The Energy Cone Model

energy_cone calculates the potential run-out of pyroclastic density currents (pdcs) using the Heim coefficient, 
the ratio of release height in the volcanic plume to total potential run-out length. For a simplified demonstration 
of the use of the energy cone model, see:
http://www.cas.usf.edu/~cconnor/menan_butte.html


The code loads a digital elevation model of the area. The intersection of the cone with the topographic surface controls
the total potential run-out distance of the pdc from the volcanc vent.

Several potential run-out distances are calculated by this code, using a minimum release height, and a maximum release height
to bound the simulations.

energy_cone takes the following inputs:
1) A Volcanic region (west, east, south, north) in UTM coordinates

2) The location of the vent in UTM xcoordinates

3) The minimum and maximum heights and the interval between them (km above sea level). This controls how many energy cones
   are drawn on your map. Use this feature to see how change in height of the pdc release height (H) affects the run-out
   distance (L), given topography in the area.

4) The H/L ratio. The Heim coefficient controls how far a pdc will run-out (L), given its release height (H) and depending 
   on local topography. Typically H/L ranges from 0.05 (highly mobile pdc) to 0.5 (low mobility pdc).

5) The minimum and maximum degree and the degree interval. You can plot the entire energy cone (full circle around
   the volcanic vent) or only a part. The degree interval controls how many radial lines are used to construct
   the energy cone. A finer interval will lead to a higher resolution, but requires more computation time.
   
6) The distance interval along radial line which controls how frequently calculations are made along each radial line
   to determine the total run-out distance. A smaller distance interval requires more calculation time, but results in
   a higher resolution map.