Transcript Field models

Chapter 10 Spatial Data Models
Introduction
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The Earth: complex, multivariate system
Computer processing of geo-referenced data in
GIS
Discretization of geospatial phenomena
Geographic conceptualization or data modeling
 Fields
 Objects
 Networks
Entities/objects
– Position, attributes
 Fields
– Measurement scale (nominal, ordinal,
interval, ratio)
– Variables (categorical and continuous)
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Field models
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A set of single-valued functions defined on
data support B: Z(·)
Data support B {xs, s=1, …, n}
Values: z(xs)
z(xs)=s(x)Z(x)dx/volume(xs)
–(x) selection functions
–volume(xs) normalization quantity
Convolution of two functions
range
is given by
and
over a finite
(1)
where the symbol
(occasionally also written as
)
denotes convolution of and . Convolution is more often taken
over an infinite range,
(2)
Valid types of
variables
Examples
irregular
points
continuous
categorical
weather
station data
regular
points
continuous
categorical
laser profiling
data
contours
continuous
noise level
data
polygons
continuous
categorical
land cover
data
grids
continuous
categorical
remotely
sensed data
triangulated
irregular
networks (TINs)
continuous
topographic
data
Field models
Graphical representations
SPIN-2 Panchromatic digital image of Gizah
1997 (from Fowler, 1999. 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
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Digital terrain analysis
Elevation  terrain & hydrologic parameters
(e.g., slope, aspect, plan and profile curvature,
flow path lengths and specific catchment area)
Rationale:
– topography affecting water and solute
movement in terrain
– used when assessing the hydrological responses
of a catchment to a rainfall
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Slope: the rate of change in elevation
Aspect: the orientation of the steepest slope
measured in degrees clockwise from north
Contributing area: the upslope area that delivers
water to a point
Wetness index
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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
 FD
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 zx 
 zy 
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 180  arctan    90
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 zx 
 zx 
Wetness index due to topography
Wetness  ln( As /(T tan  ))
Z(i+1, j-1)
Z(i+1, j)
Z(i+1, j+1)
Z(i, j-1)
Z(i, j)
Z(i, j+1)
Z(i-1, j-1)
Z(i-1, j)
Z(i-1, j+1)
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.
Field derivatives
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Topographic variables
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Reflectance and backscatter -> land
classification
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NDVI and biomass
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Multi-criteria evaluation
i, j
Z1
i, j
Z2
i, j
U
i, j
Zb
U(x) = CL(Z1(x),Z2(x),…,Zb(x))
NDVI(x) = (ZNIR(x)–ZR(x))/(ZNIR(x)+ ZR(x))