A new procedure for the representation of flow directions and calculation of upslope areas using rectangular grid digital elevation models is presented. The procedure is based on representing flow direction as a single angle taken as the steepest downward slope on the eight triangular facets centered at each grid point. Upslope area is then calculated by proportioning flow between two downslope pixels according to how close this flow direction is to the direct angle to the downslope pixel. This procedure offers improvements over prior procedures that have restricted flow to eight possible directions (introducing grid bia) or proportioned flow according to slope (introducing unrealistic dispersion). The new procedure is more robust than prior procedures based on fitting local planes while retaining a simple grid based structure. Detailed algorithms are presented and results are demonstrated through test examples and application to digital elevation data sets.

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A new method for the determination of flow directions and upslope areas in grid digital elevation models

A framework is provided for scaling and scale issues in hydrology. The first section gives some basic definitions. This is important as researchers do not seem to have agreed on the meaning of concepts such as scale or upscaling. ‘Process scale’, ‘observation scale’ and ‘modelling (working) scale’ require different definitions. The second section discusses heterogeneity and variability in catchments and touches on the implications of randomness and organization for scaling. The third section addresses the linkages across scales from a modelling point of view. It is argued that upscaling typically consists of two steps: distributing and aggregating. Conversely, downscaling involves disaggregation and singling out. Different approaches are discussed for linking state variables, parameters, inputs and conceptualizations across scales. This section also deals with distributed parameter models, which are one way of linking conceptualizations across scales. The fourth section addresses the linkages across scales from a more holistic perspective dealing with dimensional analysis and similarity concepts. The main difference to the modelling point of view is that dimensional analysis and similarity concepts deal with complex processes in a much simpler fashion. Examples of dimensional analysis, similarity analysis and functional normalization in catchment hydrology are given. This section also briefly discusses fractals, which are a popular tool for quantifying variability across scales. The fifth section focuses on one particular aspect of this holistic view, discussing stream network analysis. The paper concludes with identifying key issues and gives some directions for future research.

/pdf/scale-issues-in-hydrological-modelling-a-review-1x61lpwqjr.pdf

Scale issues in hydrological modelling: A review

The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan

A drainage basin simulation model introduced here incorporates creep and threshold slumping and both detachment- and transport-limited fluvial processes. Fluvial erosion of natural slopes and headwater channels is argued to be dominantly detachment-limited. Such slopes undergo nearly parallel retreat and replacement with alluvial surfaces under fixed base level, in contrast with gradual slope decline for transport-limited conditions. The arrangement of divides and valleys is sensitive to initial conditions, although average morphology is insensitive. Dissected, initially flat surfaces in which downstream concavity is slight exhibit nearly parallel drainage, compared to very wandering main valleys when concavity is great. Steady state is reached after a cumulative base level drop approximately 3 times the final relief. Simulated valley systems are similar to those predicted by a previous model of optimal drainage basins. A critical value of slope divergence normalized by average slope gradient is a useful criterion for defining the valley network.

/pdf/a-detachment-limited-model-of-drainage-basin-evolution-3o7nban85w.pdf

A detachment-limited model of drainage basin evolution

Spatial data for landslide susceptibility, hazard, and vulnerability assessment: An overview

The topography of a catchment has a major impact on the hydrological, geomorphological. and biological processes active in the landscape. The spatial distribution of topographic attributes can often be used as an indirect measure of the spatial variability of these processes and allows them to be mapped using relatively simple techniques. Many geographic information systems are being developed that store topographic information as the primary data for analysing water resource and biological problems. Furthermore, topography can be used to develop more physically realistic structures for hydrologic and water quality models that directly account for the impact of topography on the hydrology. Digital elevation models are the primary data used in the analysis of catchment topography. We describe elevation data sources, digital elevation model structures, and the analysis of digital elevation data for hydrological, geomorphological, and biological applications. Some hydrologic models that make use of digital representations of topography are also considered.

Digital terrain modelling: A review of hydrological, geomorphological, and biological applications

The roles and limitations of geographical information systems (GISs) in scaling hydrological models over heterogeneous land surfaces are outlined. Scaling is defined here as the extension of small-scale process models, which may be directly parameterized and validated, to larger spatial extents. A process computation can be successfully scaled if this extension can be carried out with minimal bias. Much of our understanding of land surface hydrological processes as currently applied within distributed models has been derived in conjunction with 'point' or 'plot' experiments, in which spatial variations and patterns of the controlling soil, canopy and meteorological factors are not defined. In these cases, prescription of model input parameters can be accomplished by direct observation. As the spatial extent is expanded beyond these point experiments to catchment or larger watershed regions, the direct extension of the point models requires an estimation of the distribution of the model parameters and process computations over the heterogeneous land surface. If the distribution of the set of spatial variables required for a given hydrological model (e.g. surface slope, soil hydraulic conductivity) can be described by a joint density function, f(x), where x = x 1 ,x 2 ,x 3 ,... are the model variables, then a GIS may be evaluated as a tool for estimating this function. In terms of the scaling procedure, the GIS is used to replace direct measurement or sampling of f(x) as the area of simulation is increased beyond the extent over which direct sampling of the distribution is feasible. The question to be asked is whether current GISs and current available spatial data sets are sufficient to adequately estimate these density functions.

I. D. Moore

Papers

Digital terrain modelling: A review of hydrological, geomorphological, and biological applications

Scale: Landscape attributes and geographical information systems