gis-e1060 - spatial analytics: map algebra and raster analysis

GIS-E1060 - Spatial Analytics: Map algebra and raster analysisJaakko Madetoja12.11.2020Slides partly adopted from Kirsi Virrantaus & Paula Ahonen-Rainio

Learning goals

In this session you will learn

• To explain what different types of Map algebra operations are

• To list examples where Map algebra can be used

• To explain what watershed, viewshed and cost surface

analysis are

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Grid representation

• Geometry

• Shape of a pixel: usually a square (can be a triangle, a hexagon)

• Square pixel: • 4 neighbors (joint edge)

• 8 neighbors (joint edge or corner)

• Implicit topology

• Joint edge – adjacency (viereisyys)

• Joint edge or corner – connectivity (yhdistävyys)

• Orientation, origin, resolution (size of a pixel/grid cell)

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X

X

Applications with raster data

• Environmental applications with source data from satellite images

• E.g., detecting changes in land use, vegetation

• Elevation model based analyses

• Visibility: e.g. locating telecommunication towers, view from a road in landscape planning, military applications

• Slope (kaltevuus) and aspect (suunta): e.g. watershed (vedenjakaja), catchment areas, risk of avalanche

• Analyses on statistical (grid) data (Statistics Finland)

• Terrain and mobility analyses

• For crisis management and military applications, prediction of animal movement, forestry

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Raster vs. vector

• Environmental applications: Remote sensing produces raster images

• Elevation and visibility: elevation is continuous; difficult to model with vector

• Statistical grids: Sometimes it might be a better idea to use grid as vector type

• Terrain and mobility analyses: For example shortest route analysis with raster allows mobility everywhere; with vector only on roads

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Map algebra (kartta-algebra)

• Developed by Dana Tomlin: “GIS and Cartographic modeling” (ebook)

• Map algebra is a formal language for raster analysis

• Forms the basis of raster operations

• Key concepts:

• Layers: Input1, Input2, …, InputN, Output• Definition of neighborhood, zones• Functions: Min, Max, Boolean, arithmetic,…

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Map algebra

• A set of primitive operations, which allows two or more raster layers to produce a new raster layer using operations

• Operations on one pixel, neighborhood, zone or entire layer

• By combining these, one can define a procedure to perform complex tasks

• A formal language, an open standard

• Forms the basis of raster tools in many GISs

• Spatial analyst –toolbox in ArcGIS

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Map algebra

• Operations on a raster are of four types

• Local operations are determined by the attributes of one cell, usually for many layers

• Focal operations are determined by a cell and its neighbors

• Zonal operations apply to cells within the same zone

• Global operations compute properties of the entire raster layer

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Examples

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Bolstad: GIS Fundamentals

plus 4

neighbourhood

maximum

global

maximum

Local functions

• Input1, Input2, … => Output

• Operations on one pixel at a time, e.g.

• Local Difference

• Local Maximum

• Local Ratio

• Local Sum

• Raster version of map overlay

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Figure by ESRI

Map overlay

• Example of map

overlay analysis made

by using raster data

on the right. In each

pixel the layer value is

considered and the

chosen operation is

then performed.

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Examples

• Operations can also be Boolean:

• On each layer, possible values for each cell are 1 or 0

• E.g., suitability of a region to a certain purpose by logical reasoning: different layers have binary values for each location, the result based on the logics on these values

• Local map algebra example: visualizing contours using DEM:

• Divide all values of pixels by 10, multiply the integer result by 10, subtract this value from the original; color each value according to the following: values 4 and 6, 3 and 7, 2 ja 8 and 1 ja 9 get the same color, 0 is white, 5 is black; one meter contours

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Tomlin: GIS and Cartographic Modeling

Example: Reclassification

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Example: enjoyable (landscape) areas in Espoo

for locals for tourists for landscape experts

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Reclassify land cover based on preferences:

Example: enjoyable (landscape) areas in EspooFinal preference map as a weighted sum: Locals 40%, tourists

30%, experts 30%

See exercise 4.

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Focal functions

• Input1, neighborhood => Output

• Operations on a pixel and its 4 (or 8, or 32, or…) neighboring pixels, e.g.• FocalMaximum• FocalMean• FocalStandardDeviation

• For example,• Smoothing the map layer by FocalAverage; high and low values are smoothed

away (continuous values)• Generalization by filtering out individual pixels that differ from their

surrounding (categorical values)• Mobility simulation by producing a cost surface of mobility

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Examples

• Focal Sum

• Edge detection

• This is actually calculated using a custom mask called high-pass filter:

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Example: Filtering

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Example: Edge detection

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Tomlin: GIS and Cartographic Modeling

Zonal functions

• Input1, zones => Output

• Data is related to some zoning

• For example,

• ZonalSum• ZonalMaximum• ZonalAverage

• Example:

• Calculate the amount of apartments in a block: ZonalSum• Calculate the most common soil type for each land cover area: ZonalMode (or

ZonalMajority in ArcGIS)

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Example: Zonal average

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Example

• Energy self-sufficiency in Otaniemi: how big portion of energy consumption can be gathered using solar panels on top of roofs

• Data: Solar energy data, buildings, energy consumption

• Analysis: ZonalSum to get total energy per building

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Example

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Further raster analysis

• Digital elevation model and its derivates

• Watershed

• Viewshed

• Cost surface analysis

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DEM (digital elevation model) and its derivates• Key characteristics: slope, aspect (kaltevuus ja viettosuunta)

• Slope is usually expressed as angle (0-90) or percentage

• Aspect is the direction

of downslope (0-360)

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Example: Analysing the watershed

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Example: Viewshed

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Example: landscape planning

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(Juanjo Galan, MAR-E1046 GIS in Landscape Planning)

Cost surface

Route on cost surface

• Each cell has determined cost, for example:

- the density of the vegetation

- environmental impacts

- depth of snow

• How to travel from starting point to end point with minimum cost

• Cost distance tools in ArcGIS

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Cost surface

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http://wiki.gis.com

• Cost surface raster in the

background: red is high cost and

green is low cost

• Black line shows the least

expensive route from origin to

destination

An example: Forest fire risk analysis

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(Amakihe, Bloch, Gyinaye, Toivanen;

course project work, 2014)


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Final risk map

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An example: Picking mushrooms

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Final map for finding mushrooms and hot spot analysis after

generalization

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A complex example: Flood in a mine

A flood in a mine:

• Modelling the flood

• Water will fill the lower areasfirst

• Water will reach close by areasearlier than far away areas

• How to escape

• Create a cost surface: the easierfor the water to reach, the higher the cost

• Cheapest route to escape

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(Gupta, Lu, Pajukoski;

course project work, 2013)


How fast the water will reach a given area:

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Escape route using

previous raster as a cost

surface

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Further reading

GIS and Cartographic Modeling by C. Dana Tomlin

• Part II Cartographic modeling capabilities

• E-book available

• Lots of calculation examples

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gis-e1060 - spatial analytics: map algebra and raster analysis

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