Map overlay as

modeling of spatial

phenomena

Kirsi Virrantaus

GIS-E1060

Spatial Analytics

10.11.2020

Map overlay

spatiaalisten

ilmiöiden mallina

Kirsi Virrantaus

GIS-E1060

Spatial Analytics

10.11.2020

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

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

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

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)

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)

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)

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

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

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

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

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)

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)

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)

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)

Map overlay is easily implemented by using

Map Algebra

Map overlayn voi toteuttaa helposti kartta-

algebralla

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

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 !

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 !

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

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

Simple example on Bayes

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

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

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

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

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

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

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)

What if the classification of the polygons

is not 100% certain?

Jos alueiden luokittelu ei olekaan 100%

luotettava?

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

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

What if the boundaries are not crisp?

Jos alueiden rajat eivät ole täsmällisiä?

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)

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

Case: Terrain mobility analysis

Maaston kulkukelpoisuusanalyysi

Kirsi Virrantaus

GIS-E1060

Spatial Analytics

10.11.2020

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)

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

20Q2D420Q2D4

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

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)

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

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

What happens in spatial autocorrelation

is not taken into account?

Mitä simuloinnissa seuraa jos

spatiaalista autokorrelaatiota ei

huomioida?

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

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

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.

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

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

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

Uncertainty of classification of soil maps

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

Uncertainty of the analysis results

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 !

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)

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

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.