Chapter 10 Spatial Data Models

Introduction n The Earth: complex, multivariate system n Computer processing of geo-referenced data in GIS n Discretization of geospatial phenomena n Geographic conceptualization or data modeling  Fields  Objects  Networks

n Entities/objects –Position, attributes n Fields –Measurement scale (nominal, ordinal, interval, ratio) –Variables (categorical and continuous)

Field models n A set of single-valued functions defined on data support B: Z(·) n Data support B {xs, s=1, …, n} n Values: z(x s ) z(x s )=  s  (x)Z(x)dx/volume(x s ) –  (x) selection functions – volume(x s ) normalization quantity

Convolution of two functions and over a finite range is given by (1) where the symbol (occasionally also written as ) denotes convolution of and. Convolution is more often taken over an infinite range, (2)

SPIN-2 Panchromatic digital image of Gizah 1997 (from Fowler, Image provided courtesy of SPIN-2 at Aerial Images Inc.)

A map of 105 weather stations in Idaho and their 30-year average annual precipitation values Spatial interpolation

Arithmetic and logic operations on fields n Digital terrain analysis n Elevation  terrain & hydrologic parameters (e.g., slope, aspect, plan and profile curvature, flow path lengths and specific catchment area) n Rationale: –topography affecting water and solute movement in terrain –used when assessing the hydrological responses of a catchment to a rainfall

n Slope: the rate of change in elevation n Aspect: the orientation of the steepest slope measured in degrees clockwise from north n Contributing area: the upslope area that delivers water to a point n Wetness index

n Slope and aspect tan(slope(i,j)) = [(  Z/  X) 2 +(  Z/  Y) 2 ] 1/2  Z/  X =(Z(i,j+1)–Z(i,j-1))/2  Z/  Y =(Z(i-1,j)–Z(i+1,j)) /2 n Wetness index due to topography

A 3 by 3 window centered at (i,j)

An example （ Finland ）

The study area: northern Finland near Kajaani (64.05  N, 27,41  E). The altitude: 180 m ~ 275 m, meaning the whole site has been above the highest sea level during the Glacier melting phase. Soils: mainly fine-textured tills and not pre-washed by the sea phases of the Baltic Sea. However, the lowest parts of the site belong to the run off area of Sotkamo-Pielinen glacial lake and are thus gravelly sandy tills. Thickness of the soil cover: thin in the north-west sides of the hills and much thicker in the south-east sides - the glacier flow direction. Bedrock: the resistant rock quartzite, not eroded as much as the rocks in the surrounding areas. In addition, some nutritious rocks found in the area. Vegetation: quite rich.

Topographic variables Reflectance and backscatter -> land classification n NDVI and biomass Multi-criteria evaluation Field derivatives

U(x) = CL(Z1(x),Z2(x),…,Zb(x)) NDVI(x) = (Z NIR (x)–Z R (x))/(Z NIR (x)+ Z R (x))