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

A) CELLSB) REGULARLY SPACED POINTSC) IRREGULARLYSPACED POINTSD) CONTOURSE) POLYGONSF) TINs- Triangulated Irregular Network

Representation of field phenomena

Isarithmic Mapping

Data measuredat points

Derived data

- used for continuous data

Spatial sampling

Regular lattice•restricted to X,Y locations

Irregular lattice•not restricted•based on knowledge about how smooth/rugged the surface is

e.g. elevation

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

• A raster representation is composed of a series of layers, each with a theme

• Typically used to represent ‘field-like’ geographic phenomena

Raster Data Model

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 ResolutionSpatial resolution = the distance that one side of a grid cell represents on the ground

1

2244

11

44

11

244

12

33

33

2

22

22

= 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