By Robert Joseph Peckham, Robert Joseph Peckham, Jordan Gyozo
This booklet is the 1st e-book at the improvement and alertness of electronic terrain modelling for nearby making plans and coverage aid. it's a compilation of analysis effects by means of foreign learn teams on the eu Commission's Joint examine Centre, offering clinical aid to the improvement and implementation of european environmental coverage. purposes comprise the pan-European River and Catchment Database, eu Flood Alert process, eu electronic Soil Database and replacement solar power assets, all mentioned in a GIS framework within the context of the INfrastructure for SPatial details in Europe (INSPIRE). This practice-oriented booklet is suggested to training environmental modellers and GIS specialists engaged on local making plans and coverage help applications.
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Here we have a link between surface geometry and flow on the surface: local extremes, saddle points and flats with no flow can be found only at elliptic, hyperbolic and parabolic points, respectively. In the case of bivariate functions of surfaces, similarly to single variable y = f(x) planar curves, the first derivatives (gradients) are used to identify local extreme points and the second derivatives (curvatures) are used to identify inflexion points. 4 Ridge Line (Watershed Divide) and Valley Line (Drainage Line): Flow Boundaries Finally, for the geometric characterisation of a topographic surface, valley lines and ridge lines have to be identified.
The obvious physical continuity of the topographic surface is often mixed up with the mathematical definition of continuity in literature. DEMs represented by random points, survey lines, contour lines and grids have an infinite number of missing surface elevation values in between the data points, therefore they are discontinuous, too. In the special case of vertical walls in the topography, where the same (x,y) location can have two different z elevation values, the topographic surface cannot be represented by a mathematical function thus calculation of derivatives is not permitted.
A. kp ! 0, kt ! 0. B. kp 0, kt ! 0. C. kp ! 0, kt 0. D. kp 0, kt 0. Positive and negative values define concave and convex curvature, respectively (after Mitesova and Hofierka 1993) The inflexion point of the continuous slope line, along which profile curvature is measured, is calculated as kp = 0, where it separates convex (negative) and concave (positive) curve sections. In the point of inflexion of the slope curves on the topographic surface, the value of slope acquires maximum or minimum values depending on whether we get from the convex part into the concave one or vice versa.