Statistical surfaces: DEM’s Geog 4103, March 22

Real world phenomena represented as: DISCRETE: homogeneous or spatially averaged units, e.g. subwatersheds, counties, polygons VECTOR FIELDS: discretized as grid cells or meshes RASTER

What are surfaces? Features that contain Z values distributed throughout area defines by (x,y) coordinate pairs Z values can be any measurable phenomena that varies across space (temperature, elevation, precipitation, etc…) called “field” like, or continuous data

What is a field? a conceptual model of geographic variation at every point in the frame (x,y) there exists a single value of a variable Z e.g. a field of temperature e.g. a field of land surface elevation the variable may be measured on any scale temperature - degrees Celsius elevation - meters above sea level

Field data are continuous a field is spatially continuous by definition values exist everywhere

Representation of field phenomena A) CELLS B) REGULARLY SPACED POINTS C) IRREGULARLY D) CONTOURS E) POLYGONS F) TINs- Triangulated Irregular Network

Isarithmic Mapping - used for continuous data Data measured at points Derived data

Spatial sampling e.g. elevation Regular lattice restricted to X,Y locations Irregular lattice not restricted based on knowledge about how smooth/rugged the surface is

Two methods of representing a surface inside a computer Vector surfaces: TIN’s (Triangulated Irregular Network) Raster surfaces: DEM (Digital Elevation Model)

RASTER vs. VECTOR DIGITAL ELEVATION MODEL

Triangulated Irregular Network (TIN)

Triangulated Irregular Network (TIN) continuous mesh of triangles. -triangles vary in size based on roughness/complexity of terrain. - Large vs. small triangles

Raster Data Model A raster representation is composed of a series of layers, each with a theme Typically used to represent ‘field-like’ geographic phenomena

Raster Grid but most common raster is composed of squares, called grid cells grid cells are analogous to pixels in remote sensing images and computer graphics

Raster Resolution 1 2 4 3 = grid cell resolution Spatial resolution = the distance that one side of a grid cell represents on the ground 1 2 4 3 = grid cell resolution The higher the resolution (smaller the grid cell), the higher the precision, but the greater the cost in data storage

The DEM / DTM Digital elevation models = a way of representing surfaces. Quantitative model of a topographic surface in digital form. data sets are continuous surfaces.

Elevation data Source of DEMs and TINs Process of interpolation - creating continuous data from point data