and sediment output per unit area at the basin outlet (for sediment yield from fluvial transport, see Dendy and Bolton, 1976;Milliman and Meade, 1983;de Vente et al., 2005). ...
A dataset of 809 debris flows that occurred in 537 basins in mountainous areas of northeastern Italy between the mid‐19th century and 2015 is collected and analyzed. A remarkable increase in the number of events is observed in the last four decades and is mainly ascribed to more systematic data collection. The correlation between debris‐flow volume and drainage basin area is obtained assuming a power‐law relationship. The exponent of the power‐law curve at the 50th percentile (0.67 ± 0.02) indicates negative allometry, which means that basin area grows out of proportion to debris‐flow volume. In contrast, the exponents at the 98th and 99th percentiles are close to one, implying that debris‐flow volumes grow linearly with basin areas. The isometric relationship between the largest debris flows and the corresponding basin areas is due to the enhanced debris supply provided by the activation of widespread sediment sources, the extent of which is proportional to the basin size. The probability density function of debris‐flow volume for a subset of the collected dataset is calculated using the kernel density estimation function, which permits estimating the probability of the occurrence of debris flows that exceed a given threshold volume. The comparison with debris flows in other hydroclimatic regions shows that, although debris‐flow volumes in northeastern Italy may attain high values, they are often exceeded by debris flows that occur in seismically active regions and/or are triggered by more intense rainstorms.
... It is an important parameter to understand the form-process interaction and the resultant manifestation of landscape sculpture. This dimensionless number [a product of drainage density (km −1 ) and relief (m)] is useful in describing the dynamics of drainage evolution (Church and Mark 1980). This number is a potential indicator of those hazards that are related to water movement and sediment mobilization, erosion on slopes and fluvial erosion (Slaymaker 2010). ...
Kurseong hill subdivision of the Darjeeling district, West Bengal, is associated with complex geomorphic set-up stemmed from form–process interaction on varied slope, relief, elevation, aspects, ridge–valley orientation, density and frequency of drainage, dissection, ruggedness and topographic wetness over different stratigraphy of geological rocks having different hardness. This complexity provides ample scope to evaluate the terrain and categorize the terrain into different sensitivity zones according to land utilization point of view so that different terrain segments can be classified into different grades and therefore can be rationally utilized and managed for sustainable use. Therefore, the present paper takes an attempt to evaluate the terrain sensitivity of the Kurseong hill subdivision based on multi-criteria analysis method to identify different grades of terrain according to their ability to hold and sustain the pressure of land utilization for settlements, agriculture and other land uses. Terrain sensitivity evaluation of the Kurseong hill subdivision has been done on the basis of the study of hard rock geology, some selected geomorphometric parameters derived from 3-arc-second SRTM digital elevation data as well as SOI toposheets having RF of 1:50,000 and the existing land use factors after necessary ground truthing on some selected sites. The procedure adopted for multi-criteria analysis is 1 km² grid-based rating value assignment algorithm of the selected parameters and determination of different classes of sensitive terrain and their gradation according to the capacity of the terrain to withstand present pressure of land utilization. Some measures for rational land utilization and management have also been proposed for optimal land use planning for the study area.
... The fan morphology is often controlled by the characteristics of the contributing catchment. A number of early studies (Bull 1964(Bull , 1977Denny 1965;Hooke 1968;Church & Mark 1980;Kostaschuk et al. 1986;Parker et al. 1998;Whipple & Trayler 1996) explored the relationship between the size of alluvial fans and the size of their contributing catchments to understand the mechanisms of fan construction. The larger the area of the catchment, the greater the potential to store sediment within it and therefore the more likely a decrease in the total amount of sediment delivered to the fan per transport event. ...
Alluvial and fluvial fans are the most widespread depositional landforms bordering the margins of long-lived highland regions and actively subsiding continental basins, across a broad spectrum of tectonic and climatic settings. Their significance is relevant not only to the local morphodynamics of mountain regions and proximal basinal sectors, but also to the long-term evolution of sediment-routing systems, affecting the propagation of stratigraphic signals of environmental change and the preservation potential of stratal successions over much larger spatial scales than those they occupy. Subaerial fan systems archive information on the palaeoclimate, local tectonic history and landscape response to various allogenic factors, although our ability to decipher such information is still limited. Early recognition of alluvial fans dates from the late nineteenth century, but a coordinated research community on these systems has been active only over the last few decades and the full relevance of fluvial fan systems to the geomorphology of present day continental basins and to the interpretation of ancient stratigraphic successions has been convincingly demonstrated only over the last decade. This introductory chapter summarizes advances in our knowledge of alluvial and fluvial fans, identifies potential new lines of future inquiry, and presents the contributions to this volume in the context of the current state of research.
... Schumm and Lichty, 1965;de Boer, 1992). Geomorphic systems are often considered hierarchically nested complex systems, which can have scale-dependent or scale-invariant properties (Church and Mark, 1980;Hallet, 1990). Depending upon scale, variables may be considered either dependent or independent; and the relative importance of time on geomorphic systems may vary (Schumm and Lichty, 1965), an idea that relates to the notion of fast and slow variables (Thorn and Welford, 1994). ...
Governance of coupled social-ecological systems (SESs) and the underlying geomorphic processes that structure and alter Earth's surface is a key challenge for global sustainability in the increasing uncertainty and change that defines the Anthropocene. Social-ecological resilience as a concept of scientific inquiry has contributed to new understandings of the dynamics of change in SESs, increasing our ability to contextualize and implement governance in these systems. Often, however, the importance of geomorphic change and geomorphological knowledge is somewhat missing from processes employed to inform SES governance. In this contribution, we argue that geomorphology and social-ecological resilience research should be integrated to improve governance toward sustainability. We first provide definitions of engineering, ecological, community, and social-ecological resilience and then explore the use of these concepts within and alongside geomorphology in the literature. While ecological studies often consider geomorphology as an important factor influencing the resilience of ecosystems and geomorphological studies often consider the engineering resilience of geomorphic systems of interest, very few studies define and employ a social-ecological resilience framing and explicitly link the concept to geomorphic systems. We present five key concepts—scale, feedbacks, state or regime, thresholds and regime shifts, and humans as part of the system—which we believe can help explicitly link important aspects of social-ecological resilience inquiry and geomorphological inquiry in order to strengthen the impact of both lines of research. Finally, we discuss how these five concepts might be used to integrate social-ecological resilience and geomorphology to better understand change in, and inform governance of, SESs.
... Geomorphic diversity in a river system can be identified over a range of spatial scales -from an individual 'reach' to the entire 'catchment' (Church and Mark, 1980) and at a range of time periods in a fluvial system. At the largest scale, it is controlled by basin planform and regional geology; at an intermediate scale, geomorphic variability is predominantly influenced by catchment area and hydrology; and small-scale variations are believed to be influenced by external factors, e.g., woody debris and localized geological structures or rocky outcrops (Bartley and Rutherford, 2005). ...
... The analysis of CLS involves the computation of topographic parameters, which depend on the mapping resolution, as noted very early by Evans [1972] and later confirmed by numerous studies [Chang and Tsai, 1991;Zhang and Montgomery, 1994;Wood, 1996;Shary et al., 2002;Schmidt and Andrew, 2005;Grieve et al., 2016b]. Resolution also affects feature detection, process identification, and modeling of landscape processes [Church and Mark, 1980;Mark and Aronson, 1984;de Boer, 1992;Kooi and Beaumont, 1996;Passalacqua et al., 2006]. With the advent of improved technology for acquiring high-resolution topographic (HRT) data, limitations imposed by the resolution of the input data set have been largely removed, revolutionizing the analysis of geomorphic processes [He et al., 2008;Roering et al., 2013;Tarolli, 2014;Passalacqua et al., 2015]. ...
Characteristic length scales (CLS) define landscape structure and delimit geomorphic processes. Here we use multiresolution analysis (MRA) to estimate such scales from high-resolution topographic data. MRA employs progressive terrain defocusing, via convolution of the terrain data with Gaussian kernels of increasing standard deviation, and calculation at each smoothing resolution of (i) the probability distributions of curvature and topographic index (defined as the ratio of slope to area in log scale) and (ii) characteristic spatial patterns of divergent and convergent topography identified by analyzing the curvature of the terrain. The MRA is first explored using synthetic 1-D and 2-D signals whose CLS are known. It is then validated against a set of MARSSIM (a landscape evolution model) steady state landscapes whose CLS were tuned by varying hillslope diffusivity and simulated noise amplitude. The known CLS match the scales at which the distributions of topographic index and curvature show scaling breaks, indicating that the MRA can identify CLS in landscapes based on the scaling behavior of topographic attributes. Finally, the MRA is deployed to measure the CLS of five natural landscapes using meter resolution digital terrain model data. CLS are inferred from the scaling breaks of the topographic index and curvature distributions and equated with (i) small-scale roughness features and (ii) the hillslope length scale.
... The "b" exponents of the power equation measure the proportional changes of the active area (AA) and cross-section area (CS) in relation to the distance from the headcut (DVF). According to Church and Mark (1980), if b = 1, the ratio is constant and no change occurs in terms of relative proportion or shape (i.e., the non-allometric or isometric case). Allometry occurs and is positive if b > 1, and negative if b < 1. ...
Gullies are an important part of the soil erosion process and their occurrence and development may cause serious problems to a region’s economy. Most types of gullies occur in Romania, but the majority are relatively small, discontinuous, valley-side gullies. To obtain some consistent observations on gully initiation and development in Romania’s physiographic conditions, we sampled a large spectrum of gully types (i.e., over 9000 gullies were inventoried and 12 were surveyed in detail). The case studies from the Moldavian Plateau reveal that gully development occurs in accordance with allometric principles which are characteristic to a variety of natural phenomena; sidewall processes are 5–10 times more effective in dislodging soil and rock compared to downcutting and are highly dependent on the silt-clay content in the gully perimeter; and the hydraulic efficiency of gullies is substantially lower compared to streams, and thereby the transport of debris along the gully is essentially a pulsating process. The rate of gully head cutting is over 1.5 m/year for gullies cut in sandy deposits and under 1 m/year for the gullies cut in marls and clays. A model of gully development is proposed which shows an accelerated rate of gully development immediately downstream after their initiation and a reduced progress and even cessation of advance when attaining an equilibrium length.
... Figure 8 shows how vertical amplitude of glacial cirques changes with size less than do length and width. This is an example of allometry (static rather than dynamic, as the data relate to only one point in time) (Church and Mark, 1980): large cirques are wider and longer more than they are deeper. The logarithmic regression exponents are statistically significantly different (Evans, 2010(Evans, , 2012. ...
... The allometric approach employed here is based on the observation that landforms are often self-affine fractals, i.e., form is "stretched" depending on scale (Mandelbrot, 1983;Ouchi and Matsushita, 1992;Rodriguez-Iturbe and Rinaldo, 1997). The fractal tradition typically focuses on how measured quantities vary as a power of measurement scale (Milne, 1991), whereas the allometric tradition focuses on proportional relative rates of change between two measured quantities in a system (Woldenberg, 1966;Bull, 1975;Church and Mark, 1980;Hood, 2007). Like hydraulic geometry, fractals and allometric systems are described by power functions. ...
Scaling relationships in landforms are a signature of locally stable, self-organized critical states, whichin tidal marshes result from the interaction of hydrodynamics, sediment dynamics, and biota. Empiricalscaling relationships for tidal channel planform were developed for reference tidal marshes in four of thelargest river deltas in Puget Sound to explore the potential underlying generative process of the observedpatterns and to provide design guidance for restoration of estuarine rearing habitat for juvenile salmon.The length, surface area, and drainage basin area of the largest, 2nd-largest, 3rd-largest, etc., up to 15th-largest tidal channels that drain a marsh island, as well as the lengths of the largest through 5th-largesttributaries to the largest and 2nd-largest channels scaled with marsh area. Additionally, regression ofthe scaling relationship y-intercepts against channel rank for each delta showed that the rate of channelsize decrease from one rank to the next was well fit by a power function, with R2values approaching 1.These relationships reveal predictable structure in many aspects of tidal channel planforms and allowengineers to design channel excavation in considerable detail. A simulation model of channel formationthrough recursive marsh island conglomeration in river deltas reproduced the scaling behavior of theempirically observed marsh channels, thereby linking observed patterns to the underlying generativeprocess. Previous allometric modeling has provided predictions of the number of tidal channels a marshrestoration site should have; this study provides a method to predict the size distribution of those chan-nels so that engineers, planners, and restoration scientists can better plan, design, and monitor marshrestoration.
... Figure 8 shows how vertical amplitude of glacial cirques changes with size less than do length and width. This is an example of allometry (static rather than dynamic, as the data relate to only one point in time) (Church and Mark, 1980): large cirques are wider and longer more than they are deeper. The logarithmic regression exponents are statistically significantly different (Evans, 2010(Evans, , 2012. ...
A system is described which 1) replaces existing sets of diverse terrain indices with an integrated group of statistics for process-relevant point characteristics; 2) calculates all these statistics in a single computer run from a single data set, thus achieving practical as well as conceptual simplicity; and 3) utilises altitude matrix data which is now becoming available as a by-product of photogrammetric automation, thus reducing the cost of data aquisition. The system is applicable to altitude matrix data at any horizontal resolution (grid mesh). Areas less than 5 x 5 km may be too small to provide replicable estimates of the land surface properties of a broader region. Results from seventeen matrices are provided. -from Author
... Figure 8 shows how vertical amplitude of glacial cirques changes with size less than do length and width. This is an example of allometry (static rather than dynamic, as the data relate to only one point in time) (Church and Mark, 1980): large cirques are wider and longer more than they are deeper. The logarithmic regression exponents are statistically significantly different (Evans, 2010(Evans, , 2012. ...
Within geomorphology, geomorphometry applies morphometric analysis to the land surface as a continuous surface (general geomorphometry), and to objects such as landforms, elementary forms, channels, and drainage basins extracted from that surface (specific geomorphometry). Special attention is paid here to a comprehensive taxonomy of fundamental geomorphometric variables, both those related to fields and those characterizing objects. The former include field-specific and field-invariant as well as local and regional variables. Derivatives of the land surface related to the gravity field are traditionally important in geomorphology, but an extended system of field-invariant curvatures has potential. Solar radiation and wind fields in relation to topography are of both climatic and geomorphological (process) importance. The morphometry of linear objects has been not only dominated by channels and drainage networks but also includes structural and tectonic morpholineaments. The problem of elementary form extraction from digital elevation models (DEMs) is basic to the analysis of areal objects. Scaling and scale-specificity questions are documented with quantile and allometric plots. Major prospects for the future development of geomorphometry are perceived as resulting not only from great technological development (new remote-sensing methods providing high-precision DEMs) but also from the effective integration of the empirical and theoretical streams of geomorphometry.
The timing and character of the initial marine flooding of extensional basins has implications for their tectonic history. Yet, the recognition of such flooding is difficult along rift basin margins due to the dominance of coarse-grained systems and the lack of marine fauna. This study conducts detailed facies and stratigraphic analysis of a Mio-Pliocene alluvial fan and fan-delta
succession in the Fish Creek Vallecito Basin in southern California. Our goal is to characterize the marine flooding surface, determine the paleogeographic position of the shoreline and estimate the magnitude of relative base-level rise that occurred during the marine incursion associated with the opening of the Gulf of California. Our results show that the flooding of the Elephant Trees alluvial fans is often marked by an abrupt lithologic and facies change from meter-scale boulder-rich subaerial
debrites (proximal alluvial fan facies association) to centimetre-scale granule-rich subaqueous debrites, ripple-laminated
facies association). By delineating the zone of transition between the subaerial and subaqueous facies, we place the initial flooding paleo-shoreline 4 km up the alluvial fan's paleo-depositional
slope. Considering alluvial fan slope gradients between 1° and 5°, this 4 km transgression would require an estimated 70–350m
of water depth during the initial marine incursion. Interfingering of fan-delta deposits with subaqueous marine and planktonic-rich
evaporites suggests that the basin was below sea-levelafter, and perhaps even before, the marine flooding. Subaerial subsea-level
basins exist in Death Valley and the Salton Trough today within similar extensional and transtentional tectonic regimes. This subaerial subsea-level interpretation might explain the high magnitude and abrupt relative base-level rise recorded by the facies transitions in the Fish Creek Vallecito Basin. These results suggest that the Fish Creek Vallecito Basin underwent significant
extension during its early and nonmarine depositional phase, allowing it to reach subsea-level elevations. The tectonic history of the Fish Creek Vallecito Basin maybe similar to other extensional basins where rapid subsidence allows.
Mountain-front fans are an important part of the global sediment system, acting as buffers and stores of sediment between upland sources and down-system sinks. Fans emanate from the Hajar Mountains in the eastern UAE and northern Oman which have developed from morphologically and geologically variable catchments and in a range of depositional settings, as well as spanning a wide range of shapes and sizes. There has been little prior research into the drivers of regional fan evolution and morphology at the landform scale, considering specific factors such as source-area morphology and geology and distal settings. We use remotely sensed data to map 438 fans and catchments along mountain fronts in Oman and the UAE. These data provide, for the first time, a regional overview of fan morphology using key morphometric parameters and demonstrate the utility of a remote sensing approach to understanding regional landform morphology of features at a range of spatial scales (10⁻³-10⁴ km²).
Comparing this large dataset to studies of dryland fans globally, we show that Hajar fan morphology spans almost every order of magnitude previously recorded elsewhere. It shows statistically the importance of diverse catchment and depositional setting controls on alluvial fan morphology. Across the different mountain fronts of the Hajar range, fan morphology is controlled by 1) catchment morphology and geology, 2) changes in base level and 3) long-term climatic changes and tectonic processes, although the importance of these factors relative to one another is highly spatially variable. The fans of the Musandam Peninsula drain younger rocks, are situated in an area of subsidence and have experienced foreshortening due to Quaternary sea-level variability, hence produce the smallest, steepest fans. Similarly, many of the fans of the Batinah Coast are influenced by distal foreshortening by sea-level rise and demonstrate weak regression relationships with their catchment morphologies. By contrast, the large fans of the Rub'al Khali are mostly distally unconfined and drain large catchments composed of relatively older rock types, thus producing large fans and megafans with the strongest fan-catchment morphometric relationships. The Wahiba Sands fans are similar to those of the Rub'al Khali but are limited in their extent by erosion from an axial river system. As such, the fans of the Hajar are an important natural laboratory for investigating alluvial fan morphology, processes and long-term evolution in response to a range of controls. This includes potentially acting as analogues to extra-terrestrial fan systems due to their large scales in some areas dryland context. For example, the largest megafans of the Hajar display morphometric similarities to large fluvial fans reported on Saturn's moon, Titan, perhaps suggesting comparable long-term controls.
A geomorphic unit is a landform that has been created and reworked by a particular set of earth surface processes. Each geomorphic unit has a particular morphology and sediment properties. Characteristic assemblages and patterns of geomorphic units reflect the use of available energy at any particular location in the landscape. In river systems the mix and balance of erosional and depositional processes creates characteristic, and sometimes distinctive, patterns of geomorphic units at the reach scale. As geomorphic units make up all parts of every valley bottom, the analysis of geomorphic units provides a universal resource with which to undertake systematic geomorphic analysis of river systems. In the first instance, this tool helps to interpret river morphodynamics. Particular process‐form associations determine what type of geomorphic unit is found where, how it is formed and/or reworked, and if/how that unit is related to adjacent units in the channel and/or floodplain. From this, particular assemblages of geomorphic units can be used to identify and map reach boundaries along a river course. Each reach has a particular set of process‐form relationships that determine (and/or reflect) the range of behaviour and the capacity for adjustment of that section of river. Framed in a catchment context and in relation to evolutionary trajectory, interpretation of geomorphic unit assemblages, and how they change over time, informs analysis of river condition and the potential for geomorphic recovery of each reach. A scaffolding framework to conduct such analyses and interpretations provides an important bridge between expert manual analysis and machine learning analysis using Big Data, allowing for the identification and interpretation of the distinctive traits of each and every river system.
Pin valley is an ideal area for alluvial fans’ development. Being least disturbed and devoid of vegetation, fans of this area provide exquisite information and extraordinary opportunity to understand different factors that affect their morphology. Despite aforesaid advantages these fans are hitherto not studied. Thus, the present study is an attempt to understand the morphology of these fans and explore factors affecting fan morphology, primarily through morphometry. Data were derived from various satellite imageries, topographical sheets, DEM and field observations. Various parameters of 51 fans and of their basins were measured and relationships among different parameters were examined. The results of the study are generally comparable to literature though these fans are much steeper than their counterparts in similar environmental settings. Multi-proxy approach was used to explore controlling factors. Fan Conicality Index (FCI) and sweep angle of fan (SA) suggest confinement imposed by surrounding environment has considerably reduced the size of these fans. Further, valley-floor width to height ratio (Vf), feeder channel and geological group-wise analyses reveal that active tectonic attitude, order of feeder channel, lithology and characteristics of contributing basin along with associated depositional processes exercise significant control on morphology of these fans.
Most terrestrial allochthonous organic matter enters river networks through headwater streams during high flow events. In headwaters, allochthonous inputs are substantial and variable, but become less important in streams and rivers with larger watersheds. As allochthonous dissolved organic matter (DOM) moves downstream, the proportion of less aromatic organic matter with autochthonous characteristics increases. How environmental factors converge to control this transformation of DOM at a continental scale is less certain. We hypothesized that the amount of time water has spent traveling through surface waters of inland systems (streams, rivers, lakes, and reservoirs) is correlated to DOM composition. To test this hypothesis, we used established river network scaling relationships to predict relative river network flow‐weighted travel time (FWTT) of water for 60 stream and river sites across the contiguous United States (3,090 discrete samples over 10 water years). We estimated lentic contribution to travel times with upstream in‐network lake and reservoir volume. DOM composition was quantified using ultraviolet and visible absorption and fluorescence spectroscopy. A combination of FWTT and lake and reservoir volume was the best overall predictor of DOM composition among models that also incorporated discharge, specific discharge, watershed area, and upstream channel length. DOM spectral slope ratio (R²=0.77) and Freshness Index (R²=0.78) increased and specific ultraviolet absorbance at 254 nm (R²=0.68) and Humification Index (R²=0.44) decreased across sites as a function of FWTT and upstream lake volume. This indicates autochthonous‐like DOM becomes continually more dominant in waters with greater FWTT. We assert that river FWTT can be used as a metric of the continuum of DOM composition from headwaters to rivers. The nature of the changes to DOM composition detected suggest this continuum is driven by a combination of photo‐oxidation, biological processes, hydrologically varying terrestrial subsidies, and aged groundwater inputs.
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Allometry refers to a physical principle in which geometric (and/or metabolic) characteristics of an object or organism are correlated to its size. Allometric scaling relationships typically manifest as power laws. In geomorphic contexts, scaling relationships are a quantitative signature of organization, structure, or regularity in a landscape, even if the mechanistic processes responsible for creating such a pattern are unclear. Despite the ubiquity and variety of scaling relationships in physical landscapes, the emergence and development of these relationships tend to be difficult to observe – either because the spatial and/or temporal scales over which they evolve are so great or because the conditions that drive them are so dangerous (e.g. an extreme hazard event). Here, we use a physical experiment to examine dynamic allometry in overwash morphology along a model coastal barrier. We document the emergence of a canonical scaling law for length versus area in overwash deposits (washover). Comparing the experimental features, formed during a single forcing event, to 5 decades of change in real washover morphology from the Ria Formosa barrier system, in southern Portugal, we find differences between patterns of morphometric change at the event scale versus longer timescales. Our results may help inform and test process-based coastal morphodynamic models, which typically use statistical distributions and scaling laws to underpin empirical or semi-empirical parameters at fundamental levels of model architecture. More broadly, this work dovetails with theory for landscape evolution more commonly associated with fluvial and alluvial terrain, offering new evidence from a coastal setting that a landscape may reflect characteristics associated with an equilibrium or steady-state condition even when features within that landscape do not.
Alluvial fans are one of the most important of types of geomorphic landforms in mountainous regions, especially in dry and semi-dry region, which flow processes create them with reducing the slope and opening the valley after leaving the mountain.This study investigate the effects of geographic directions on the dimensions of alluvial fans in down streams in Shirkouh Mountain in the central part of Iran's plateau with dry climate. . This mountain is limited to the mountains Boohrook and Dasht-e- Fakhrabad from the east, Tang Chenar and Turanposht from the south, Farashah and Taft city in the west, and with a short distance to Yazd city in the north. It is determines about 24 alluvial fans in the different slopes of the Mountain. After determining the landforms, four geometric characteristics of them includes fans area and length, fans width in the center and in the base were calculated in different slope with different orientations using GIS. Then, using the same software, geometric characteristics of the watersheds include area, environment, average height, average slope, basin length, gravilious coefficient, basin shape coefficient, and drainage density of basin were measured in four directions of geography. Then, using SPSS software, the correlation and also the regression between geometric parameters of the alluvial fans and geometric factors of their upstream basins was calculated. Analyzing showed that geometric factors of the basins in eastern slopes with northern direction and also in northern slopes has been less affected on the fans dimensions. But on the eastern slopes with southern directions and western slopes as well, whose basins are higher and exposed to moist masses, Geometric characteristics of catchment are the most important parameters affecting and controlling the dimensions of fans.
We analyse recent morphological evolution of braiding rivers of disparate regions of the Earth to develop and address the hypothesis that braiding of rivers tends to be reduced by human presence and related activities. Firstly, through a large-scale literature survey we observe generalised paths of bed degradation, channel narrowing and shift towards single-thread configuration in braided reaches due to multiple anthropogenic stressors. Secondly, we select three rivers from different geographic contexts characterised by complementary anthropic stressors for a detailed analysis (the lower Waitaki River in New Zealand, the middle Piave River in Italy and the lower Dunajec River in Poland) which shows that these rivers have undergone very similar trajectories of morphological change. In previous works, these morphodynamic changes have been related to the alteration of the fundamental physical processes of braided rivers, due to anthropogenic changes in constraints and controls. Here, a closer analysis of these alterations shows that analogous morphological evolutionary trajectories can result from very different paths of causation, i.e., from different management causes and different alteration of physical processes. Through the use of pattern predictors we analyse observed morphological trajectories and potential for recovery. We highlight the role of different geographic contexts as sources of constraints and drivers to the river evolution, with reference both to the physical and human environment, showing that the observed similar trajectories are the product of different local conditions and characteristics. These observations have implications for river management and restorations.
This paper analyzes static allometric relationships between the area supplying ice to a fjord glacier, and the fjord trough properties of length, width and depth. The analysis is guided by an underlying assumption that the fjords are eroded into a pre-glacial, fluvial landscape composed primarily of plutonic rocks. The relation between fjord length and ice contributing area appears to be isometric (i.e. the two variables change in constant proportion throughout the study area). Differing degrees of negative allometry exist between ice contributing area, and width, average depth and maximum depth. Abrasion rate models of Boulton and Hallet were applied to a V-shaped valley to gain insight into its transformation into a U-shaped trough; the results of the two models were compared.
Contemporary physical geography is commonly defined as description, analysis, and modelling of the physical, chemical, and biological phenomena at or close to the earth's surface. The sub‐discipline's view of the real world is limited to phenomena that can be observed and/or measured and in this respect differs in no significant way from other physical sciences—but its connection with a geographer's view of the world is tenuous. Changes in natural hazards research are reviewed in order to exemplify the inadequacy of positivistic physical geographers’ perspectives to cope with the style and multiplicity of research questions that are current in that geographical tradition. Roy Bhaskar's version of critical realism gives high priority to philosophical inquiry that aims to understand the nature of reality and provides space for empiricism, analysis of the complex, hierarchical structure of the real world, and questions of value and human behaviour. Openness to recognition of the provisional nature of falsificationism and the limitations of the hypothetico‐deductive framework on the part of physical geographers could revitalize geographical discourse. The search for knowledge of a real world that includes human value systems would seem to require an accompanying concern for the redressing of injustice.
La compréhension que les spécialistes de la géographie physique ont du monde réel
La géographie physique d'aujourd'hui se définit de manière générale comme la description, l'analyse et la modélisation de phénomènes physiques, chimiques et biologiques sur la surface de la Terre ou tout près d'elle. Si la conception que la sous‐discipline se fait du monde réel se limite à des phénomènes qui peuvent être observés ou mesurés et, à cet égard, elle est comparable en tout point aux autres sciences physiques, son rapport avec la conception du monde par le géographe demeure néanmoins flou. Un tableau de l'évolution des travaux de recherche sur les risques naturels permet d'illustrer à quel point les perspectives positivistes des spécialistes de la géographie physique sont inadaptées pour répondre aux nombreux types de questions de recherche que soulève ce courant géographique. Roy Bhaskar soutient dans sa définition du réalisme critique que la priorité soit accordée à une réflexion philosophique qui s'inscrit dans une optique de comprendre la véritable nature de la réalité tout en laissant une place à l'empirisme, l'analyse de la structure hiérarchique complexe du monde réel et aux questions portant sur les valeurs et sur les comportements humains. Une ouverture de la part des spécialistes de la géographie physique visant la reconnaissance de la nature provisoire du réfutationnisme et des limites du raisonnement hypothético‐déductif pourrait revaloriser le discours géographique. La quête du savoir d'un monde réel qui comprend des systèmes de valeurs humaines exigerait aussi que l'on se préoccupe d'obtenir une réparation de l'injustice.
Overwash is a physical process of coastal sediment transport driven by storm events, and is essential to landscape resilience in low-lying barrier environments. This work establishes a comprehensive set of scaling laws for overwash morphology: unifying quantitative descriptions with which to compare overwash features by their morphological attributes across case examples. Such scaling laws also help relate overwash features to other morphodynamic phenomena. Here, morphometric data from a physical experiment are compared with data from natural examples of overwash features. The resulting scaling relationships indicate scale invariance spanning several orders of magnitude. Furthermore, these new relationships for overwash morphology align with classic scaling laws for fluvial drainages and alluvial fans.
The planimetry of debris flow fans could be represented by the combination of geometric figures. Two planimetric models of debris flow fans are presented in this paper based on aerial photograph observation and statistical analysis of 52 debris flow fans in Xiaojiang Valley of southwestern China and in Alpine valleys of northeastern Italy. The combination of an isosceles triangle with a semicircle best fits the fans in Xiaojiang Valley and a circular sector is best for the fans in northeastern Italian Alps. By using statistical analysis, two groups of morphometric relationships between debris flow fans and debris flow basins are established. The basin area and basin relief are identified as the significant factors influencing the plan shapes and the dimensions of debris flow fans. The statistical analysis on geomorphic parameters of debris flow drainage basin could provide an empirical method to predict the debris flow depositional extent.
Recognizing and reconciling spatial and temporal scales are central to any question posed by a geomorphologist. This chapter focuses on space and time, why they are inseparable, thus difficult to consider in their entirety. The time-dependent approaches of early geomorphology were displaced by time-independent and process-oriented approaches in the 1950s and 1960s. Today, geomorphology struggles to combine space and time using radionuclide dating, modern spatial technologies, and quantitative techniques. However, different variables become important at different scales. This chapter concludes with some thoughts on how geomorphologists might negotiate the range of spatial and temporal scales that constitute geomorphology's domain.
Many of the fundamental questions in science concern relations among two or more variables. “Are these variables related?” “What is the nature of the relationship?” “Can the value of one variable be predicted, given the values of some others?” “Does the relationship conform to some theoretically-derived one?” “Do two samples conform to the same relationship?” Geographers have at times used regression analysis to provide answers to all of these questions, often with little realization of the assumptions of the technique or of alternative statistical procedures for addressing these questions.
Introduction to mountain geomorphic hazards Mountain geomorphic hazards defined A geomorphic hazard results from any landform or landscape change that adversely affects the geomorphic stability of a site or drainage basin (Schumm, 1988) and that intersects the human use system with adverse socio-economic impacts (White, 1974). If there are no people affected, there is no hazard and if the landform or landscape is unchanged there is no geomorphic hazard. Barsch and Caine (1984) have described the distinctive relief typologies of major mountain systems. Mountain geosystems are not exceptionally fragile but they show a greater range of vulnerability to disturbance than many landscapes (Körner and Ohsawa, 2005) and their recovery rate after disturbance is often slow. During the past three decades, the world's population has doubled, the mountain regions' population has more than tripled and stresses on the physical and biological systems of mountain regions have intensified many fold. The combination of extreme geophysical events with exceptional population growth and land use modifications underlines the urgency of better understanding of these interactions and working out the implications for adaptation to and mitigation of the effects of drivers of change on landforms and landscapes. Geomorphic hazards intensify and risks multiply accordingly. The major drivers of change and ‘key’ vulnerability The three drivers of environmental change in mountains are relief, as a proxy for tectonics (Tucker and Slingerland, 1994), hydroclimate and runoff (Vandenberghe, 2002) and human activity (Coulthard and Macklin, 2001).
Spatial autocorrelation analysis in geomorphology: Definitions and tests. Spatial autocorrelation can be defined as the similarity of values of a given variable, in relation with their spatial location. Autocorrelation functions are used to quantity the spatial regularity of a phenomenon (a form of spatial complexity) and to assess the lag of spatial dependence in order to design a sampling procedure for which the data are independent, which permits the use of traditional statistical tests. Three points have been developed: i) Definition of autocorrelation functions used for categorical and quantitative variables: Geary's c, Moran's I, semivariogram, non ergodic covariance and correlation, J statistics; ii) Definition of the randomization tests used to test the null hypothesis of no autocorrelation: iii) examples illustrating the two previous objectives. Three sets of simulated data were used to compare different autocorrelation functions (Geary's c, non ergodic covariance and correlation): the first one has no spatial structure, the second one has a periodic spatial structure whereas the third one is characterized by a linear gradient. Spatial autocorrelation has also been assessed on measured geomorphological data. Two sets were studied: i) a set of elementary channel segments of 500 m in length on which mean active channel width and degradation have been measured, ii) a set of pixels of an image of two basins representing the different types of hillslope erosion forms. In the first case, the nested structure of homogeneous geomorphological reaches is highlighted at different spatial scales. The second example, which illustrates autocorrelation assessment on a categorical variable, shows that omnidirectional analysis can underestimate the autocorrelation lag when the studied phenomenon is characterized by a preferential geographical orientation. In this particular case, it may not be not possible to define a sample of data which are spatially independent and on which it is possible to use classical statistical tests.
The steady state exists in a system of fans when all of the fans are increasing in thickness at approximately the same rate. Laboratory and field observations suggest that the steady-state slope of an alluvial fan is determined by debris size, depositional process, and water discharge. Large fans have larger drainage basins and hence larger discharges than small fans. Consequently, fan slope generally decreases with increasing fan area. Under otherwise equivalent conditions, fans composed of coarse material are steeper than those composed of fine material, and fans built largely by debris flows or sieve deposition are steeper than fans on which fluvial processes dominated.
The area of an alluvial fan is approximately proportional to the 0.9 power of the area of the drainage basin discharging to the fan. The constant of proportionality is, in part, a function of the erodibility of the bedrock in the source area. By using multiple linear-regression techniques to analyze this functional relationship in three groups of fans in Death Valley, California, and vicinity, we determined coefficients of relative erodibility for some of the dominant rock types. Comparison of these coefficients with weathering characteristics observed in the field and with changes during weathering experiments in the laboratory suggests that fracture density is more important than mineralogy in determining rock erodibility.
Recent quantitative studies of drainage basins and stream channels have yielded significant results that promise greatly to enlarge our knowledge of fluvial processes and erosional landforms. However, the tentative conclusions derived from these preliminary investigations have raised in turn a host of fascinating new problems, which are now receiving attention by increasing numbers of research workers. Several current projects involve collection and analysis of new data, with reexamination and rigorous testing of certain basic concepts of geomorphology the immediate objective.
In recent years, several different approaches to the study of drainage basins and stream channels have been used, and a considerable variety has been investigated. From the results of these recent investigations, there can be little doubt that lithology and geologic structure affect the properties of drainage basins and stream channels in ways which are complex but nonetheless detectable by quantitative methods. However, the geologic and hydraulic data collected thus far are not sufficient in either number of areal scope to enable one to state very precisely what cause-and-effect relationships exist, or the extent to which they may differ in various geologic and geographic environments. Efforts at present are concentrated on accumulation of data and on sorting out the several independent and dependent variables. This is a slow process because of the relatively small number of persons involved, the complex interrelationships of the variables, and the large number of different kinds of areas to be studied.
This report adds new data from a high mountain area characterized by geologic and geographic conditions markedly different from those in areas previously studied. Besides the effects of different bedrock lithologies, extreme relief, and vertical changes in climate, the additional factor of glaciation might be expected to affect channel properties and the characteristics of bed material in high mountain streams. Furthermore, it has long been supposed that mountain streams are not graded; that is, they are not in equilibrium, but instead are actively downcutting. This implies that they differ in some possibly measurable way from equilibrium or graded streams. Hence, a principal objective in this study of mountain streams was to test the range of validity of certain conclusions reached in earlier investigations. Briefly, the procedure involved collection and analysis of stream data obtained in the high mountains, and comparisons of the results with information of similar character obtained in other, mostly nonmountainous, areas.
Any attempt to segregate geologic controls of characteristics and lithologic composition of bed material requires detailed knowledge of the bedrock geology of the drainage basin. Because the author had recently spent several field seasons mapping the geology of a large area in the southern portion of the Sangre de Cristo Range, New Mexico, the choice of a site for stream studies was resolved by the purely practical consideration of expediency. However, one additional advantage of this area over the other possible choices is the fact that the arroyos described by Leopold and Miller (1956) are located in the Rio Grande Depression, at the foot of the range, and afford a basis for local comparison. The order of discussion will be as follows. A brief resume of local geography and geology, emphasizing aspects of the physical setting, which affect stream properties, will define the general framework of these studies. Next, field procedures will be described, and data obtained from measurements of channel dimensions, bed material, and other properties will be presented. The subsequent sections will describe the results of efforts of geology on stream characteristics. Finally, the problem of grade or equilibrium in mountain streams will be considered.
The frequency distributions of fifteen morphometric variables are examined for three orders of drainage basin, and are found to be significantly non-normal. The effects of the logarithmic transformation on these distributions and the effects of other transformations on the variables not satisfactorily normalised by the logarithmic transformation are investigated. The importance and implications of the conclusions reached are emphasized by an illustration using drainage density.
All aspects of surface form can be considered to reflect surface roughness. Horizontal variation includes the concepts of texture and grain, while vertical variation is discussed under relief. The relationships between these are embodied in slope and the dispersion of slope magnitude and orientation. The distribution of mass within the elevation range of a topographic surface is described under hypsometry. Parameters for further investigation are selected from these categories after an examination of the relationships among the variables using correlation analysis.
J.S. Pethick writes that the further notes on the drainage density basin area contributed by Gardiner et al contain a gross misrepresentation of his original paper. Gardiner argues against the three hypotheses with which the paper opens as if they were factual statements. Ferguson writes that Gardiner et al have identified one statistical error, but have introduced several new errors and red herrings while missing the main point; he tries to classify and stress one important implication. A. J. Gerrard offers a short contribution on the relation between Dd and A for Datmoor to highlight the problems involved in such analyses. Gardiner et al reply that they still have not been able to extract the influence of the variable area. - Janet Johnson
A review encompassing events from one day to a number of years. Some of the sudden events may be rather infrequent. Conjectural responses to environments over varying timescales are plotted on logarithmic graphs. While almost no parameter of direct geomorphological interest is measured regularly, some environmental parameters are, and these provide the best time series we have. Other sources include comparison of photos and maps, the interpretation of associated effects (eg. tree rings), and sedimentary records. -Keith Clayton
The line intersection method for estimating drainage density involves counting the number of intersections with the drainage net per unit length of sample traverse line and multiplying the result by a correction coefficient. Theoretical and empirical evidence indicates that this coefficient should be 1.571.
Although the probabilistic-topologic approach to drainage-basin geomorphology that I initiated unifies a wide variety of quantitative empirical geomorphic relationships, some geomorphologists have objected variously that it abandons the scientific method, that its emphasis on topologic properties causes it to miss the geomorphic components of drainage basins, that it lacks physical content, and that it is too complicated to be of practical value. In fact, however, it gives results that are generally simpler, better, and more practical than those given by other methods. It has physical content because it is founded on postulates that are observational statements about actual drainage basins. It emphasizes topologic properties because they dominate the orientation-free planimetric aspects of drainage basins. Finally, it is necessarily probabilistic because of the prominent random element in natural landscapes, which may result from instabilities that amplify small perturbations into large ones.
Mainstream length in river networks from various parts of the world varies statistically in proportion to basin area raised to a power that decreases from about 0.6 for small to medium basins (1–103 km2) to near 0.5 for the largest in the world (nearly 107 km2). This relationship is predicted by the statistical theory of channel networks, which is founded on the basic postulates that (1) natural channel networks in the absence of strong geologic controls are very nearly topologically random and (2) interior and exterior link lengths and associated areas in basins with homogeneous climate and geology have separate statistical distributions that are approximately independent of location. The calculation was carried out by a Monte Carlo method, which produced a random sample of networks from the postulated population, and was checked by analytical results for networks up to magnitude 500. The necessary empirical data on link lengths and associated areas were obtained by measurement on maps of an 80-km2 basin in relatively flatlying coal-bearing sandstones in eastern Kentucky. Agreement with observation is excellent for the small to medium basins, but the ratio of predicted to observed mainstream length progressively decreases to about 0.7 for the largest basins. This discrepancy can be accounted for by moderate downstream increase in channel sinuosity and decrease in drainage density. The particular data on link lengths and associated areas used in the calculation have only slight influence because mean link length varies statistically directly as the square root of mean associated area, so that taking data from different areas merely displaces the predicted points nearly parallel to their trend.
Allometry is the study of the relative rates of change of two variables of a system. In the study of landforms, or the processes acting upon them, the power function Y = a Xb is useful for correlating changes in variables. Allometric analysis includes the study of dynamic interrelations during geomorphic history, or the static interrelations at a given time. Such analyses may include aspects of geomorphic open systems that are tending toward a steady state, have attained a steady state, or do not tend toward a steady state. The highly flexible allometric model can be used to demonstrate adjustment between interdependent variables of hillslopes, streams, and depositional environments. It is highly unlikely that geomorphic steady states exist, because the dependent variables of a geomorphic open system cannot attain a time-independent state where the independent variables do not remain constant. Independent variables, such as climate, uplift, base level, erodibility of surficial materials, and impact of man, are changing at rates that are sufficiently rapid as to preclude attainment of steady state, particularly for those landforms that require geologic time spans to approach steady-state configurations. For most studies of processes and landforms, a broad perspective of the interrelations of materials, processes, and landforms can be obtained by using the model of allometric change in which landscape elements and processes are changing at different rates.
Rivers are open systems and achieve a steady state or grow allometrically, according to the general equation y = axb. This equation yields a straight line on double logarithmic paper and reflects a lognormal or Yule stochastic process. Horton's laws are shown to be statements of these processes, and successive stream orders are seen to be new logarithmic cycles to the base of the bifurcation ratio for a river system. A new absolute order is suggested, derived by raising the bifurcation ratio to successive integer powers equivalent to stream order minus one.
Dimensional Analysis Permits Quantitative Geomorphic Studies To Be Placed On A Sound Geometrical And Mechanical Basis Form Elements Of Fluvially Dissected Landmasses Are First Analyzed According To Dimension. Stream Length, Relief, Length Of Overland Flow, And Basin Perimeter Have The Dimension Of Length L. Drainage Density, Texture Ratio, And Curvature Of Profile Have An Inverse Length Dimension L-1. Areal Measures And Volumes Have The Dimensions Of Length Squared L2 And Length Cubed L3, Respectively. Dimensionless Parameters Include Stream-Order Number, Stream Azimuth, Ground-Slope Angle, And Channel Gradient. Combinations Of Dimensional Elements Produce Dimensionless Numbers, Such As Stream-Length Ratio, Basin Circularity Ratio, Ruggedness "Number, And Hypsometric Integral, Which Provide Descriptive Indices Of The Terrain, Irrespective Of Scale. Corrsin'S Dimension Space Is A Useful Graphic Device For Clarifying The Dimensions Of Physical Properties As Unique Vectors Extending From An Origin To Appropriate Points In Space With Respect To Three Orthogonal Coordinates Scaled In Integer Powers. Application Of Dimensional Analysis And The Pi Theorem To Drainage Density As A Function Of Runoff Intensity, An Erosion Proportionality Factor, Relief, Fluid Density And Viscosity, And Gravity Yields Four Dimensionless Groups: A Ruggedness Number, An Erosion-Intensity Number (Here Named The Horton Number), A Reynolds Number, And A Froude Number. Complete Geometrical Similarity Of Landforms In Two Regions Exists When All Corresponding Linear Dimensions Are In The Same Scale Ratio, And All Corresponding Dimensionless Numbers Are The Same. As An Illustration, Approximate Similarity In Planimetric Form, But Not In Relief And Slope, Is Established Between Small Areas Of Mountainous Terrain In The Verdugo Hills, California, And The Great Smoky Mountains, North Carolina. Examples From The Clinch Mountain Area Of Western Virginia Illustrate A Case Of Extremely Close Similarity In Landforms Developed On Different Rock Types And A Case Of Striking Dissimilarity Where Structural And Lithologic Controls Are Strong. Accelerated Land Erosion, In Which Gullying Results In Badlands, Is Interpreted As A Drainage-Density Transformation In Response To Sharp Increases In The Horton Number. Despite A Many-Fold Increase In Drainage Density, The Geometry Number Tends To Be Conserved By Reduction Of Relief And Increase Of Slope. Geometrical Similarity Is Preserved In Planimetric Aspect But Not In Vertical Aspect. The Resultant System Reaches A New Steady State Capable Of Exporting Greatly Increased Load Because Of Steepened Valley-Side And Channel Gradients.
Three models that specify allowable branching events during the growth of stream channel networks through time are introduced. These models identify the possible topologie "growth paths" that may be followed as a network grows from a single link to one of magnitude n. The probability of occurrence of channel networks is calculated for magnitudes 2 to 6. One model has probabilities identical with those for Shreve's model of topologically random channel networks. The three models are compared with published data on 12 topologic studies of stream networks of magnitudes 4 to 6. The model with Shreve's probabilities fits 7 of the 12 data sets, a second model also fits 7 of them, and the third model does not fit any. Only one data set is not fit by at least one model. The results suggest that network growth by branching of exterior links alone is not adequate for development of the topologie diversity observed in natural stream channel networks. This conclusion conflicts with the prevalent view of contemporary ...
Topographic texture is measured by two distinct parameters: drainage density (D) and channel frequency (F). In maturely dissected regions the functional relation between D and F is (1) F = 0.694D2. The dimensionless ratio F/D2 varies inversely with valley-side slope (θ) and basin relief (R), area and channel length held constant, but is not affected by basin circularity or basin perimeter (P). The ratio F/D2 is interpreted as a measure of the completeness with which a channel system fills a basin outline, for given values of N (number of channels). For an ideal basin of 1 square mile area, it is postulated that the equation N = 0.694L2 (L = total channel length) is a growth model, although it is based on essentially instantaneous measurements from many different basins. When relief is considered, regression analysis gives equation (2), N = 0.8147L1.75/R0.25, A = 1, which may also be a growth model. If both equations (1) and (2) are valid as growth models, equation (3), R = 1.899/L, must also be true, when...
Hack and Gray have both found that data on mainstream lengths and basin areas can be represented by the equation L′ = CAn′, where C is about 1.4 (measurements in miles), and n′ is about 0.6. Hack has suggested that the deviation of n′ from ½ can be explained by an elongation of drainage basin shapes with increasing area. We point out that variations of stream sinuosity with area can also affect the value of n′. A simple approximate formula is deduced that relates mainstream length, sinuosity, basin shape, and area, and shows how the contributions of sinuosity and shape variation to the quantity (n′ − ½) may be separated and evaluated. Data that illustrate these points are presented for both real and simulated stream systems. Our conclusions are: (1) Variation in mainstream sinuosity with area can be responsible for a significant part of the deviation of n′ from ½. (2) The generally accepted statement that drainage basins become more elongated as their area increases needs further investigation.
The application of the principles of dimensional analysis to obtain the relationships between characteristics of the unit hydrograph and topographic and morphometric properties of a watershed is not possible unless careful consideration is given to the selection of variables. Evidence is presented which shows that, in small watersheds, drainage-area size A, length of the main stream L, and length to center of area Lea are highly correlated. In addition, the results indicate that, when consideration is given to regional influence, the slope of the main stream S, can be expressed as a function of A, L, or Leo. Introduction. Unit-hydrograph synthesis for ungaged basins is based on empirical expressions which relate pertinent physical characteristics of the watershed to geometric aspects of the unit graph. These relationships are predicated on the basis that the unit hydrograph of an area repre- sents the integrated effect of all the sensibly constant basin factors and their modifying influence on the translation and storage of a runoff volume from a uniform excess rain occur- ring during a unit period of time. Dimensional analysis (Murphy, 1950) has proved to be a useful tool in engineering fields in establishing relationships within a system of variables. Strahler (1958) discussed the applica- tion of these principles to the field of geomor- phology in connection with fiuvially eroded land- forms. These studies give rise to the thought that the principles of dimensional analysis may be used to derive the desired relationships between watershed characteristics and unit-graph properties required for hydrograph synthesis. A study of this type was made by Gray (1960), who used hydrologic and topographic data col- lected from 42 small watersheds located through- out the United States. The results of the study indicated, however, that the approach used was relatively unsuccessful. Consequently, an addi- tional investigation was undertaken to determine a plausible reason for this failure. According to the theory of dimensional analy- sis, the variables must be selected with great care so that ther terms formed in their combi-
A specific equation describing the relationship of stream length to drainage area was originally formulated for very small rivers and basins in localized areas of the eastern United States. Use of the same equation for larger rivers and basins on a world-wide scale produces gross error of prediction. A general or best-fit equation is offered which describes more accurately the length-area relationship for moderate and large-size drainage systems. The theoretical implications of the general equation are just the inverse of those inherent in the original equation.
The most commonly used quantitative parameters for characterizing
channel networks are derived from a Horton analysis (bifurcation ratios,
stream length ratios, and so forth). Although these parameters give
useful information about individual networks, they are generally
ineffective in distinguishing differences in network structure due to
lithologic controls and degree of maturity. As Shreve has noted, this
failure is due in part to the random nature of network topology and link
lengths and in part to the fact that the Horton analysis tends to
average out many of the details that characterize such differences.
Parameters derived from considerations of statistical geometric
similarity, on the other hand, are relatively successful in
characterizing network structure. For a simple example, let
le and li be the mean exterior and interior link
lengths, respectively, and ae and ai be the means
of the associated drainage areas. Four dimensionless parameters that can
be constructed from this set are λ = le/li
α = ae/ai Ke =
le2/ae and Ki =
li2/ai. Data on λ, α,
Ke and Ki for natural networks drawn from
different geologic populations indicate that these quantities are
effective in detecting differences due to varying lithology and degree
of maturity.
The principle of allometric growth was first developed by biologists, and states that the ratio of the relative growth rate of an organ to that of the whole organism remains constant. Allometric relations in biology are identical with the power-function relations found in all empirical sciences. The instances of allometric growth in geomorphology so far suggested are n i fact examples of size-related allometric relations, and not of allometric growth relations. Data from an experimental study of drainage network evolution did not support the concept of allometric growth, and a brief theoretical survey suggests that there is no reason to expect that river systems should exhibit allometric growth.
Alluvial fan construction within the interior valleys of southern British Columbia was dependent upon temporary conditions resulting from deglaciation. Glacial drift was reworked by streams and mudflows to form fans whose composition is dependent upon the nature of the drift supply and the hydrologic character of the parent basin.Stratigraphic evidence suggests that fan building commenced soon after valley floors became ice-free, continued during post-glacial aggradation by major rivers and for some time after wards. Most recently, fans were built upon degradational river terraces. Mazama volcanic ash within fans indicates that their construction continued until after 6600 years B.P. After deposition ceased many fans were dissected either as local base-levels were lowered under the control of degrading major rivers or by fan-head trenching initiated as the debris supply declined. Where fan building persisted during degradation, multi-level fans were constructed.
Quantitative geomorphic measurements were made on modern 1:24,000-scale topographic maps for 90 order-3 and 90 magnitude-10 basins randomly selected from a 250 square-mile area of horizontal, homogeneous sandstones in eastern Kentucky. Operator variations were greatest in locating sources and least in measuring areas, and were readily reduced to acceptable limits by training and practice. Similar measurements were made on 153 magnitude-5 basins in the study area. The sample is approximately topologically random with weak, but apparently systematic, deviation. (Author)
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The concept of allometric change, developed and widely applied in biology, is outlined, and the nature of static allometric changes in stream channel size, relative to drainage area, is considered at a variety of scales. Field observations from Devon, England, allow analysis of the allometric variations along individual channels, between tributaries within a network, and between streams within a region. Data collected from the literature allow these to be viewed in a global perspective. The analysis confirms the applicability and value of the concept of allometric change to channel form studies and suggests a tendency for streams to reach a steady-state allometric situation when channel capacity increases at the same rate as drainage area. The importance of a range of factors in affecting the nature of the allometric relationships is also assessed.
Simple least-squares regression analysis is applied to almost all empirical curve-fitting problems in earth science (and related fields). Its use, however, should be restricted to predictive situations. For comparisons with theory or among fitted lines, the related technique termed functional analysisshould be employed. To apply this method, the ratio of the random components of the variances of the variables must be estimated. Principles are illustrated with examples from geomorphometry, especially the stream frequency-drainage density relation.
Distinctions between cause and effect in landform development depend on the span of time involved and the size of the geomorphic system under consideration. Depending upon the temporal and areal frame of reference, variables such as channel morphology may be either dependent or independent. In terms of geologic time, landforms represent a stage in an erosion cycle and are dependent on time. On a short-term basis, components of geomorphic systems may be regarded as systems in dynamic equilibrium or in a steady state and are independent of time.
When the Canadian Government decided to relocate the town of Aklavik in the delta of the Mackenzie River, Northwest Territories, the search for a new site involved detailed site investigations of four prospective locations. One was on the gently sloping surface of an alluvial fan between the Richardson Mountains and the western rim of the Mackenzie Delta. Predictions from surficial evidence and from a detailed study of aerial photographs were invalidated when drilling in the perennially frozen ground disclosed at least 40 feet of organic silt and no sand or gravel as had been expected. The adjacent mountains of Cretaceous age supply materials eroded from sandstone and shales. The action of frost probably induces mechanical disintegration. Turbulent stream flow continues the erosion process, which appears to be still further aided by the annual growth of fast-growing sedges and grasses on the surface of the stream meanders. The short but warm growing season leads to rapid decay of this grass cover; this combined with the annual layers of stream-bed material results in the fans being composed predominantly of organic silt with only minor quantities of coarse-grained material.
Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However,
many are statistically "selfsimilar," meaning that each portion can be considered a reduced-scale image of the whole. In that
case, the degree of complication can be described by a quantity D that has many properties of a "dimension," though it is
fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves.
Rates of sediment production in midwestern United States United States Department of Agriculture, Soil Conservation Service, Technical Publication 65 Sediment routing with sediment delivery ratios
- Xi
- G M Brune
- R C Bryce
XI References Brune, G. M. 1948: Rates of sediment production in midwestern United States. United States Department of Agriculture, Soil Conservation Service, Technical Publication 65. (40 pp.) Bryce, R. C. 1975: Sediment routing with sediment delivery ratios. United States Department of Agriculture, Agricultural Research Service, Report ARS-S-40, 61-65.
Alluvial fans in the Death Valley region, California and Nevada. United States Geological Survey
- C S Denny
Denny, C. S. 1965: Alluvial fans in the Death Valley region, California and Nevada. United States Geological Survey, Professional Paper 466. (62 pp.)