A new method for determination of most likely landslide initiation points and the evaluation of digital terrain model scale in terrain stability mapping

This paper introduces a new approach for determining the most likely initiation points for landslides from potential instability mapped using a terrain stability model. This approach identifies the location with critical stability index from a terrain stability model on each downslope path from ridge to valley. Any measure of terrain stability may be used with this approach, which here is illustrated using results from SINMAP, and from simply taking slope as an index of potential instability. The relative density of most likely landslide initiation points within and outside mapped landslide scars provides a way to evaluate the effectiveness of a terrain stability measure, even when mapped landslide scars include run out zones, rather than just initiation locations. This relative density was used to evaluate the utility of high resolution terrain data derived from airborne laser altimetry (LIDAR) for a small basin located in the Northeastern Region of Italy. Digital Terrain Models were derived from the LIDAR data for a range of grid cell sizes (from 2 to 50 m). We found appreciable differences between the density of most likely landslide initiation points within and outside mapped landslides with ratios as large as three or more with the highest ratios for a digital terrain model grid cell size of 10 m. This leads to two conclusions: (1) The relative density from a most likely landslide initiation point approach is useful for quantifying the effectiveness of a terrain stability map when mapped landslides do not or can not differentiate between initiation, runout, and depositional areas; and (2) in this study area, where landslides occurred in complexes that were sometimes more than 100 m wide, a digital terrain model scale of 10 m is optimal. Digital terrain model scales larger than 10 m result in loss of resolution that degrades the results, while for digital terrain model scales smaller than 10 m the physical processes responsible for triggering landslides are obscured by smaller scale terrain variability

An Analytical and Numerical Study of Optimal Channel Networks

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the optimal configurations. The fractal character of river networks is reflected in the power law behaviour of various quantities characterising the morphology of the basin. In the context of a finite size scaling Ansatz, the exponents describing the power law behaviour are calculated exactly and show mean field behaviour, except for two limiting values of a parameter characterizing the dissipated energy, for which the system belongs to different universality classes. Two modified versions of the model, incorporating quenched disorder are considered: the first simulates heterogeneities in the local properties of the soil, the second considers the effects of a non-uniform rainfall. In the region of mean field behaviour, the model is shown to be robust to both kinds of perturbations. In the two limiting cases the random rainfall is still irrelevant, whereas the heterogeneity in the soil properties leads to new universality classes. Results of a numerical analysis of the model are reported that confirm and complement the theoretical analysis of the global minimum. The statistics of the local minima are found to more strongly resemble observational data on real rivers.Comment: 27 pages, ps-file, 11 Postscript figure

Development of Mountain Climate Generator and Snowpack Model for Erosion Predictions in the Western United States Using WEPP: Phase IV

Executive Summary: Introduction: This report summarizes work conducted during the funding period (December 1, 1991 through September 30, 1992) of a Research Joint Venture Agreement between the Intermountain Research Station, Forest Service, U. S. Department of Agriculture and the Utah Water Research Laboratory (UWRL), Utah State University (USU). The purpose of the agreement is to develop a Western Mountain Cilmate Generator (MCLIGEN) similar in function to the existing (non-orographic area) Climate Generator (CLIGEN), which is part of the Water Erosion Prediciton Project (WEPP) procedure. Aso, we are developing a Western U.S. Snowpack Simulation Model for includsion in WEPP. In the western U.S., topographic influences on climate make the climate too variable to be captured by one representatbie station per 100 km, as is done in CLIGEN. Also, few meteorological observations exist in high-elevation areas where Forest Service properties are located. Therefore, a procedure for estimating climatological variables in mountainous areas is needed to apply WEPP in these regions. A physically based approach, using an expanded and improved orographic precipitation model, is being utilized. It will use radiosonde lightning data to estimate historical weather sequences. Climatological sequences estimated at ungaged locations will be represented using stochastic models, similar to the approach used in the existing CLIGEN. By using these stochastic models, WEPP users will be able to synthesize climate sequences for input to WEPP. MCLIGEN will depend on historically based, physically interpolated weather sequences from a mesoscale-climate modeling system which is comprised of four nested layers: 1. an existing synoptic scale forecast model (200 x 300 km) 2. a regional scale slimate model (60 x60 km) 3. a local scale climate model (10 x 10 km); and 4. a specific point climate predictor, referred to as ZOOM. Two additional MCLIGEN components are: 5. a local scalses stochastic climate generator; and 6. a point energy balance snowmelt model Progress made during the reporting period in developing the physically based interpolation climate modeling system stochastic models, and snowpack models is summareized below

Unified View of Scaling Laws for River Networks

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added

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 sub-networks 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.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR

Development of Mountain Climate Generator and Snowpack model for Erosion Predictions in the Western United States Using WEPP, Progress Report No. 1

Executive Summary: This report summarizes work conducted during the initial funding period (November 1, 1989 through June 30, 1990) of a Cooperative Agreement between the United States Forest Service (USFS) and the Utah Water Research Laboratory (UWRL), Utah State University. The purpose of the agreement is to develop a procedure for incorporating western mountain climate into the existing Climate Generator (CLIGEN), which is part of the Water Erosion Prediction Project (WEPP) procedure. In the Western U.S., few meteorological observations exist in high elevation areas where Forest Service properties are located. Therefore, a procedure for estimating climatological variables in mountainous areas is needed to apply WEPP in these regions. A physically-based approach, an expanded and improved orographic precipitation model, is proposed in this report. It will use radiosonde data and also lightning data to simulate convective storms. Climatological sequences thus estimated at ungaged locations will be represented using stochastic models, similar to the approach used in the existing CLIGEN, and their parameters will be available to users through maps. By using these stochastic models, WEPP users can synthesize climate sequences for input to WEPP. Several alternative approaches to developing the Mountain Climate Generator (MCLIGEN) have been formulated and evaluated. These options vary in their spatial resolution. Some will provide synthetic climate inputs whereas others will provide synthetic sequences of water delivery to the ground surface or overland flow delivery. The latter will reduce the user\u27s responsibility for judging adequate snowpack or hydrological simulations, but will enormously increase the effort required for parameterization during the developmental phase. Based on our evaluation, we recommend that Option 2 for generating fine scale climate sequences be adopted. This option appears to satisfy the WEPP spatial resolution requirements of the USFS and requires a reasonable level of developmental effort. We also recommend that Option 3 be available to the users. We recomment that under this option snowpack initial conditions at a specified date be available based on a return period or exceedance probability. Under this option discontinuous simulation periods could be considered. The data, models, and parameters needed to implement the recommended approach can be divided into three parts: 1) climatological process models, 2) a snowpack imulation model, and 3) stochastic models of climatological variables and parameter regionalization. A chapter of the report is devoted to each of these three parts. Each chapter includes a literature review and a description of the proposed methodology and work plan for its development. We further recommend that a comprehensive plan for data collection for validation of the entire WEPP methodology applied to the mountainous Western U.S. be developed. Also, we propose that UWRL take the lead in settin gup a user group for orographic precipitation modelers

Development of Mountain Climate Generator and Snowpack model for Erosion Predictions in the Western United States using WEPP, Reserach Completion Report for Phase II

Executive Summary: This report summarizes work conducted during the funding period (July 1 through September 30, 1990) of a Cooperative Agreement between the United States Forest Service (USFS) and the Utah Water Research Laboratory (UWRL), Utah State University. The purpose of the agreement is to develop a Western Mountain Climate Generator (MCLIGEN) similar in function to the existing Climate Generator (CLIGEN), which is part of the Water Erosion Prediction Project (WEPP) procedure. Also, we are developing a Western U.S. snowpack simulation model for inclusion in WEPP. In the Western U.S., few meteorological observations exist in high elecation areas where Forest Service properties are located. Therefore, a procedure for estimating climatological variables in mountainous areas is needed to apply WEPP in these regions. A physically-based approach, using an expanded and improved orographic precipitation model, is being utilized. It will use radiosonde data and also lighning data to simualte convective storms. Climatological sequences thus estimated at ungaged locatiosn will be represented using stochastic models, similar to the approach used in the existing CLIGEN, and their parameters will be available to users through maps. By using these stochastic models, WEPP usters can synthsize climate sequences for input to WEPP. During the reporting period we have implemented the the Rhea orographic precipitation model and begun preliminary model testing in two regions. Also, we have begun formulation of model modifications for handling convective events. Various snowplack and meteorological data sets have been acquired and others have been ordered. Some of these have been applied in ititial applications of several snowpack models which have been recorded in a modeular form. Work has commenced on the statistical analysis of western climate sequences, including the preliminary assessment of the alternative stochastic model structures. Additional review of literature has been commenced for establishing desing storms and design hydrographs for events of various return periods in mountainous regions. Accomplishments are summarized in three parts: 1) climatological process models, 2) snowpack simulation models, and 3) stochastic models of climatological variablse and parameter regionalization. A chapter of the report is devoted to each of these three parts

Flow Computations on Imprecise Terrains

We study the computation of the flow of water on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x,y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time

Basins of attraction on random topography

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes