Modeling Spatial Problems

1
Modeling Spatial Problems

• Description of models.
• Models of surfaces.
• Cell-based calculations to fill the raster.
• Interpolating to fill the raster.

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Description of Models

• A model is a representation of reality.
• Models are created as a simplified, manageable
  view of reality.
• Models help you understand, describe, or predict
  how things work.

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Types of Models

• Representation models.
• Represent the objects in the landscape.
• Process models.
• Simulate processes in the landscape.
• Data Models.
• Vector
• Raster
• TIN

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Representation Models

• Describe the objects in a landscape through a set
  of data layers.

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Representation Models

• Common data models/descriptive models.
• Spatial relationships within an object (the shape
  of a building).
• Between the other objects in the landscape (the
  distribution of buildings).
• Model the attributes of the objects (who owns
  each building).

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Process Models

• Describe the interaction of the objects that are
  modeled in the representation model using map
  calculation.

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Process Models

• Complexity can be added through logic.
• Map query by Boolean and logical operators.

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Time Out for Definitions

• Boolean operators
• And, Or, XOr, Not
• Relational operators
• , gt, lt, ltgt, gt, lt
• Arithmetic operators
• , /, -, , Log, Exp, Sin, Cos, Sqrt

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Boolean Operators

• And finds where values are true (nonzero) in the
  cells of both input rasters
• Or finds where nonzero values are present in the
  cells of one or both input rasters
• Xor finds where nonzero values are present in
  the cells of one input raster or another input
  raster, but not both
• Not finds where nonzero values are not present
  in the cells of a single input raster

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Process Models

• Suitability modeling where should I put it?
• Distance modeling how far is it?
• Hydrologic modeling where will the water flow
  to?
• Surface modeling what is the pollution level?

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Process Models

• Additional complexity is added through
  specialized functions.
• Given particle size of eroded sediment and stream
  flow rate, how far will pollution go?

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Process Models

• Sometimes hundreds of operations and functions
  may be necessary.

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Process Model Implementation
14
Cell-based Modeling

• Whats needed to calculate an output value for
  each cell?
• A cell value.
• The manipulation being applied.
• Which other cells need to be included?

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Cell-based Modeling

• Five types of functions associated with
  cell-based modeling.
• Local functions (work on single cells).
• Focal functions (cells within a neighborhood).
• Zonal functions (cells within zones).
• Global functions (cells within the raster).
• Application functions (combined in a series).

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Cell-based Modeling

• Local cell functions do not depend on neighbors.
• Focal functions depend on values from a specified
  neighborhood shape, e.g., slope.
• Zonal functions depend on values from
  neighborhoods without specific shape.

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Cell-based Modeling

• Global functions compute an output raster dataset
  in which the output value at each cell location
  is potentially a function of all the cells in the
  input raster datasets.
• Euclidean distance (distance from the closest
  source cell) ((x1 - x2)2 (y1 - y2)2)1/2 .
• Weighted (cost) surface.
• Shortest path.

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Detour
19
Zone Definition
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Zone Definition

• Any two or more cells with same value is a zone.
• They can be connected or disconnected.
• If connected they usually represent a single
  feature.
• Each group of connected cells within a zone is a
  region.

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Zone Definition Attribute Table
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Cell-based Modeling/NoData

• The case of NoData.
• Every cell location in a raster has a value
  assigned to it. Where we have no information we
  assign an arbitrary value or NoData.
• Computation of an expression with NoData.
• Return NoData for the location no matter what.
• Ignore NoData and compute with available values.

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Cell-based Modeling/NoData
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Cell-based Modeling/NoData

• Local function output will be NoData.
• Focal function default is to compute with
  remaining values. NoData override.
• Zonal function default is to compute with
  remaining values. NoData override.

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Cell-based Modeling/NoData

• Euclidean distance NoData is ignored except for
  source cells, but output raster will contain
  NoData.
• Weighted (cost) surfaces NoData is a barrier to
  computation and NoData will be returned. Must
  have valid values for source cells.

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Application Functions

• Density creates a normalized surface.
• Surface generation interpolates a continuous
  surface.
• Surface analysis manipulates surface data, e.g.,
  DEM to produce new data layers.

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Application Functions

• Hydrologic analysis surface shape/water flow.
• Geometric transformation to match a coordinate
  system.
• Generalization to smooth noisy data.
• Resolution changes to make one raster match
  another.