Download - Map overlay as modeling of spatial phenomena
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Map overlay as
modeling of spatial
phenomena
Kirsi Virrantaus
GIS-E1060
Spatial Analytics
10.11.2020
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Map overlay
spatiaalisten
ilmiöiden mallina
Kirsi Virrantaus
GIS-E1060
Spatial Analytics
10.11.2020
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Contents
• 1. What is Map overlay
• 2. Map overlay variations
• 3. Uncertainty in Map overlay
– Map overlay. Text Book Ch 10 (O´Sullivan & Unwin)
• Case study: Cross country mobility analysis
– Horttanainen,P., &Virrantaus,K., Uncertainty evaluation of military terrain
analysis results by simulation and visualization
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Sisältö
• 1. Mitä on Map overlay?
• 2. Map overlayn variaatiot
• 3. Epävarmuus map overlayssa
– Map overlay. Kirjan luku 10 (O´Sullivan & Unwin)
• Case: Maaston kulkukelpoisuusanalyysi.
– Horttanainen,P., &Virrantaus,K., Uncertainty evaluation of military
terrain analysis results by simulation and visualization
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Learning goals
• You can describe the basic forms of map overlay model
• You understand that map overlay is modeling and not a
straightforward calculation
• You understand the phenomenon of uncertainty in map overlay
result
• You have ”a vague idea” about how to use analytical and stochastic
simulation approaches in uncertainty estimation
• You are better prepared for using map ovelray in your problem
solving
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1. What is Map Overlay ?
• first formalized by McHarg (1969)
• the idea is older: ”historical background” – map transparencies on the top of each others, analysis on the basis of several map layers
• ”overlay procedure creates a new map data layer as a function of two or more source data layers”
• can be seen as multicriteria decision making problem(Malczewski, 1999)
• can be performed to any geometrical data type that fill the studyspace and make a field (be not confused at the table 10.1 in thebook)
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1.Mitä on Map Overlay ?
(päällekkäisanalyysi)
• ensimmäinen eksakti määrittely jo 1969 (McHarg)
• perusidea ikivanha: ”historiallinen tausta” – skissipaperillepiirretään kartalta merkittäviä asioita, toinen skissipaperi toisen päälle, analysoidaan aluetta useiden karttojen perusteella
• ”päällekkäisanalyysi” tuottaa uuden karttatason useiden lähtökarttatasojen perusteella”
• vrt. monikriteerisen päätöksentekoon (Malczewski, 1999)
• voidaan toteuttaa kaikille geometrisille datatyypeille, jotka peittävät koko kohdealueen ja näin muodostavat kentän (älä hämäänny kirjan taulukosta 10.1)
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Typically map overlay is understood as so-called local operation, that
means operations per pixel.
Local operations can, of course, be also considered as neighbourhood
operations in which the focus is in the center pixel but the neighbourhood is
taken into account somehow. For example when spatial autocorrelation in
modeled. (Fig. from Heuvelink, 1998)
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Basic map overlay with binary maps
• ”sieve mapping” – the term used by the authors of the textbook
• basic form based on binary logic, Boolean logic
– suitability to some use is analysed by logical reasoning in which severaldata layers give (binary) values to each locations and the reasoning is based on the logics based on these values
• the logic of the analysis (criteria) often collected by the experts(knowledge driven)
• typically implemented as raster operation, possible (but morecomplicated) to compute also for vector data objects
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Perus map overlay binäärisillä
karttatasoilla
• kirjan kirjoittajat käyttävät termiä ”sieve mapping” (sieve = siivilä)
• perusmuoto perustuu binäärilogiikkaan, Boolen logiikka – onko vai eikö ole jotain?
– analysoidaan esim. alueen soveltuvuutta johonkin käyttöön, alue saa ominaisuuksia karttatasoilta, jotka antavat (binäärisen) arvon jokaiselle lokaatiolle; tulos perustuu logiikkaan näiden perusteella
• overlayn sisältö perustuu usein asiantuntijoiden kokemukseen ja kriteereihin (tietämyspohjainen)
• tyypillisesti rasterioperaatio, mahdollista (mutta monimutkaisempaa) laskea vektoriaineistolle – slivers = merkityksettömän pienet leikkausalueet
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Problems with map overlay in general
• input data
– are often in different coordinate systems
– are originally often in different scales
– (scanned) maps have often been generalized and objects may take more space than in reality (roads)
– data has often been interpolated (DEMs)
• if the uncertainty of the data sets is not known then the results are of no value
– if serious decisions are made on the basis of results the knowledge about the reliability is vital
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Map overlayn yleisiä ongelmia
• lähtödata on usein
– eri koordinaattijärjestelmissä
– eri mittakaavoissa
– yleistettyä dataa (skannatut kartat), tietyt kohteet on kuvattuspatiaalisesti suurempina kuin ne todellisuudessa ovat (esim. tiet)
– interpoloitua dataa (esim. korkeusmalli)
• jos lähtödatan epävarmuutta ei tunneta ei tuloksilla ole juuriarvoa
– erityisesti, jos tulosten perusteella tehdään vakavia päätöksiä
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Weaknesses of simple Boolean Overlay
• it is assumed that source data are Boolean
– the two-valued (Y/N) logic in sieve mapping creates spatial discontinuities that do not reflect the natural situation
• Example: if 30 degrees is used as a threshold, then 29 degrees slope is not risky for landslide but 31 degrees slope is
• it is assumed that
– any interval or ratio scale attributes are known without significant measurement error
– any categorical attribute data are known exactly without uncertainty
– the boundaries of discrete objects are certain/crisp (the problem is that many boundaries are imprecise)
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Yksinkertaisen map overlayn
heikkouksia• oletetaan että lähtötiedoissa kaikki on binääristä
– kaksiarvoinen (K/E) logiikka luo epäluonnollisiaepäjatkuvuuskohtia
• esimerkiksi kun käytetään 30 astetta kynnysarvona, jonkaalapuolella esim. 29 astetta maalaji ei ole altis vyörymälle, mutta yläpuolella, esim. 31 astetta on
• oletetaan, että
• kaikki välimatka- ja suhdeasteikolla mitatut ominaisuudetovat virheettömiä
• kaikki luokkamuuttujien arvot tunnetaan oikein, ilmanepävarmuutta
• kaikkien kohteiden rajat ovat täsmällisiä (ongelmana on, että useiden ilmiöiden rajatviivat ovat epätäsmällisiä)
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It should be remembered that: using
map overlay = modeling
• map overlay must always be well designed– which are the relevant data for the problem ?
– how the various data layers are weighted ?
– how the various operations work on data ?
– how the decision rules are defined ?
• the entire decision must be well modeled and understood
• ”clear understanding instead of fancy computations”
(Clemen)
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On muistettava, että map overlayn
käyttö = mallintamista
• päällekkäisanalyysi on suunniteltava hyvin
– mikä on ongelman kannalta relevantti data?
– kuinka eri datatyypit (tasot) painotetaan?
– miten eri operaatiot vaikuttavat ?
– kuinka päätössäännöt määritetään ?
• koko päätöksenteko tulee mallintaa ja ymmärtää
• “clear understanding instead of fancy computations”
(Clemen)
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Map overlay is easily implemented by using
Map Algebra
Map overlayn voi toteuttaa helposti kartta-
algebralla
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Map Algebra (Tomlin, 1990)
• map algebra is quite simple tool as such
• map algebra gives a tool for implementing map overlays
• In the exercises you will use Raster calculator of ArcMap, it offersthe possibility to easily implement raster operations
• different map overlay functions in Local operations
• for example
– LocalProduct
– LocalDifference
– LocalSum
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Kartta-algebra (Tomlin, 1990)
• kartta-algebra on sellaisenaan varsin yksinkertainen työkalu, joka mahdollistaa map overlayn toteutuksen
• Harjoituksissa käytetään ArcMapin Raster calculator –käyttöliittymää, jolla voi helposti toteuttaa erilaisia rasterianalyysejä
• eri overlay -mahdollisuuksia Local operaatioilla
• esimerkkejä
– LocalProduct
– LocalDifference
– LocalSum
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Map overlay definitions given by
Malczewski (1999)
• overlay operation can be based on arithmetic, algebraic, logical,
stochastic, or fuzzy operations
– addition, subtraction, multiplication, division
– average, power, order, minimum, maximum
– intersection, logical AND; union, logical OR; complement, logical
NOT
– probabilistic and fuzzy definitions for intersection, union
and complement
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Malczewskin määrittelemä map overlay
(1999)
• päällekkäisanalyysi voi perustua aritmeettisiin, algebrallisiin,
loogisiin, stokastisiin tai sumeisiin operaatioihin
– yhteenlasku, vähennys, kerto, jako
– keskiarvo, potenssi, järjestys, minimi, maksimi
– leikkaus, looginen AND; unioni, loginen OR, komplementti,
looginen NOT
– todennäköisyyteen ja sumeuteen perustuvat leikkauksen,
unionin, komplementin määritelmät
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2. Towards a generic model
• O´Sullivan and Unwin propose a general model for map overlay
based on the concept of :
– favorability function
– map overlay evaluates the favorability of the subareas for
some activity
– can be evaluated by using a simple mathematical function at
each location
• explained in the text book on pages 304…311
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2. Yleinen map overlay:n malli
• O´Sullivan ja Unwin esittävät yleisen,
– ns. edullisuus/suotuisuusfunktioon perustuvan mallin
– Boole-tyyppinen overlay arvioi alueen osa-alueiden
soveltuvuutta/suotuisuutta tiettyyn tarkoitukseen
– voidaan kuvata yksinkertaisella matemaattisella funktiolla,
jokaisessa lokaatiossa
• kuvattu kirjassa ss. 304…311
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Simple (Boolean) form: Favorability function
• can be written
m
F(s) = XM (s)
M=1
-F(s) = favorability, for example cross country mobility, get values 0 or 1 in each location; s refers to location
-m source data layers, all have equal importance
-X(s) is the source data value in pixel s, value 0 or 1
-pi indicates the multiplication; thus the result is also binary
-in Map Algebra: Local Product
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Yksinkertainen binäärinen muoto:
Edullisuusfunktio
• voidaan kirjoittaa yksinkertaiseen muotoon
F(s) = XM (s)
M=1
-F(s) = edullisuus/suotuisuus, esim. kulkukelpoisuus
-arvioidaan binääriarvoilla 0 tai 1 jokaisessa lokaatiossa
-m kappaletta lähtötietokarttatasoja X, kaikki samanarvoisia
-X(s) lähtötiedon arvo pikselissä s, saa arvon 0 tai 1
-pii tarkoittaa kertolaskua
-analyysin tulos on siis 1 tai 0
-kartta-algebra: Local product
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Improvements to the basic model
-the favourability function can get value in more graduated scale than
binary, for example ordinal (low-medium-high) or even ratio
-criteria can be coded on the scales mentioned
-criteria can be weighted according to the relative importance
-criteria can be weighted according to the knowledge of experts,
values
-instead of multiplication some other function, for example adding
the scores
-Boolean overlay is a special case of the general function
F= f(w1X1,, …,wmXm)
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Perusmallin parannuksia
-tekijät voidaan ilmaista järjestysasteikolla (matala, keskitaso, korkea) tai suhdeasteikolla; jatkuva asteikko 0…1
-antamalla kriteereihin perustuvia sääntöjä
-kriteereitä voidaan painottaa
-kriteereihin voidaan liittää tietämyspohjaista painotusta, asiantuntijoiden arvoja
-kertolaskun sijaan voidaan myös laskea yhteen
-Boolen overlay on erikoistapaus yleisestä mallista
F= f(w1X1,, …,wmXm)
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Indexed overlay
• Malczewski calls this as weighted linear combination/simpleadditive weighting
• the use of single metric in ordinal scale
– like in the cross-country mobility 1…7
• each layer can be weighted according to their importance
• summing up, normalization; the result get also values 1…M
• multiplication has been changed to to adding
• maybe the most typical way of using map overlay in practice
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Indeksoitu overlay
• Malczewski kutsuu tätä painotetuksi lineaariseksi kombinaatioksi/yksinkertaiseksi lisääväksi painotukseksi
• käytetään kaikilla tasoilla samaa järjestysasteikkoa 0…M
– kuten kulkukelpoisuusanalyysissä 1…7
• voidaan painottaa jokaista tasoa niiden keskinäisen merkityksensuhteessa
• summataan yhteen, normalisoidaan, tulos myös asteikolla 1…M
• kertolasku on vaihdettu yhteenlaskuun
• ehkä yleisin tapa käyttää map overay-analyysiä käytännössä
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Modeling dependent variables
in map overlay, WOF
• WOF = the term ”weights of evidence”
• The method is based on the use of conditional probability
– the conditional probability of A, when we know that B already
occurred P(A:B) and and that A is dependent on B
– B either increases or decreases the probability of A
– compare to the joint probability of independent events, in which
the probabilities of events do not effect on each others, they are
independent
• Two flips of coins are independent events
P(HH) = P(H) x P(H) = 0.5 x 0.5 = 0.25
• But for example raining today and raining yesterday are not totally
independent
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Toisistaan riippuvien asioiden mallinnus map
overlayssä, WOF
• WOF = ”Weights of evidence” (kirjan kirjoittajien nimitys)
• menetelmä perustuu ehdollisen todennäköisyyden käyttöön
– A:n ehdollinen todennäköisyys, kun tiedetään, että B on jo tapahtunut P(A:B)
– B lisää tai vähentää A:n todennäköisyyttä
– vrt. toisistaan riippumattomien tapahtuminen yhdistetty todennäköisyys, jossa tapahtumien todennäköisyydet eivät vaikuta toisiinsa
• Kaksi kolikon heittoa ovat riippumattomia toisistaanP(HH) = P(H) x P(H) = 0.5 x 0.5 = 0.25
• Mutta esimerkiksi ”sataako tänään” jos ”eilen satoi”, eivät ole täysin riippumattomia
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Example
• Example: Probability that is rains today when we know that it
rained yesterday
– In most climates it is probable that it also rains tomorrow if it
rains today (called also autocorrelation)
– compare to the spatial autocorrelation !
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Esimerkki
• Esimerkki: Todennäköisyys, että sataa huomenna, kun tiedetään,
että tänään satoi
– useimmissa ilmastoissa on todennäköisempää, että jos tänään
sataa niin myös huomenna sataa
– vrt. spatiaaliseen autokorrelaatioon, joka onkin omaksuttu
aikasarjoista !
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Bayes conditional probability
• when we know that the other event has occured
• it is denoted
P(A:B); the probability of A, given B
-is not the same than P(AB), because we know that B already
occurred and it either reduces or increases the change of A;
gives evidence to the change of A
In case when the events are dependent
P(A:B) = P(A) x (P(B:A)/P(B)) (Bayes)
-last term = weight of evidence, 1…0, either increases or reduces
the probability of A
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Ehdollinen todennäköisyys
• kun tiedetään, että toinen tapahtuma on jo tapahtunut
• merkitään
P(A:B); tarkoittaa A:n todennäköisyys, kun tiedetään, että B on jo tapahtunut
-ei ole sama kuin P(AB), koska kun tiedetään, että B on jo tapahtunut, sillä on vaikutuksensa siihen mitä A on
P(A:B) = P(A) x (P(B:A)/P(B))
-jälkimmäinen termi , 0…1, joko vahvistaa tai vähentää A:n tapahtumista, jos suhde on yli 1, B:n esiiintyminen vahvistaa, jos alle, se pienentää A:n todennäköisyyttä
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Simple example on Bayes
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Weight of evidence –probability based
overlay
• Bayesian approach to map overlay
– the conditional probability of event A given that the otherevent B is known to be occurred
– the fact that B already occurred provides additional evidenceto the probability of A
• applying Bayes to map overlay means that the weight of evidenceis taken into account in the reasoning of the result
• In raster map case the probabilities are calculated in each pixel
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Todennäköisyyksiin perustuva overlay,
WOE
• Bayesiläinen lähestymistapa map overlayn käyttöön
– ehdollinen todennäköisyys: A:n ehdollinen todennäköisyys, kun tiedetään että toinen tapahtuma B on tapahtunut
– tosiasia, että B on jo tapahtunut vaikuttaa A:n todennäköisyyteen
• Bayes map overlayssa tarkoittaa sitä, että otetaan weight of evidence huomioon tulosta laskettaessa
• Rastertapauksessa todennäköisyydet lasketaan jokaisessa pikselissä
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Landslide probabilities in map overlay
– in a 10 000 sqkm region we have identified 100 landslides; we define as the baselineprobability of a land slide event in a sqkm area ; P(landslide) = 0.01 (priorprobability)
– 75 of slides occurred in areas with steeper slope than 30 degrees thus we can say thatthe probability of that the landslide that happened is in a steep slope area (priorprobability)
(P(slope>30 :landslide)=0.75
– we know that 1000 skm of the entire area is steeper than 30 degrees; the probability of being steep in the area is
P(slope>30 degrees) = 0.1
– the slope increases clearly the probability of having a land slide and can be used in the conditional probability calculation as the weight of evidence
– in map overlay we have landslide layer and slope layer and the probability of getting a landslide when there is a steep slope is calculated by the formula below
P(landslide:slope>30) = P(landslide) P(slope>30 :landslide)/P(slope>30) (posterior probability)
=0.075 = 0.01(0.75/0.1) , see page 308
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Maanvyörymämahdollisuuden analyysi
– koko 10 000 neliökm:n alueella on tapahtunut 100 vyörymää, tästä päätellään, että maanvyörymän todennäköisyys neliökilometrin alueella on 100/10 000 = 0,01
P(landslide) = 0,01
– tiedetään, että 75% (75 kpl) maanvyörymistä on tapahtunut 10% alueella (1000 neliökm), joten päätellään, että todennäköisyys, että tapahtunut maanvyörymä on jyrkän rinteen alueella on
P(slope>30 :landslide) = 0.75 ja myös P(slope>30 )=0.1
– nyt halutaan ennustaa maanvyörymän todennäköisyys kun alueesta tiedetään, että sen kaltevuus on yli 30 astetta; sovelletaan ehdollista todennäköisyyttä ja map overlayta
– jaetaan alue neliökilometrin pikseleihin ja otetaan kaltevuus jo tapahtuneeksi tekijäksi, jolloin se vahvistaa tietyillä alueilla maanvyörymätodennäköisyyttä
– Sovelletaan weights of evidence kaavaaP(landslide:slope>30) = P(landslide) P(slope>3:landslide)/P(slope>30)
=0.075 = 0.01(0.75/0.1), kirjassa sivulla 308
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Use of regression analysis
• if there is available input and output data the model can calibratedby using regression model
• the weighted linear combination model, added intercept constantand error term
• problems are caused by categorical variables, however also themodel can be formulated to fit them
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Regressioanalyysin käyttö
• jos on käytössä aineistoa sekä input että output datasta, voidaan regressiomalli kalibroida PNS-menetelmää käyttäen
• lähtökohtana painotettu lineaarinen malli, lisättynä vakiolla ja virhetermillä
• ongelmana luokkamuuttujadata, joskin voidaan kehittää myös siihen sopivia menetelmiä
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3. Generic map overlay assumptions –
data is 100% true
• When map overlay is used by a GIS software, it is
typical that all data is assumed to be 100% correct
• However this is not always the case
• If the question is about a serious modeling task, also the
reliability of the results must be considered
• There are two different problem types:
– Pixel value is uncertain “inside” the polygon
– Boundaries of the polygon are “vague”, the boundary is
imprecise (epätäsmällinen)
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What if the classification of the polygons
is not 100% certain?
Jos alueiden luokittelu ei olekaan 100%
luotettava?
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Uncertain value of the pixels –
attribute value or class
• In map overlay analysis operations are performed per
pixel and the result is based on the pixel attribute value
or class
• Almost always the pixel value/class is not 100% certain
and thus also the result contains uncertainty
• A method for estimating the uncertainty of the result is
required
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Calculating uncertainty of map overlay
result (Heuvelink, 1998)
• There are two approaches to uncertainty calculation of
map overlay analysis, error propagation
• Input data is the uncertainty probability distribution of
each data layer
• Analytical approach
– The calculation is based on mathematical error propagation
– Leads often to massive computations
• Stochastic simulation approach
– Instead of calculations based on probabilities Monte Carlo
simulation can be used
– The simulation means that the result is calculated repeatedly
with the input values that are randomly sampled from the joint
probabilities of the layers
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What if the boundaries are not crisp?
Jos alueiden rajat eivät ole täsmällisiä?
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Imprecise boundaries
• Quite often the boundaries of the polygons on the layers
are not crisp
• So-called vague polygons
• Pixels on the boundary can belong in two classes
• Fuzzy models can be used for the polygons and map
overlay operations can also be fuzzy (Malczewski)
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Polygons and grid
Most red cells are red
but some of them are
half grey or half green
How we can deal with
these cells in map
overlay ?
Polygons are
modeled with fuzzy
boundaries; pixels on
the boundary belong
either to green, red or
grey according to the
fuzzy rules
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Case: Terrain mobility analysis
Maaston kulkukelpoisuusanalyysi
Kirsi Virrantaus
GIS-E1060
Spatial Analytics
10.11.2020
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1. The problem: Reliability of the
Cross-country mobility
• Cross-country analysis model
– developed at the Finnish Defence Forces/Engineering School
• Problem of the analysis: How difficult it is to advance in the terrain ?
• Result of the analysis: A map showing 7 classes of mobility by 7 colours (1=no-go…7=go; blue=water/built area; not in theanalysis)
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Solution: indexed map overlay
• Cross country mobility analysis based on :
– soil type (quarternary deposit map)
– elevation model
– amount of vegetation
– thickness of snow
– depth of frost
• Model is map overlay type
• All layers are of grid structure, equal pixel size, equal orientation
• Model type is indexed overlay
– layers get weights according to the experts´ knowledge
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20Q2D420Q2D4
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2. Our research goals
• 1) to analyse the reliability of the previous result map:
– how uncertain the result map is in a specified pixel location?
– what is the effect of the uncertainties of different source data types to the uncertainty of results in a specified pixel location?
• 2) to present the results in a way
– which can be used and interpreted by the users in the decisionmaking - together with topographic maps
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3. Soil map uncertainty
• in this presentation the uncertainty model of soil map is dealt with, because
– soil class is the primary variable in the analysis
– other data sets: snow, frost, vegetation, slope
• soil map is an interesting data set
– it is categorical and imprecise data
– it is manually produced and no metadata (no quality data) is available on the soil maps
• quality information must be collected afterwards
• In this case information on quality was collected from geologists –knowledge based information
• The data was modified into a misclassification matrix (väärinluokittelumatriisi)
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Use of misclassification matrix
information• Misclassification matrix tells the total Percentage of Correctly
Classified (PCC)
• It also gives you the classification uncertainty per soil type class as a
percentage of correclty classified
• Misclassification matrix gives also some percentage information
about wrong classification, to which classes the wrong classification
brings pixels
• This information can be presented graphically as a histogram and can
be used as an estimate of a probability distribution of
classification per soil type
• This distribution can be used in stochastic simulation for creating
errors of classification per soil type
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4. Monte Carlo simulation
• Monte Carlo simulation was applied for data
– all source data sets were simulated by using the uncertaintyinformation available
– the previously mentioned distributions were used for soil data
• analysis was computed by simulated data
• in evaluation of the results
– the simulated realizations (the mean of them) were used as “real data”
– the original data was the estimate
– the uncertainty of the estimate was evaluated
• in our earlier research we had no model of spatial dependency, in this project it was added
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What happens in spatial autocorrelation
is not taken into account?
Mitä simuloinnissa seuraa jos
spatiaalista autokorrelaatiota ei
huomioida?
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20Q2D4 21N4A1
0 1 2 3 4 5 6
20Q2D4 21N4A1
0 1 2 3 4 5 60 1 2 3 4 5 600 11 22 33 44 55 66
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5. Spatial autoregressive process(according to Goodchild et al., -92)
– in order to add spatial dependency and to get more realistic results
– the 4-neighbourhood is taken into account by giving equal weight for all4 neighbours
– spatially dependent random field for the error in classification per soilclass type is created
– by solving X in X=ρWX + ε ;
• based on spatial correlation parameter ρ and probabilities from the misclassification matrix; W is the adjacency matrix of pixels of equal soil type; ε is N-random vector with standard normal distribution
– 21 different values were used for the parameter ρ, the spatialdependency level, 100 simulations
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Spatially dependent random fields with varying parameter values
By using information about soil type arrangement (W) and correlation parameter value
spatially dependent random fields of uncertainty could be created per each soil type.
These random fields were then used in selecting the soil type in simulation together with the
misclassification matrix information.
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6. Evaluation methods
• misclassification matrices only give the uncertainties for each soil
class, so by using the matrix and PCC values we can only compare
two test areas but not evaluate the uncertainty in each pixel – both in
case of source data and results
• analysis by a simple regression model was made but the cross-
country mobility model seemed to be too complicated to be analysed
statistically
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7. Visualization of the evaluation results
• visual analysis seemed to be the most powerful – and only - tool in
analysing and interpreting the spatially dependent results
– for the users and
– especially by the users themselves
• in the following two examples that show the possibilities
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Example 1: Visual analysis of the
uncertainty of soil types
– in area 1 the yellow silt and pink sandy heath have high uncertainty (in
the MM they have low % for correctly classified)
– in the upper right corner of the area 2 there is a marsh polygon with
very low uncertainty (in the MM marsh has 100% correct classification)
– the darker the value the higher the uncertainty
– the effect of increasing ρ can be seen
– the user can easily compare the source map and the uncertainty map
layer associated to it
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Uncertainty of classification of soil maps
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Example 2: Visual interpretation of the
results
• on the left side the cross-country analysis result– 4 lower rows give results in different seasons for test area 2
• in the other columns the uncertainty of the cross-country
analysis results is shown– by using increasing spatial dependency value ρ
– the darker the value the higher the uncertainty
• the user can easily find the spatially changing
uncertainty by comparing the maps
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Uncertainty of the analysis results
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8. Conclusions: Visualizations are
perfect tools • the visualisations of uncertainties of source data sets and the
original result map can be compared in specific locations
• the visualizations of the uncertainty of the result map can be
compared with the original result map in specific locations
• we can also generate maps, which show the risk of having wrong
class in the results (for example + - 1 class) in a specified pixel !
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Conclusions: Spatial uncertainty model
is needed • visual analysis can not be made without a spatially dependent
uncertainty model
• the quality of imprecise geographic data (like soil map in this case) can not be described by traditional quality measures
• each imprecise data set should be provided by a spatiallydependent uncertainty layer which describes in a very user-friendlyway some features of the quality (like spatial and thematic accuracyin our case)
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9. Future: Developing the simple model
• the parameter ρ - different values for each soil type can maybe
found and added to the model
• the membership vector of fuzzy soil model instead of probability
vector from the misclassification matrix in simulation gives more
local uncertainty information
• kriging together with fuzzy model in order to get better model
for boundary areas
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Literature
• O´Sullivan&Unwin, Geographical information analysis, Chapter 10
• Heuvelink, G., Error propagation in environmental modeling, 1998.
pp 33…42.
• Horttanainen,P., Virrantaus,K., Uncertainty evaluation by simulation
and visualization, Geoinformatics 2004, Gävle, 7.-9.6.2004.