Structure function and Multifractal spectrum applied to Digital Elevation Model

A Digital Elevation Model (DEM) provides the information basis used for many geographic applications such as topographic and geomorphologic studies, landscape through GIS (Geographic Information Systems) among others. The DEM capacity to represent Earth?s surface depends on the surface roughness and the resolution used. Each DEM pixel depends on the scale used characterized by two variables: resolution and extension of the area studied. DEMs can vary in resolution and accuracy by the production method, although there are statistical characteristics that keep constant or very similar in a wide range of scales. Based on this property, several techniques have been applied to characterize DEM through multiscale analysis directly related to fractal geometry: multifractal spectrum and the structure function. The comparison of the results by both methods is discussed. The study area is represented by a 1024 x 1024 data matrix obtained from a DEM with a resolution of 10 x 10 m each point, which correspond with a region known as ?Monte de El Pardo? a property of Spanish National Heritage (Patrimonio Nacional Español) of 15820 Ha located to a short distance from the center of Madrid. Manzanares River goes through this area from North to South. In the southern area a reservoir is found with a capacity of 43 hm3, with an altitude of 603.3 m till 632 m when it is at the highest capacity. In the middle of the reservoir the minimum altitude of this area is achieved.

Barnstable, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic quadrangle map of Barnstable, Massachusetts. The edition date is 1893 and the map was reprinted in 1907. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Barre, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic quadrangle map of Barre, Massachusetts. The suvery (ground condition) date is 1887, the edition date is March, 1894 and the map was reprinted in 1942. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Becket, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic quadrangle map of Becket, Massachusetts. The survey (ground condition) date is 1886. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Belchertown, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Belchertown, Massachusetts quadrangle. The suvey (ground condition) dates are 1885 and 1887; the edition date is November, 1893. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Berlin (N.Y.) Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic quadrangle map entitled Berlin, (N.Y.) which also shows towns and features in Massachusetts. The survey dates (ground condition) for this map are 1885-88, and the edition date is 1890. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Blackstone, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Blackstone, Massachusetts quadrangle. The survey date (ground condition) of this map is 1886 and the edition date is October, 1893. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Boston (1900), Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic (DRG) of the historic 15-minute USGS topographic map of the Boston, Massachusetts quadrangle. The survey date (ground condition) of this map ranges from 1898 to 1900, the edition date is July, 1903 and it was reprinted in 1918. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Boston North (1943), Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic (DRG) of the historic 15-minute USGS topographic map of the Boston North, Massachusetts quadrangle. The survey date (ground condition) of this map is 1943, the edition date is 1946. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Boston South (1950), Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic (DRG) of the historic 15-minute USGS topographic map of the Boston South, Massachusetts quadrangle. The survey date (ground condition) of this map is 1943, it was revised in 1949 and reprinted with corrections in 1950. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Boston Bay (1886), Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Boston Bay, Massachusetts quadrangle. The survey dates (ground condition) dates for this map are 1886 and 1887. This map includes coverage of Cohasset, Hull, Quincy, Marblehead, Lynn, Swampscott and, in general, the coastal areas encompassing Boston Harbor and the larger area of the Bay. The Boston Harbor Islands are also depicted. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Boston Bay (1900), Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Boston Bay (1900), Massachusetts quadrangle. The survey date (ground condition) of this map is 1899-1900, the edition date is July 1903, and this map was repinted in 1928. This map includes coverage of Cohasset, Hull, Quincy, Marblehead, Lynn, Swampscott and, in general, the coastal areas encompassing Boston Harbor and the larger area of the Bay. The Boston Harbor Islands are also depicted. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.

Brookfield, Massachusetts 15 Minute Digital Raster Graphic

This layer is a digital raster graphic of the historic 15-minute USGS topographic map of the Brookfield, Massachusetts quadrangle. The survey date (ground condition) of this map is 1886-1887, the edition date is April, 1893 and the map was reprinted in 1942. A digital raster graphic (DRG) is a scanned image of a U.S. Geological Survey (USGS) standard series topographic map, including all map collar information. The image inside the map neatline is geo-referenced to the surface of the earth and fit to the Universal Transverse Mercator projection. The horizontal positional accuracy and datum of the DRG matches the accuracy and datum of the source map. The names of quadrangles which border this one appear on the map collar in their respective positions (N,S,E,W) in relation to this map.