Nicole M. Gasparini

An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks

We describe a newset of data structures and algorithms for dynamic terrain modeling using a triangulated irregular network (TINs). The framework provides an efficient method for storing, accessing, and updating a Delaunay triangulation and its associated Voronoi diagram. The basic data structure consists of three interconnected data objects: triangles, nodes, and directed edges. Encapsulating each of these geometric elements within a data object makes it possible to essentially decouple the TIN representation from the modeling applications that make use of it. Both the triangulation and its corresponding Voronoi diagram can be rapidly retrieved or updated, making these methods well suited to adaptive remeshing schemes. We develop a set of algorithms for defining drainage networks and identifying closed depressions (e.g., lakes) for hydrologic and geomorphic modeling applications. We also outline simple numerical algorithms for solving network routing and 2D transport equations within the TIN framework. The methods are illustrated with two example applications, a landscape evolution model and a distributed rainfall-runoff model. # 2001 Elsevier Science Ltd. All rights reserved.

The Channel-Hillslope Integrated Landscape Development Model (CHILD)

Numerical models of complex Earth systems serve two important purposes. First, they embody quantitative hypotheses about those systems and thus help researchers develop insight and generate testable predictions. Second, in a more pragmatic context, numerical models are often called upon as quantitative decision-support tools. In geomorphology, mathematical and numerical models provide a crucial link between small-scale, measurable processes and their long-term geomorphic implications. In recent years, several models have been developed that simulate the structure and evolution of three-dimensional fluvial terrain as a consequence of different process “laws” (e.g., Willgoose et al., 1991a; Beaumont et al., 1992; Chase, 1992; Anderson, 1994; Howard, 1994; Tucker and Slingerland, 1994; Moglen and Bras, 1995). By providing the much-needed connection between measurable processes and the dynamics of long-term landscape evolution that these processes drive, mathematical landscape models have posed challenging new hypotheses and have provided the guiding impetus behind new quantitative field studies and Digital Elevation Model (DEM) -based analyses of terrain (e.g., Snyder et al., 2000). The current generation of models, however, shares a number of important limitations. Most models rely on a highly simplified representation of drainage basin hydrology, treating climate through a simple “perpetual runoff” formulation.

Predictions of steady state and transient landscape morphology using sediment‐flux‐dependent river incision models

[1]xa0Recent experimental and theoretical studies support the notion that bed load in mountain rivers can both enhance incision rates through wear and inhibit incision rates by covering the bed. These effects may play an important role in landscape evolution and, in particular, the response of river channels to tectonic or climatic perturbation. We use the channel-hillslope integrated landscape development (CHILD) numerical model with two different bedrock incision models that include the dual role of the sediment flux to explore the transient behavior of fluvial landscapes. Both models predict that steady state channel slopes increase in landscapes with higher rock uplift rates. However, the incision models predict different transient responses to an increase in uplift rate, and the behavior of each incision model depends on both the magnitude of change in uplift rate and the local drainage area. In some cases, the transient channel behavior is indistinguishable from that predicted for transport-limited alluvial rivers. In other cases, knickpoints form in some or all of the drainage network, as predicted by the detachment-limited stream power model. In all cases the response in the lower parts of the network is highly dependent on the response in the upper parts of the network as well as the hillslopes. As the upper parts of the network send more sediment downstream, channel incision rates may rise or fall, and slopes in the lower parts of the channel may, in fact, decrease at times during the transient adjustment to an increase in rock uplift rate. In some cases, channel incision in the upper parts of the network ceases during the transient while the hillslopes adjust to the new uplift rate; drainage density may also change as a function of uplift rate. Our results suggest that if the sediment flux strongly controls bedrock incision rates, then (1) the transient fluvial response will take longer than predicted by the detachment-limited stream power model, (2) changes in channel slope may be much more complex than predicted by the detachment-limited stream power model, and (3) changes in the fluvial system will be closely tied to sediment delivery from the hillslopes. Importantly, our results outline quantitative differences in system behavior produced by competing models and provide a framework for identifying locations in natural systems where differences in channel morphology can be used to discern between competing fluvial erosion models.

Formation of fluvial hanging valleys: Theory and simulation

[1]xa0Although only recently recognized, hanging tributary valleys in unglaciated, tectonically active landscapes are surprisingly common. Stream power–based river incision models do not provide a viable mechanism for the formation of fluvial hanging valleys. Thus these disequilibrium landforms present an opportunity to advance our understanding of river incision processes. In this work, we demonstrate that thresholds apparent in sediment flux–dependent bedrock incision rules provide mechanisms for the formation of hanging valleys in response to transient pulses of river incision. We simplify recently published river incision models in order to derive analytical solutions for the conditions required for hanging valley formation and use these results to guide numerical landscape evolution simulations. Analytical and numerical results demonstrate that during the response to base level fall, sediment flux–dependent incision rules may create either temporary or permanent hanging valleys. These hanging valleys form as a consequence of (1) rapid main stem incision oversteepening tributary junctions beyond some threshold slope or (2) low tributary sediment flux response during the pulse of main stem incision, thus limiting the tributarys capacity to keep pace with main stem incision. The distribution of permanent and temporary hanging valleys results from four competing factors: the magnitude of base level fall, the upstream attenuation of the incision signal, the lag time of the sediment flux response, and the nonsystematic variation in tributary drainage areas within the stream network. The development of hanging valleys in landscapes governed by sediment flux–dependent incision rules limits the transmission of base level fall signals through the channel network, ultimately increasing basin response time.

Downstream fining through selective particle sorting in an equilibrium drainage network

The phenomenon of downstream fining has been attributed to both particle abrasion and selective particle sorting; the latter is generally considered to play the dominant role within resistant lithologies. It has been recognized that tributaries can disrupt fining patterns; however, few downstream-fining studies have considered the entire fluvial network structure. Here we combine a theory for selective transport with a model of river-basin evolution in order to simulate the dynamics of selective sorting throughout a drainage network. Previous numerical modeling studies of single-thread or braided channels have treated downstream fining as a phenomenon driven by differential deposition rates. We show, however, that in an eroding drainage network, downstream fining emerges as a natural dynamic adjustment to variable water, sediment, and energy inputs, even under conditions of uniform size distribution in sediment flux. Thus, although selective deposition and abrasion clearly can and do play a role in some fluvial systems, neither is necessary to produce downstream fining within a drainage network.

A simple algorithm for the mapping of TIN data onto a static grid: Applied to the stratigraphic simulation of river meander deposits

Abstract Triangulated irregular networks (TIN) in landscape evolution models have the advantage of representing geologic processes that involve a horizontal component, such as faulting and river meandering, due to their adaptive remeshing capability of moving, adding and deleting nodes. However, the moving node feature is difficult to integrate with the accumulation of a three-dimensional (3D) subsurface stratigraphy, because it requires 3D subsurface interpolation, which results in stratigraphic data loss due to heterogeneity of the subsurface and averaging effects. We present a simple algorithm that maps any changes in the configuration of TIN landscape nodes onto a static grid, facilitating the creation of a fixed stratigraphic record of TIN surface change. The algorithm provides a practical solution not only for the stratigraphic problem, but also for other problems that involve linking of models that use TIN and raster discretization schemes. An example application is presented using the river meandering module incorporated in the CHILD landscape evolution model. Examples are shown of cross-sections, and voxel distributions and geo-archaeological depth–age maps. These illustrate the type of insights that can be obtained from process-based modeling of subsurface fluvial architecture, and highlight potential applications of stratigraphic simulation.