methods of data analysis and spatial modellingkjuh

8/13/2019 Methods of Data Analysis and Spatial Modellingkjuh

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METHODS OF DATA ANALYSIS AND SPATIAL MODELLING

The major difference betweem eora!hica" information #$#tem# and #$#tem# forca!abi"itie# for tran#formin the oriina" #!atia" data in order to be ab"e to an#wer

!artic%"ar &%erie#' Some tran#formation ca!abi"itie#( #%ch a# tho#e nece##ar$ for data

c"eanin or %!dtin( or for chanin #ca"e# !rojection#( wi"" be common to botheora!hica" information #$#tem# and com!%ter)a##i#ten cartora!h$' The#e

tran#formation method# were di#c%##ed in *ha!ter +' Geora!hica" information #$#tem#(

howe,er( !ro,ide a ,er$ m%ch "arer rane of ana"$#i# ca!abi"itie# that wi"" be ab"e too!erate on the to!o"o$ or #!atia" a#!ect# of the eora!hica" data( on the non)#!atia"

attrib%te# of the#e data( or on non)#!atia" and #!atia" attrib%te# combined' The#e ana"$#i#

ca!abi"itie# wi""( in mo#t eora!hica" information #$#tem#( be !ro,ided in #%ch a wa$

that a %#er can wor- interacti,e"$ in order to !erform the ana"$#e# and #$nthe#e# re&%ired'

Fi%re .'/ !re#ent# a hierarchica" o,er,iew of the main -ind# of ca!abi"itie# that can be

%#ed for data %ti"i0ation and ana"$#i# in eora!hica" information #$#tem#' The#e

ca!abi"itie# rane from #im!"e method# for retrie,in #%b#et# of information from thedataba#e( thro%h %ni,ariate and m%"ti,ariate method# of #tati#tica" ana"$#i# to #!atia"

ana"$#e# %#in neihbo%rhood f%nction# and inter!o"ation method#' 1eca%#einter!o"ation method# and #tati#tica" method# of c"a##if$in data are more com!"e2 than

man$ of the other data ana"$#i# techni&%e# %#ed( the$ are de#cribed in more detai" in

*ha!ter 3 and 4' F%rthermore( a# we #ha"" #ee( #!atia" mode"in method# can be %#ed tocreate an a"mo#t %n"imited rane of ca!abi"itie# for data ana"$#i# b$ #trinin toether

#et# of #im!"e ana"$#i# ca!abi"itie#( or b$ writin #!ecia" #im%"ation !roram#'

The enera" !rob"em of data ana"$#i# i# #tated in Fi' .'5' The %#er ha# a !artic%"ar!rob"em or &%er$' The databa#e contain# information in the form of ma!# that can be

%#ed to an#wer the %#er6# !rob"em' A"" that i# nece##ar$ i# to e#tab"i#h a "in- betweendataba#e and o%t!%t that wi"" !ro,ide that an#wer in the form of a ma!( tab"e#( or fi%re#'The "in- i# an$ f%nction that can be %#ed to con,ert data from one or more in!%t ma!#

into an o%t!%t ma!' Thi# cha!ter i# abo%t how "in-# can be defined and %#ed'


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T7ANSFO7MATIOAN

MAINTENAN*E

Editin

8!datin

8TILI9ATION AND ANALYSIS

to!o"o$

7otation( tran#"ation

Sca"e tran#formation( #tretch

:)D di#!"a$

Area( !erimeter ca"c%"ation

!ro!ertie#

7etrie,a"Loica";mathematica" ana"$#i#

rec"a##ification

To!o"o$

7etrie,a"

O,er"a$ and inter#ection

=reion6ana"$#i#

Neihbo%rhood ana"$#i#

S!readin

Detectin #ha!e( narrowne## etc'

Inter!o"ation

deternini#tic

1)#!"ine#

Thie##en !o"$on#

*onto%r# b$

In,er#e di#tance

>eihtin

#tati#tica"

Trend #%rface#

A%toco,ariance

Ana"$#i#?riin etc'


3/11

Fi' .'/ Schematic o,er,iew of the hierarch$ of data tran#formation o!eration# in

eora!hica" information #$#tem#'

Definition of the database

1efore oin f%rther it i# a i# we"" to define c"ear"$ the nat%re of the eora!hica"databa#e that wi"" !ro,ide the information re&%ired' In mo#t eora!hica" information

#$#tem# it i# a##%med it i# a##%med that the information in the databa#e i# !re#ent in the

form of !oint#( "ine#( and area# and their a##ociated attrib%te#' >hi"e it i# not e##entia"for the %#er to -now whether the #!atia" e2tent# of the data are encoded in a ,ector or a

ra#ter form( certain o!eration# wi"" be ea#ier in the ,ector form( and other# wi"" be ea#ier

form'

Sim!"e data retrie,a"

If the data ha,e been encoded in a ,ector #$#tem %#in an o,er"a$ or "a$er #tr%ct%re @#ee*ha!ter 5( then the data that ha,e been ro%!ed toerther on that "a$er can be ,er$

#im!"$ retrie,ed' For e2am!"e( if a #$#tem a""ow# B+ different "a$er# to be %#ed( and if

major road# ha,e been entered into "a$er /( minor road# on "a$er 5( rai"wa$# on "a$er :(ri,er# on "a$er +( and #o on( it i# tri,ia" to be ab"e to di#!"a$ on"$ major road#( or minor

road# and ri,er# and ri,er#( #im!"$ b$ ca""in %! the a!!ro!riate "a$er#' The#e "a$er

faci"itie# were ,er$ common on the ear"$ *AD)*AM t%rn)-e$ #$#tem# and are dea" for

#it%ation# where there are few different -ind# of ra!hica" e"ement# in the databa#e' Ineora!hica" databa#e the#e method# are hard"$ a!!ro!riate beca%#e of the "are n%mber

of attrib%te# that each e"ement ma$ ha,e' 1i#ide#( the #im!"e "a$er #$#tem re&%ire# that

data be c"a##ified for a !artic%"ar "a$er before in!%t( which ha# to be done man%a""$ thi# i#not fea#ib"e for a "are databa#e'

1oo"ean Loic

The a"ternati,e !roced%re i# to retrie,e data b$ %#in the r%"e# of 1oo"ean "oic to o!erate

on the attrib%te# and #!atia" !ro!ertie#' 1oo"ean a"ebra %i#e# the o!erator# AND( O7(

1oo"ean "oic i# often !ortra$ed ,i#%a""$ in the form of Cenn diaram# @Fi' .':' If #et


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A i# the #et of item# ha,in attrib%te a( and #et 1 i# the #et of item# ha,in attrib%te b(

then the #tatement

A AND 1( A O7 1( A O7 1( A NOT 1(

>i"" ret%rn item# that ha,e attrib%te combination# co,ered b$ the #haded !ortion# of there#!ecti,e Cenn diaram' For e2am!"e( in a databa#e of #oi" ma!!in %nit#( each

ma!!in %nit ma$ ha,e attrib%te# de#cribin te2t%re and !H of the to!#oi"' If #et A i# the

#et of a"" ma!!in %nit# for which the to!#oi" ha# a c"a$ "oam te2t%re( and if #et 1 i# the#et of a"" ma!!in %nit# for which the to! #oi" !H e2ceed# 3'( then "oica" retrie,a"

#tatement# wi"" wor- a# fo""ow#

A AND 1 find# a"" ma!!in %nit that ha,e to!#oi" te2t%re c"a#$ "oam and a !H 3'

combined( A O7 1 find# a"" ma!!in %nit# that ha,e either a to!#oi" te2t%re of c"a$ "oam or a

!H 3'( either #e!arate"$ or in combination(

A O7 1 find# a"" ma!!in %nit# that ha,e either a to!#oi" te2t%re of c"a$ "oam( or a

!H 3'( b%t not in combination with each other' A NOT 1 find# a"" ma!!in %nit# that ha,e a to!#oi" te2t%re of c"a$ "oam in which

the !H i# 3' or "e##'Note that %n"i-e arithmetic o!eration#( 1oo"ean o!eration# are not comm%tati,e' The

re#%"t of A AND 1 O7 * de!end# on the !riorit$ of AND with re#!ect to O7'

Parenthe#e# are %#%a""$ %#ed to indicate c"ear"$ the order of e,a"%ation @Fi' .':' In thee2am!"e( if #et * i# a"" ma!!in %nit# of !oor"$ drained #oi"( then @A AND 1 O7 *

ret%rn a"" ma!!in %nit# with a to!#oi" te2t%re of c"a$ "oam combined with a !H 3' or

a"" !oor"$ drained #oi"' Thi# retrie,a" i# not ,er$ #!ecific' On the other hand( A O7

@1 AND * ret%rn# a"" ma!!in %nit# with the combination of !H 3' and !oor drainaeor tho#e with a to!#oi" te2t%re of c"a$ "oam'

1oo"ean o!eration #ho%"d not be tho%ht of a# bein on"$ a!!"icab"e to the attrib%te# of

the eora!hica" e"ement#( beca%#e the$ can a"#o be a!!"ied to the #!atia" !ro!ertie#' Fore2am!"e( find a"" ma!!in %nit# with c"a$ "oam te2t%re in combination with a !H 3'

that e2ceed . ha in area' More com!"icated #earche# ma$ in,o",e the #ha!e# of area#( the

!ro!ertie# of the bo%ndarie# of area# or the !ro!ertie# of neihbo%rin area#' Fore2am!"e( in -now a"" area# of wood"and borderin %rban area#( or in ,i#%a" c"a##ification

of "and#ca!e to retrie,e a"" o!en area# that ha,e a !artic%"ar #ha!e and are bo%nded b$ a

certain -ind of hederow @cf' 1%itenh%i# et a"' /45'

7ec"a##ification and di#!"a$

Once the eora!hica" data ha,e been retrie,ed( it i# %#%a""$ nece##ar$ to rec"a##if$ themand to redi#!"a$ them #o that the ,i#%a" !re#entation ref"ect# the new data #tr%ct%re a#

!ercei,ed b$ the %#er' >hen the data are !o"$on# in ,ector format( rec"a##ification

!roced%re# m%#t en#%re that when two or more adjacent !o"$on# recei,e the #ame newname( the "ine# between them are di##o",ed and a new !o"$on networ- i# con#tr%cted to

obtain the #tati#tic# of the new ma! and for a c"ean ma! imae @Fi# .'+( .'.'

1oo"ean o!eration# on two or more ma!#


5/11

Cer$ often the %#er wi"" want to e2tract data from two or more ma!# for e2am!"e( he

ma$ want to -now where a i,en -ind of "and %#e occ%r# on a !artic%"ar -ind of #oi"' The

#oi" information wi"" ha,e been encoded in one ma!( the "and)%#e information in another'The c"a##ica" method of #o",in thi# !rob"em i# to "a$ tran#!arent co!ie# of each ma! on a

"iht tab"e and to trace off the corre#!ondin area# @c'f' P"ate# /)5' Thi# i# a time)

con#%min and inacc%rate !roce##( #o one of the fir#t re&%irement# of man$ eora!hica"information #$#tem# ha# been the abi"it$ to inter#ect two !o"%on networ-# #o that

1oo"en "oic can be a!!"ied to the re#%"t' Fi%re .'B #how# the re#%"t# of o,er"a$inon

two #im!"e ma!#( each containin #i2 !o"$on#' In thi# e2am!"e( the re#%"tin networ-contain /. !o"$on#' The n%mber# of !o"$on# on the initia" ma!#( ba%t a"#o on the form

of the bo%ndarie#' The more con,o"%ted the bo%ndarie# on the #o%rce ma!#( the more

deri,ed !o"$on# can be e2!ected'

The !rob"em of how to o,er"a$ two or more !o"$on networ-# occ%!ied the attention# of

com!%ter cartora!her# for man$ $ear#' The major #t%mb"in b"oc- wa# how to dea"

with the ,er$ "are n%mber of #ma"" and #eemin"$ %nim!ortant !o"$on# that re#%"ted

when "ine# on the two ma!# were a"mo#t b%t not &%ite( identica"' The#e =non#en#e6 area#m%#t be fi"tered awa$ or mered with the adjacent "arer "o"$on# in order to i,e a

#ati#factor$ ma! imae of c"ean !o"$on o%t"ine#( a !roced%re that ma$ "ead to "o## ofinformation or to the creation of mi#information' The !rob"em of the error# that can

occ%r when !o"$on# are o,er"aid i# di#c%##ed more f%""$ in *ha!ter B' Another major

!rob"em with !o"$on o,er"a$ in ,ector format wa# the ,er$ hea,$ com!%tin demand#when #earchin for inter#ection# of the bo%ndar$ "ine# on the two ma!#( reconnectin the

"ine# and b%i"din the new !o"$on networ- toether with it a##ociated attrib%te#' The

and i# incor!orated in the ODYSSEY !roram @Laborator$ for *om!%ter Gra!hic#

/4:' Now man$ other commercia" eora!hica" #$#tem# inc"%de !o"$on o,er"a$#oftware'

A enera" a!!roach to ma! o,er"a!

The inter#ection of two or more !o"$on net# b$ o,er"a$ i# a #!ecia" ca#e of m%ch "arer

#et of o!eration# that can be %#ed to ana"$#e area data' In order to enera"i0e it i# %#ef%"to con#tr%ct the fo""owin conce!t%a" mode" of the eora!hica" databa#e'

A reion i# defined a# a #et of "oci #harin a !artic%"ar attrib%te or a certain ,a"%e of a

!artic%"ar attrib%te' The "oci are defined in term# of #et# of and Y coordinate#' The#in!"e# reion i# a !oint( ha,in on"$ one Y coordinate !airJ the mo#t com!"e2 enc"o#e#

man$ "oci' Note that a reion ma$ con#i#t of one or more !o"$on# or ma$ be !erforated

b$ reion# of another -ind @cf' Fi' 5'/ @d'e'

An attrib%te i# a i,en eora!hica" ,ariab"e or !ro!ert$' Attrib%te# can be e2!re##ed on

binar$( nomina"( inter,a"( or ratio #ca"e#' Each attrib%te can be tho%ht of a# definin a

#e!arate o,er"a$'


6/11

An o,er"a$ i# a #et of m%t%a""$ e2c"%#i,e conti%o%# reion# a##ociated with a !artic%"ar

area' Each o,er"a$ i# defined b$ a i,en attrib%te'

Note that thi# mode" ha# a #tr%ct%re that i# ,er$ #imi"ar to that %#ed for ra#ter

re!re#entation# of #!atia" data de#cribed in *harter 5' In fact( the on"$ difference i# thatin the ra#ter databa#e #tr%ct%re #!ace i# nece##ari"$ &%anti0ed into re%"ar( %#%a""$ #&%are

ce""#( wherea# in thi# mode" no &%anti0ation# i# im!"ied' P%t another wa$( the ra#ter

databa#e i# a di#crete a!!ro2imation to the #tr%ct%re !ro!o#ed here'

It i# a"#o a##%med that for e,er$ "oc%# on a ma!( a new attrib%te can be enerated a# a

f%nction of attrib%te# on the o,er"a$# a"read$ !re#ent in the databa#e' So( for e,er$ "oc%#(

with coordinate# ( Y( a ,a"%e of a new attrib%te can be e2!re##ed a#

8 f@A(1(*( ' ' ' @.'/

>here A(1(*( ' ' ' are the ,a"%e# of the attrib%te definin the fir#t( #econd( third ' ' 'o,er"a$( and f i# a f%nction that ha# $et to be defined @Fi' .'3' The idea behind thi#

f%nction i# of co%r#e the #ame a# that behind the ="in-6 that wa# in Fi' .'5'

*"a##e# of tran#formation# !oint#( reion#( and neihbo%rhood#

There are three major c"a##e# of tran#formation that can be %#ed to contro" thetran#formation f%nction# #%e#ted b$ e&n @.'/' The fir#t ro%! of f%nction# o!erate#

on"$ on the ,a"%e# of a"" the attrib%te# re"atin to each "oc%#( @the ,ertica" ,ector# of

attrib%te ,a"%e#' In other word#( the f%nction or o!eration# i# inde!endent of the effect#

of the ,a"%e# of the attrib%te# at neihbo%rin "oci( and of enera" !ro!ertie# of thereion# or #et# to which the "oci ma$ a"#o be"on @Fi' .'4@a'

The #im!"e#t of the#e !%re"$ =!oint6 tran#formation# are the mathematica" o!eration# ofaddition( #%b#traction( m%"ti!"ication( di,i#ion( e2!onentiation( ta-in "oarithm#( and

e,a"%atin trionometrica" f%nction#' K%#t a# #im!"e are the findin of e2treme# or

a,erae# or a!!"$in 1oo"ean "oic' The ,a"%e of the attrib%te on the new o,er"a$ co%"dbe a c"a## ,a"%e or name( or it co%"d be the re#%"t obtained from a !rinci!a" com!onent

ana"$#i# or a c"%#terin a"orithm' The f%nction for com!%tin the ,a"%e on the new

o,er"a$ co%"d a"#o be a #im%"ation !roram de#ined to com!%te a #in"e o%t!%t ,a"%e a#

a f%nction of #e,era" in!%t ,a"%e( that in thi# mode" of eora!hica" data wo%"d beobtained from the other o,er"a$#' Tab"e .'5@a "i#t# a n%mber of the more o,er"a$ %#ed

=!oint6 f%nction#' Note that the inter#ection of two !o"$on networ-# de#ribed abo,e i#

e##entia""$ a #im!"e "oica" o!eration for combinin two o,er"a$#'

Mo#t eora!hica" information #$#tem#( !artic%"ar"$ commercia" #$#tem#( inc"%de

method# for !erformin #ome =!oint6 o!eration#( e,en if the#e are %#%a""$ main"$ "imitedto 1oo"ean "oic and rec"a##ification' The ,a"%e of the#e method# in #!atia" ana"$#i# id

often more the re#%"t of #!atia" a%toco,ariance @"oci c"o#e toether are more "i-e"$ to ha,e

#imi"ar ,a"%e than "oci that far a!art than of an$ de"iberate attem!t to mode" #!atia"

interaction#'


7/11

The #econd c"a## of f%nction# re"ate# to !ro!ertie# of the reion or #et to which a i,en

"oc%# be"on#' The#e !ro!ertie# miht be tho#e of "enth( area( !erimeter or #ha!e( orthe$ miht re"ate to the n%mber of "oci ha,in a certain ,a"%e on one o,er"a$ that occ%r

within the area defined b$ a reion on another' For e2am!"e( one ma$ wi#h to !rod%ce a

new ma! in which admini#trati,e area# are coded accordin to the n%mber of #choo"#within their bo%ndarie# from an o,er"a$ of admini#trati,e area# and #choo" "ocation#'

A"ternati,e"$( one ma$ wi#h to ca"c%"ate a new ,a"%e for a "oc%# accordin to the

!ro!ertie# of the bo%ndar$ of the reion in which the !oint "ie#' An e2am!"e from"and#ca!e ma!!in wa# &%oted abo,e' The#e =reion6 o!eration# are #%mmari0ed in

Tab"e .'5@b( #ome are i""%#trated in Fi' .'4 @b and c;

The third c"a## of f%nction re"ate# the !oint to it# neihbo%r#' The#e are a"" f%nction# thate2!"icit"$ ma-e %#e of #ome -ind of #!atia" a##ociation# in order to determine the ,a"%e

for the "oc%# on the new o,er"a$' The#e ma$ inc"%de whether or not neihbo%rin !oint#

ha,e the #ame ,a"%e a# the !oint in &%e#tion( or the di#tance on a i,en o,er"a$ from the

!oint in &%e#tion to a !oint ha,in a different ,a"%e' Neihbo%rhood f%nction# a"#oinc"%de the ca"c%"ation of a ,a"%e re!re#entin a weihted a,erae( ma2im%m ,a"%e(

minim%m ,a"%e( mea#%re of di,er#it$ or rate of chane of a !art of the #tati#tica" #%rfacere!re#ented b$ the o,er"a$ in an area aro%nd the !oint( and #o on' Some of the#e

f%nction( #%ch a# com!%tation of #"o!e( a#!ect( and ride and ,a""e$ "ine# were de#cribed

in cha!ter :' Other#( #%ch a# method# of #!atia" inter!o"ation( wi"" be di#c%##ed incha!ter 4' Neihbo%rhood o!eration# are #%mmari0ed in Tab"e .'5@c and #ome are

i""%#trated in Fi' .'4 @d''h'

A fo%rth c"a## of o!eration# in eora!hica" information ana"$#i# concern# ,ariation# in#!atia" !attern# o,er time' Mo#t eora!hica" information #$#tem# in c%rrent %#e treat the

databa#e a# a #tatic mode" of the "and#ca!e' A i,en ana"$#i# !roceed# in one direction

from e2i#tin #oi" ma!#' 1%t there are man$ #it%ation# where the "and#ca!e chane#ra!id"$ o,er time a# a re#%"t of !roce##e# of ero#ion( #a"ini0ation( defore#tation( %rban

rowth( "owerin or rai#in the ro%ndwater "e,e"( and #o on' In the#e #it%ation( ana"$#e#

ba#ed on a databa#e that ha# been b%i"t %! with a !hi"o#o!h$ of #emi)!ermanence cannotho!e to !rod%ce re"e,ant an#wer#' Gi,en that the ,ariation of a !roce## o,er time i#

%nder#tood( howe,er( there i# no rea#on wh$ d$namic e"ement# #ho%"d not be

incor!orated into the ana"$#i# of eora!hica" data'

*artora!hic mode"in %#in nat%ra" "an%ae command#

The %#er of a eora!hica" information #$#tem# i# not nece##ari"$ intere#ted in -nowine2act"$ how the ,ario%# !oint( reion or neihbo%rhood o!eration# are !rorammed( nor

in the e2act method# %#ed for orani0in the data in the com!%ter' He or #he i# m%ch

more "i-e"$ to ha,e a ood enera" -now"ede of arithmetica" and "oica" !roce##e# andwo%"d !refer to %#e the#e e2i#tin #-i""# for the eora!hica" ana"$#e# that m%#t be done'

Idea""$( the %#er wo%"d "i-e to be ab"e to e2!re## hi# tho%ht# in a "an%ae that i# a"#o

,er$ #imi"ar to that %#ed in hi# dai"$ wor-' The reat !o!%"arit$ of a!read#heet !roram#(

on b%#ine## microcom!%ter# for e2am!"e( i# a #tri-in e2am!"e of how %#er# re#!ond to


8/11

com!%ter #$#tem# that are de#ined #!ecifica""$ to co!e with their need# in term# the$ can

ea#i"$ %nder#tand' So( if a !"anner want# to create a b$ffer 0one aro%nd a #et of road( he

dae# not rea""$ want to ha,e to diiti0e the b%ffer 0one interacti,e"$ aro%nd a"" the road#he ha# di#!"a$ed on a #creen( b%t

Lin-in command #e&%ence# into cartora!hic mode"#

1$ "in-in the =!rimiti,e6 !oint( reion( and neihbo%rhood command# toether in

#e&%ence( #o that the o%t!%t o,er"a$ from one command i# the in!%t to the ne2t( Tom"in(Steinit0( and co""ea%e# ha,e #hown that it i# !o##ib"e to create an %n"imited n%mber of

tai"or)made ma!)!roce##in ca!abi"itie# that can be %#ed to tac-"e man$ ana"$tica"

!rob"em# in eora!hica" information !roce##in' The$ ca"" the#e command #e&%ence#=cartora!hic mode"#6' And the !roce## =cartora!hic mode"in6' The idea i# that the %#er

when confronted b$ a !rob"em #ho%"d not immediate"$ r%#h to the neare#t a,ai"ab"e

-e$board b%t #ho%"d fir#t attem!t to wor- o%t for him#e"f the data needed in order to!ro,ide the an#wer' The ne2t #te! i# to wor- o%t %#in c"ear "oic how one #ho%"d

!roceed from the data to the re&%ired an#wer' Thi# mean# #ettin %! a f"ow chart in

which a"" the nece##ar$ #te!# are c"ear"$ #hown' Thi# i# fo""owed b$ tran#"atin the

!roce##in #te!# into the "an%ae of the MAP command# @or the "an%ae of the #$#tembein %#ed if it i# not the Ma! Ana"$#i# Pac-ae' On"$ when thi# "ine of rea#onin ha#

been c"ear"$ tho%ht o%t and tran#"ated #ho%"d the %#er o to the com!%ter'

The ea#ie#t wa$ to a!!reciate how #%ch a #$#tem of cartora!hic mode"in and ma!

=a"ebra6 can be %#ed for ana"$0in eora!hica" data i# to fo""ow thro%h a n%mber of

#im!"e e2am!"e# that i""%#trate c"ear"$ the !rinci!"e# in,o",ed'

Three


9/11

@a Point o!eration#O!eration ?e$word Modifier S%mmar$ decri!tion

S%mmation ADD >eihtin O,er a"" "oci and ,a"%e# of two or

more attrib%te# to i,e new ,a"%e

S%btraction S81T7A*T >eihtin S%btract

M%"ti!"ication M8LTIPLY >eihtin M%"ti!"$

Di,i#ion

E2!onentiation

Tri' F%nction

S&%are root

A,erain

*o,erin

*o,erin

1oo"ean

combination

Findin e2treme#

E2traction ori#o"ation

Detrmine

fre&%enc$

di#trib%tion

Match fre&%enc$

di#trib%tion to

theoretica"

di#trib%tion

A##in a con#tant

,a"%e to an o,er"a$

Di,ide rane of

ce"" ,a"%e# intoe&%a" c"a##e#

Two)wa$

com!ari#on of two

o,er"a$#

S*O7E

M%"ti,ariate

o!eration# and

c"a## a""ocation

P*OMP

*L8STE7

ALLO*ATE

Fo%rier tran#form#

< fi"terin

FO87IE7 *om!%te two)dimen#iona" Fo%rier

tran#form# and a!!"$ fi"ter# for

hih or "ow com!onent#'7ecom!%te ma! b$ %ni,er#a"

Fo%rier tran#form

@b =7eion6 or "eend %nit o!eration#

O!eration ?e$word Modifier# S%mmar$ de#cri!tion

7ec"a##if$ orren%mber "eend

%nit#

7EN8M1E7


10/11

Determine

A7EA

PE7IMETE7

LENGTH

N%mber of

#e!arate

occ%rrence#

7EPO7T SI9E Line#(

7eion#

Determine #ha!e

of reion and;or

ho"e#

E8LE7

7ec"a##if$

accordin to area

SI9E

O,er"a$ inter#ect

two !o!$on# net#

OCE7LAY La$ two !o"$on# networ-# o,er

each other and !rod%ce new

!o"$on net @,ector or ra#ter'

1oo"ean #earch on

reion#

A# for !oint#

*"a##if$ reion

accordin toinc"%#ion#

A# for !oint#

@c Neihbo%rhood f%nction# o!eration#

O!eration ?e$word Modifier# S%mmar$ De#cri!tion

*ontin%it$ of

adjacent %nit#

*L8MP Di#tance

criterion or

friction

criterion

S*AN

SPAN

DSEA7*H

SLOPE

ASPE*T

P7OFILE

SP7EAD

*ONTO87

T7END

INCE7SE

OPTIMAL

CIE> O,er

ST7EAM O,er Find #horte#t ro%te between two

!oint# on a contin%o%# #%rface'PATH>AY Find #horte#t !arh a"on networ- in

term# of time( co#t( di#tance( ect'

Point in !o"$on PPOINT Find the area containin a i,en

!oint

E2am!"e /' Pre!are a #%itabi"it$ ma! for #ma""ho"der mai0e c%"ti,ation( %#in the FAOLand E,a"%ation Methodo"o$ @FAO /3BJ Mc7ae and 1%rnham /4/'


11/11

The FAO "and e,a"%ation methodo"o$ !roceed# b$ con,ertin "and characteri#tic#( or

!rimar$ "and attrib%te# that are recorded b$ a #oi" #%r,e$( into a #et of "and &%a"itie# thatare re"e,ant for the "and %ti"i0ation t$!e %nder con#ideration @in thi# ca#e #ma""ho"der

mai0e' Fo%r "and &%a"itie# are im!ortant for deteminin the !h$#ica" "and #%itabi"it$ for

rowin mai0eJ the#e are n%trient #%!!"$( o2$en #%!!"$( water #%!!"$ and ero#ion#%#ce!tibi"it$' The#e "and &%a"itie# can be ran-ed accordin to the fo""owin c"a##e#

No "imitationJ

Moderate "imitationJSe,ere "imitation'

Each "and &%a"it$ i# determined b$ a##e##in $he a!!ro!riate "and characteri#tic#' >a

ater a,ai"abi"it$ i# a f%nction of #oi" de!th and #oi" #erie#J o2$en a,ai"abi"it$ and n%trienta,ai"abi"it$ can be deri,ed direct"$ from the #oi" #erie# information( and the ero#ion

#%#ce!tibi"it$ or ha0ard can be con#idered to be a f%nction of #"o!e radient and #oi"

#erie#' The act%a" ,a"%e of the con,er#ion f%nction are i,en in >ie"ema-er and 1o2em

@/45'

Fi%re .' #how# a f"ow chart of o!eration# that co%"d be %#e to determine the "and#%itabi"it$' The #oi" #erie#

Soi" de!th Soi" Serie# DEM

S"o!e *"a##e#

>ater

A,ai"abi"it$

O2$en

A,ai"abi"it$N%trient

A,ai"abi"it$

Ero#ion

Ha0ard

S8ITA1ILITY *LASSES

*HA7A*TE7ISTI*S

8ALITIES

ECAL8ATION

methods of data analysis and spatial modellingkjuh

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