Geometry Of River Networks Research Articles

The length and spacing of river tributaries

River networks are composed of a mainstem and tributaries. These tributaries dissect landscapes, regulate water and habitat availability, and transport sediment and nutrients. Despite the importance of tributaries, we currently lack theory and data describing whether and how tributary length and spacing varies within watersheds, thereby limiting our ability to accurately describe river network geometry. We address this knowledge gap by analyzing 4,696 tributaries across six landscapes with varying climate, tectonic setting, and lithology. Our results show that both tributary length and spacing systematically increase with downstream distance along the mainstem river, following a power-law scaling. This power-law scaling can be modulated by basin shape, with tributaries becoming shorter and, in some cases, more closely spaced as basin elongate. Furthermore, the power-law scaling may break down in cases where river networks have been disturbed by pervasive faulting, raising the possibility that the scaling we observe is not unique to all branching networks, and instead may be universal across undisturbed fluvial networks. These findings can be used to improve predictions of river network geometry and potentially to distinguish fluvial river networks from other branching networks.

Basin-scale riverine ecosystem services vary with network geometry

Riverine ecosystems provide a variety of services supporting biodiversity, human livelihoods, and the maintenance of river health. Multiple anthropogenic threats to riverine ecosystem services (RES) have been identified and considered in river management strategies. However, the way in which the river network is spatially arranged across the landscape – river network geometry – may also play a role in the delivery of RES. Here we studied the effect of river network geometry on the delivery of five RES in 14 catchments of the Great Barrier Reef region, Australia. Our investigation has three parts. First, we conducted a sensitivity analysis on modelled RES, holding all non-geometric catchment characteristics, other than catchment size and slope, constant to allow attribution of modelled differences directly to differences in geometry. Second, we analysed the relationships between observed RES and network structural indices. Third we compared observed RES with modelled results. Modelled results suggest that RES are sensitive to the differences in river network geometry. Furthermore, correlation analyses show good agreement between observed RES and network structural indices, and there is good correlation between the modelled and observed RES. These results suggest an important role of river network geometry in the delivery of multiple RES by mediating upstream inputs as they pass through the river network. A one size fits all approach to river management may thus be ineffective and specific management interventions will be needed in catchments of different network geometries.

Morphological controls on surface runoff: an interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework

Abstract. Recent research explored an alternative energy-centred perspective on hydrological processes, extending beyond the classical analysis of the catchment's water balance. Particularly, streamflow and the structure of river networks have been analysed in an energy-centred framework, which allows for the incorporation of two additional physical laws: (1) energy is conserved and (2) entropy of an isolated system cannot decrease (first and second law of thermodynamics). This is helpful for understanding the self-organized geometry of river networks and open-catchment systems in general. Here we expand this perspective, by exploring how hillslope topography and the presence of rill networks control the free-energy balance of surface runoff at the hillslope scale. Special emphasis is on the transitions between laminar-, mixed- and turbulent-flow conditions of surface runoff, as they are associated with kinetic energy dissipation as well as with energy transfer to eroded sediments. Starting with a general thermodynamic framework, in a first step we analyse how typical topographic shapes of hillslopes, representing different morphological stages, control the spatial patterns of potential and kinetic energy of surface runoff and energy dissipation along the flow path during steady states. Interestingly, we find that a distinct maximum in potential energy of surface runoff emerges along the flow path, which separates upslope areas of downslope potential energy growth from downslope areas where potential energy declines. A comparison with associated erosion processes indicates that the location of this maximum depends on the relative influence of diffusive and advective flow and erosion processes. In a next step, we use this framework to analyse the energy balance of surface runoff observed during hillslope-scale rainfall simulation experiments, which provide separate measurements of flow velocities for rill and for sheet flow. To this end, we calibrate the physically based hydrological model Catflow, which distributes total surface runoff between a rill and a sheet flow domain, to these experiments and analyse the spatial patterns of potential energy, kinetic energy and dissipation. This reveals again the existence of a maximum of potential energy in surface runoff as well as a connection to the relative contribution of advective and diffusive processes. In the case of a strong rill flow component, the potential energy maximum is located close to the transition zone, where turbulence or at least mixed flow may emerge. Furthermore, the simulations indicate an almost equal partitioning of kinetic energy into the sheet and the rill flow component. When drawing the analogy to an electric circuit, this distribution of power and erosive forces to erode and transport sediment corresponds to a maximum power configuration.

Propagating uplift controls on high-elevation, low-relief landscape formation in the southeast Tibetan Plateau

AbstractHigh-elevation, low-relief surfaces are widespread in many mountain belts. However, the origin of these surfaces has long been debated. In particular, the southeast Tibetan Plateau has extensive low-relief surfaces perched above deep valleys and in the headwaters of three of the world's largest rivers (Salween, Mekong, and Yangtze Rivers). Various geologic data and geodynamic models show that many mountain belts grow first to a certain height and then laterally in an outward propagation sequence. By translating this information into a kinematic propagating uplift function in a landscape evolution model, we propose that the high-elevation, low-relief surfaces in the southeast Tibetan Plateau are simply a consequence of mountain growth and do not require a special process to form. The propagating uplift forms an elongated river network geometry with broad high-elevation, low-relief headwaters and interfluves that persist for tens of millions of years, consistent with the observed geochronology. We suggest that the low-relief interfluves can be long-lived because they lack the drainage networks necessary to keep pace with the rapid incision of the large main-stem rivers. The propagating uplift also produces spatial and temporal exhumation patterns and river profile morphologies that match observations. Our modeling therefore reconciles geomorphic observations with geodynamic models of uplift of the southeast Tibetan Plateau, and it provides a simple mechanism to explain the low-relief surfaces observed in several mountain belts on Earth.

Asymmetrical river valleys and their tectonic significance in the Maxianshan area, NE Tibetan Plateau

The geometry of river networks is particularly sensitive to active tectonic deformation. Morphotectonic analyses conducted using geomorphic indices and numerical models are useful methods with which to identify such deformation. The northeastern (NE) margin of the Tibetan Plateau is characterized by active tectonics, easily erodible bedrock and well-developed valleys, and is thus an ideal region for studying the effects of tectonics on the landscape evolution. Here we firstly identify the systemic asymmetrical valleys in the Maxianshan area, NE Tibetan Plateau. To quantitatively analyze the asymmetrical characteristics of these valleys identified in the southern Maxianshan, 33 parallel streams were investigated by using two drainage basin analytical techniques, namely, the transverse topographic symmetry factor (T) and asymmetry factor (AF). Our results show that the mean T value is 0.14 (magnitude) and 319.08° (direction) and the majority of the AF results are <50, indicating a north-westward migration. In addition, we suggest that this north-westward migration could be caused by the variable rates of uplift experienced across the Maxianshan area, an assertion which is also supported by the inversion results of GPS measurements and earthquake distributions. In contrast to previous studies, we conclude that the variable rates of uplift are probably caused by the distribution of stress within the four quadrants of a strike-slip fault. This mechanism is validated by using the landscape evolution model SIGNUM and studying examples from other strike-slip fault zones, such as the Haiyuan Fault Zone on the NE Tibetan Plateau, Qujiang Fault Zone and Daqing Fault Zone on the southeastern (SE) Tibetan Plateau and Tieluzi Fault Zone in central China. By using quantitative methods and modeling, our study appears to demonstrate that asymmetrical valleys are important geomorphic characteristics of strike-slip faults.

A global dataset of river network geometry

The plan-form structure of the world’s river basins contains extensive information regarding tectonic, paleo-geographic and paleo-climate conditions, but interpretation of this structure is complicated by the need to disentangle these processes from the autogenic behavior of fluvial processes. One method of interpreting this structure is by integrating channel length and drainage area as characterized by the scaling relationship between slope and area, resulting in a characteristic length parameter, referred to in recent studies as χ. In this paper, we apply this methodology at a continental scale by calculating χ for the world’s river networks. Mapping of χ', a modified version of χ including the influence of precipitation distribution on river discharge and correction of base level for χ' in closed basins, illustrates the geometric structure of global river networks, thus highlighting where tectonics or changing climate have resulted in an apparent disequilibrium of the river channel geometry. Our global χ maps quantify a dynamic view of Earth’s river networks and help to identify past and ongoing evolution of Earth’s landscape.

Effect of River Network Geometry on Flood Frequency: A Tale of Two Watersheds in Iowa

AbstractAlthough numerous studies conducted over the past four decades have shown the significant role that drainage network geometry plays in determining the streamflow response and hence the peak...

River network properties shape α‐diversity and community similarity patterns of aquatic insect communities across major drainage basins

AbstractAimSpatial dynamics and habitat connectivity affect community composition and diversity in many ecosystems. For many decades, diversity patterns in riverine ecosystems were thought to be related to local environmental conditions. Recent theoretical work, however, suggests that diversity in rivers is strongly affected by dispersal along the dendritic landscape structure and that environmental conditions are intrinsically linked to the network position. In this study we tested hypotheses on network position by relating river network geometry and connectivity to multi‐level biodiversity patterns across large scales.LocationThree major alpine drainage basins in Switzerland were studied (Rhine, Rhone, Ticino), extending over an elevational gradient of &gt; 2500 m and covering a total area of 41,285 km2.MethodsWe sampled all may‐, stone‐ and caddisfly species at 217 sites which representatively cover the three river networks. Using generalized additive models, we related diversity patterns in aquatic insects to centrality within the network as a direct river network property, and to catchment area and elevation, which are related to network position.ResultsCentrality within the river network, and catchment area and elevation had significant and interacting effects on α‐diversity and community similarity. Alpha diversity was lowest in peripheral headwaters and at high elevations. Species richness generally increased with increasing catchment area. Well‐connected, central communities within the river network had greater α‐diversity than more peripheral communities did. Elevation was a strong predictor of α‐diversity, with the most diverse communities found at mid‐elevation sites. Community similarity decreased with increasing along‐stream distance between sites.Main conclusionsOur results highlight the fact that diversity patterns of aquatic insects in river systems are related to local factors such as elevation, but interact with network properties and connectivity along waterways, and differ among insect orders. These findings are consistent with dispersal‐limited processes and indicate that riverine diversity should be addressed and protected taking the river network structure into account.

Is local selection so widespread in river organisms? Fractal geometry of river networks leads to high bias in outlier detection

Identifying local adaptation is crucial in conservation biology to define ecotypes and establish management guidelines. Local adaptation is often inferred from the detection of loci showing a high differentiation between populations, the so-called FST outliers. Methods of detection of loci under selection are reputed to be robust in most spatial population models. However, using simulations we showed that FST outlier tests provided a high rate of false-positives (up to 60%) in fractal environments such as river networks. Surprisingly, the number of sampled demes was correlated with parameters of population genetic structure, such as the variance of FST s, and hence strongly influenced the rate of outliers. This unappreciated property of river networks therefore needs to be accounted for in genetic studies on adaptation and conservation of river organisms.

Influence of rainfall spatial resolution on flash flood modelling

Abstract. High resolution radar rainfall fields and a distributed hydrologic model are used to evaluate the sensitivity of flash flood simulations to spatial aggregation of rainfall at catchment scales ranging from 10.5 km2 to 623 km2. The case study focuses on the extreme flash flood occurred on 29 August 2003 on the eastern Italian Alps. Four rainfall spatial resolutions are considered, with grid size equal to 1-, 4-, 8- and 16-km. The influence of rainfall spatial aggregation is examined by using the flow distance as a spatial coordinate, hence emphasising the role of river network in the averaging of space-time rainfall. Effects of rainfall spatial aggregation are quantified by using a dimensionless parameter, represented by the ratio of rainfall resolution (Lr) to the characteristic basin length (Lw), taken as the square root of the watershed area. Increasing the Lr/Lw parameter induces large errors on the simulated peak discharge, with values of the peak discharge error up to 0.33 for Lr/Lw equal to 1.0. An important error source related to spatial rainfall aggregation is the rainfall volume error caused by incorrectly smoothing the rainfall volume either inside or outside of of the watershed. It is found that for Lr/Lw 1.0, around 50% of the peak discharge error is due to the rainfall volume error. Remaining errors are due to both the distortion of the rainfall spatial distribution, measured with respect to the river network, and to the reduced spatial variability of the rainfield. Further investigations are required to isolate and examine the effect of river network geometry on the averaging of space-time rainfall at various aggregation lengths and on simulated peak discharges.

Growing mountain ranges and quenched river networks

River networks in mountain ranges owe their existence to the competing effects of tectonic uplift and climate-controlled erosion. However, paradoxically, the universal geometric properties of river networks are independent of both tectonics and climate. Currently, this paradox has still not been resolved. Here we propose a solution that consists in considering that the geometry of river networks is established on the lowland margins of incipient uplifts, and is quenched into the erosion zone as the mountain belts widen with time. In our model, the geometry of river networks simply reflects the downward coalescence of alluvial rivers on un-dissected surfaces outside of mountain belts, and is therefore independent of erosion processes. To cite this article: S. Castelltort, G. Simpson, C. R. Geoscience 338 (2006).

Fractal river networks of Southern Africa

Research Article| September 01, 2005 Fractal river networks of Southern Africa Jacek Stankiewicz; Jacek Stankiewicz (corresponding author), CIGCES, Department of Geology, University of Cape Town, Rondebosch 7701, South Africa, jacek@cigces.uct.ac.za Search for other works by this author on: GSW Google Scholar Maarten J. de Wit Maarten J. de Wit CIGCES, Department of Geology, University of Cape Town, Rondebosch 7701, South Africa, maarten@cigces.uct.ac.za Search for other works by this author on: GSW Google Scholar Author and Article Information Jacek Stankiewicz (corresponding author), CIGCES, Department of Geology, University of Cape Town, Rondebosch 7701, South Africa, jacek@cigces.uct.ac.za Maarten J. de Wit CIGCES, Department of Geology, University of Cape Town, Rondebosch 7701, South Africa, maarten@cigces.uct.ac.za Publisher: Geological Society of South Africa First Online: 09 Mar 2017 Online ISSN: 1996-8590 Print ISSN: 1012-0750 © 2005 Geological Society of South Africa South African Journal of Geology (2005) 108 (3): 333–344. https://doi.org/10.2113/108.3.333 Article history First Online: 09 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Jacek Stankiewicz, Maarten J. de Wit; Fractal river networks of Southern Africa. South African Journal of Geology 2005;; 108 (3): 333–344. doi: https://doi.org/10.2113/108.3.333 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietySouth African Journal of Geology Search Advanced Search Abstract Fractals and scaling laws abound in nature, and it is said that geometry of river networks and basins is an epitome of this. This study investigates how, in the southern section of the tectonically unique African continent, scaling parameters and deviations from ‘perfect fractal patterns’ relate to parameters like geomorphology through which the river flows, and the underlying geology. A number of river network scaling laws and scaling parameters have been put forward, but it has been suggested that all river networks can be divided into universality classes represented by just 2 of these scaling parameters. One of these is the fractal dimension of individual streams, usually labelled d and having a value of ~1.1. The other parameter, Hack’s exponent h, expresses the dependence of stream length (l) on drainage area (a) via Hack’s Law l = cah. There is no universal value for h. Different networks often have different values for h, and inside a given network the parameter is often observed to change with scale. We use the natural laboratory of networks in southern Africa to investigate the variations in Hack’s exponent and find evidence to confirm the existence of scaling regimes. We attempt to explain these variations in scaling using the regime model of Dodds and Rothman (2000). At the smallest scale we find that non-convergent mountain streams exist in different settings, but their spacing is determined by underlying rock type. In this type of drainage a~l, and hence h ≈ 1. Once streams begin to converge, the value of h drops, and is inversely correlated to the roughness of the underlying topography. This trend stops once basin sizes reach a threshold value, above which basins may be self-similar. This threshold varies in individual networks. In the smoothest topographies it occurs as low as 400 km2, but can occur as high as 1400 km2 in other networks. While we have identified a number of guidelines for correlating scaling parameters with basin settings, there exist significant variations around these guidelines which we can only attribute to randomness, or small variations in the initial conditions during the initial formation of the river basins. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

River networks of southern Africa: Scaling laws governing their geometry and deviations from scaling

Africa is tectonically and hypsometrically different to all other continents and therefore provides a unique natural laboratory for the study of river network geometry. Southern Africa is one of the more unusual geomorphological regions of this continent, hence our interest in the geometry of the rivers draining this region. The 14 river basins analyzed here come from the larger networks of the Orange and Limpopo rivers, as well as from the southernmost section of the continent where rivers meander through an exhumed belt of folded Paleozoic mountains. Basic scaling laws, such as Horton's laws and Hack's law, hold for the rivers studied here, but the parameters governing these relationships vary between networks. A strong inverse correlation between Horton's ratio of stream numbers and mean source stream slope is observed. We believe this is the first time such a relation has been reported. Horton's ratio of basin areas is proportional to that of stream numbers but always greater than it; this contradicts existing models that equate the two parameters. An expression for the ratio of stream lengths in terms of the ratio of stream numbers is derived theoretically and verified for the available data. The parameter governing Hack's law, h, varies not only between networks but also with scale inside each network. Existing models provide up to four scaling regimes. Given the spatial resolution of this study, the two regimes at the middle scales are visible here. These are termed the short‐range and randomness regimes, with a crossover occurring at a drainage area of approximately 800 km2. The values for h in the smaller short‐range regime have an inverse correlation with the roughness of the topography. Observed values for h imply basins appear more elongated with increasing area; this would be more pronounced in rivers draining a smooth topography. In the randomness regime the values of h are lower, mostly between 0.5 and 0.6, with a weak positive correlation to topography roughness. This range of h corresponds to self‐similar basins, but a more detailed analysis of individual stream fractality is necessary before such a conclusion can be made.

Geometry of river networks. III. Characterization of component connectivity.

Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we explore the presence of randomness in river network structure and the details of its consequences. We first show that an averaged view of network architecture is provided by a proposed self-similarity statement about the scaling of drainage density, a local measure of stream concentration. This scaling of drainage density is shown to imply Tokunaga's law, a description of the scaling of side branch abundance along a given stream, as well as a scaling law for stream lengths. We then consider fluctuations in drainage density and consequently the numbers of side branches. Data are analyzed for the Mississippi River basin and a model of random directed networks. Numbers of side streams are found to follow exponential distributions, as are intertributary distances along streams. Finally, we derive a joint variation of side stream abundance with stream length, affording a full description of fluctuations in network structure. Fluctuations in side stream numbers are shown to be a direct result of fluctuations in stream lengths. This is the last paper in a series of three on the geometry of river networks.

Geometry of river networks. II. Distributions of component size and number.

The structure of a river network may be seen as a discrete set of nested subnetworks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon, and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power-law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.

Geometry of river networks. I. Scaling, fluctuations, and deviations.

This paper is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary, suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, here we report a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of a subbasin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density, and provide observations and explanations of deviations from scaling. We show that fluctuations about scaling are substantial, and grow with system size. We find strong deviations from scaling at small scales which can be explained by the existence of a linear network structure. At intermediate scales, we find slow drifts in exponent values, indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations, and will not be improved by increases in network resolution.

FRACTAL BEHAVIOR IN MILITARY HISTORY

Since their discovery by B. Mandelbrot in the 1960s, fractals have been recognized in the most diverse systems of nature.1 They describe such different phenomena as the geometry of river networks and the frequency distribution of earthquake magnitudes.2 Somewhat closer to the science of history, fractal theory has been widely applied to economics and econometrics.3 In general, fractal distributions are diagnostic of 'scale invariant processes'. Using the requirement of scale invariance as a guideline, military conflicts are good candidates for having a fractal distribution. Indeed, wars and other armed conflicts show a continuum of sizes. They can cause as few as one, or as many

Scaling, Universality, and Geomorphology

Theories of scaling apply wherever similarity exists across many scales. This similarity may be found in geometry and in dynamical processes. Universality arises when the qualitative character of a system is sufficient to quantitatively predict its essential features, such as the exponents that characterize scaling laws. Within geomorphology, two areas where the concepts of scaling and universality have found application are the geometry of river networks and the statistical structure of topography. We begin this review with a pedagogical presentation of scaling and universality. We then describe recent progress made in applying these ideas to networks and topography. This overview leads to a synthesis that attempts a classification of surface and network properties based on generic mechanisms and geometric constraints. We also briefly review how scaling and universality have been applied to related problems in sedimentology—specifically, the origin of stromatolites and the relation of the statistical properties of submarine-canyon topography to the size distribution of turbidite deposits. Throughout the review, our intention is to elucidate not only the problems that can be solved using these concepts, but also those that cannot.

Multifractal behaviour of river networks

Abstract. A numerical multifractal analysis was performed for five river networks extracted from Calabrian natural basins represented on 1:25000 topographic sheets. The spectrum of generalised fractal dimensions, D(q), and the sequence of mass exponents, τ(q), were obtained using an efficient generalised box-counting algorithm. The multi-fractal spectrum, f(α), was deduced with a Legendre transform. Results show that the nature of the river networks analysed is multifractal, with support dimensions, D(0), ranging between 1.76 and 1.89. The importance of the specific number of digitised points is underlined, in order to accurately define, the geometry of river networks through a direct generalised box-counting measure that is not influenced by their topology. The algorithm was also applied to a square portion of the Trionto river network to investigate border effects. Results confirm the multifractal behaviour, but with D(0) = 2. Finally, some open mathematical problems related to the assessment of the box-counting dimension are discussed. Keywords: River networks; measures; multifractal spectrum

On scaling exponents of spatial peak flows from rainfall and river network geometry

The hypothesis of statistical self-similarity, or scaling invariance, in the spatial variability of rainfall, channel network structures and floods has been supported by recent advances in data analyses. This hypothesis is used here to calculate the statistical scaling exponents of peak river flows using a random cascade model of spatial rainfall intensities and the Peano basin as an idealized model of a river basin. The ‘maximum contributing set’ approximately determines the magnitudes of peak flows in a self-similar manner in different subbasins of the Peano basin. For an instantaneously applied random, spatially uniform rainfall, the Hausdorff dimension of the maximum contributing set appear, as the statistical simple scaling exponent of peak flows. This result is generalized to an instantaneously applied cascade rainfall, and it is shown to give rise to statistical multiscaling in peak flows. The multiscaling exponent of peak flows is computed and interpreted as a Hausdorff dimension of a fractal set supporting rainfall intensity on the maximum contributing set of the Peano basin. Potential implications of this interpretation are illustrated using the regional food frequency analysis of the Appalachian flood data in the United States and a rainfall data set from the tropical Atlantic ocean. It is argued that the hypothesis of self-similarity identifies a powerful theoretical framework which can unify a statistical theory of regional flood frequency with important empirical features of topographic, rainfall and flood data sets and distributed rainfall-landform-runoff relationships.