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Video showing a Landscape Genesis Modeling To model the intermediate locations of the cone's borderlines during built-up, a linear interpolation is carried out between each vertex of the borderline polygon and the center point, both known from the input data (Fig. 3). The increment depends on the number of frames assigned for the build-up of the cone. The series of concentric polygons documenting the horizontal growth is saved as one single ESRI file. As a next step, the standard profile is transformed horizontally between the center point and each vertex of the present borderline polygon (dotted lines in Fig. 3). As a result, we obtain an individual profile for every vertex of the border line. All profiles originate in the center and run outwards in a star-shaped figure.
The vertical extent is computed as the difference between the altitude of the highest elevation of the volcano taken from the 1900 map and the lowest DEM vertex of the pre-volcano terrain within the horizontal final extent of the volcano. This difference is divided by the number of frames assigned to the event. Thus, we have the increment the volcano grows along the vertical axis during each frame. A linear interpolation by time can be performed using this increment. All profiles are now scaled in the vertical as well. Thus, the maximum vertical extent of every profile of a frame is identical and represents the current height of the volcano for this frame. Consequently, we have to deal with two different scale factors for the horizontal and the vertical transformation of every profile. In the next step, the volcanic cone has to be prepared for integration into the digital (raster) elevation model. So far, the volcano is just described by a number of profiles. As mentioned above, the raster width used in the project is 40 m; the program could handle any other width, too, however. Affected are all points of the grid that lie within the box defined by the extreme points of the volcano's horizontal extent (of course, the same coordinate system for all data is a precondition). For every grid point G inside this box the two neighboring profiles of the star-shaped figure have to be found (Fig. 4). They are used to compute a new profile running through the grid point under consideration. The distances of profile points 2, 3 and 4 from center point 1 on the new profile are interpolated using the angles between this profile and the neighbor profiles. The height of the grid point can finally be interpolated on the new profile. When this procedure is repeated for all grid points within the chosen box, a grid based height model of the volcano is available for the box area. These heights now have to be added to the pre-volcano elevations of the general elevation model to obtain new absolute heights. If the old terrain was very uneven, however, the computed cone would be distorted accordingly. Therefore, the volcano grid heights always are added to the horizontal plane defined by the lowest DEM-vertex within the volcano's extent, instead. All steps described above have to be repeated for each volcano or maar and for every single frame. At the end of processing, we obtain a sequence of elevation models describing the genesis of the maars and volcanoes in this period. It has to be considered, too, that in some cases several volcanic events take place at the same time at different locations. 
Figure 4 Interpolation of the height of a grid point (G) from heights of neighboring profile points (see text). Lava and pyroclastic flows Although the geological facts behind their genesis are entirely different, both manifestations of volcanic flow deposits can be modeled in a very similar way. Input data. The outline of a flow deposit has to be digitized from the geological map in a way similar to the procedure described for volcano cones above. In addition, a line must be specified describing the directions of progression. Again, the number of frames has to be chosen in order to have a value for the increments needed in the computation. Finally, the thickness of the flow must be known at any location. These values derive from digital height models describing the surface of the deposits. If those are not available with sufficient quantity and quality, a constant average thickness has to be used. For reasons already mentioned, all input-data (outlines and DEMs) have been generated as or converted into ARC/INFO® formats and provided as ASCII-files. Modeling. In order to model the progression of the flow, its front part is moved ahead in increments (Fig. 5). To give the movement a smooth appearance, many front lines have to be defined. Since it would be too tedious to digitize all these lines manually, a program was developed to define these front lines as arcs between the left and right outline, considering also the flow directions given with the input data. A polygon, enclosing the area the flow has moved ahead since the last frame, is generated using the current and the last front line arcs, and labeled according to the frame number. Problems arise in sharp curves where the front line arcs may intersect (Fig. 6). This requires some additional editing (e.g. with ARCEDIT®) to get topologically correct polygons. A point-in-polygon test is now performed in every frame for each polygon labeled with the current frame number. If a DEM grid elevation point is located inside the last increment of a lava flow movement, its elevation will be replaced by the corresponding elevation of the flow's surface. Pyroclastic flows, consis-ting of gases to a large extent, settle when coming to a halt. This effect was modeled using a multiple thickness during the propagation phase and reducing heights to the final surface location afterwards. Modeling of volcanoes/maars and flow deposits is integrated into one single program. Thus, it can be performed in one step, if all necessary input data are available.
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