GPS for general knowledge

5/28/2018 GPS for general knowledge

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GIS for Educators Topic 7: Coordinate Reference Systems

Objectives: Understanding of CoordinateReference Systems.

Keywords: Coordinate Reference SystemCRS!" #a$ %rojection" On t&e '(y

%rojection" )atitude" )ongitude"*ort&ing" Easting

Overview:

Map projectionstry to $ortray t&e surface of t&e eart& or a $ortion of t&eeart& on a f(at $iece of $a$er or com$uter screen. + coordinate referencesystemCRS! t&en defines" wit& t&e &e($ of coordinates" &ow t&e two,dimensiona(" $rojected ma$ in your GIS is re(ated to rea( $(aces on t&e eart&.

-&e decision as to w&ic& ma$ $rojection and coordinate reference system to

use" de$ends on t&e regiona( etent of t&e area you want to wor/ in" on t&eana(ysis you want to do and often on t&e avai(abi(ity of data.

Map Projection in detail

+ traditiona( met&od of re$resenting t&e eart&0s s&a$e is t&e use of g(obes.-&ere is" &owever" a $rob(em wit& t&is a$$roac&. +(t&oug& g(obes $reserve t&emajority of t&e eart&0s s&a$e and i((ustrate t&e s$atia( configuration ofcontinent,si1ed features" t&ey are very difficu(t to carry in one0s $oc/et. -&eyare a(so on(y convenient to use at etreme(y sma(( sca(es e.g. 2 : 233 mi((ion!.

#ost of t&e t&ematic ma$ data common(y used in GIS a$$(ications are ofconsiderab(y (arger sca(e. -y$ica( GIS datasets &ave sca(es of 2:453 333 orgreater" de$ending on t&e (eve( of detai(. + g(obe of t&is si1e wou(d be difficu(tand e$ensive to $roduce and even more difficu(t to carry around. +s a resu(t"cartogra$&ers &ave deve(o$ed a set of tec&ni6ues ca((ed map projectionsdesigned to s&ow" wit& reasonab(e accuracy" t&e s$&erica( eart& in two,dimensions.

7&en viewed at c(ose range t&e eart& a$$ears to be re(ative(y f(at. 8oweverw&en viewed from s$ace" we can see t&at t&e eart& is re(ative(y s$&erica(.

#a$s" as we wi(( see in t&e u$coming ma$ $roduction to$ic" are re$resentationsof rea(ity. -&ey are designed to not on(y re$resent features" but a(so t&eir s&a$eand s$atia( arrangement. Eac& ma$ $rojection &as advantagesanddisadvantages. -&e best $rojection for a ma$ de$ends on t&e scaleof t&ema$" and on t&e $ur$oses for w&ic& it wi(( be used. 'or eam$(e" a $rojectionmay &ave unacce$tab(e distortions if used to ma$ t&e entire +frican continent"but may be an ece((ent c&oice for a large-scale (detailed) mapof yourcountry. -&e $ro$erties of a ma$ $rojection may a(so inf(uence some of t&edesign features of t&e ma$. Some $rojections are good for sma(( areas" someare good for ma$$ing areas wit& a (arge East,7est etent" and some are betterfor ma$$ing areas wit& a (arge *ort&,Sout& etent.

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The three families of map projections

-&e $rocess of creating ma$ $rojections can be visua(ised by $ositioning a (ig&tsource inside a trans$arent g(obe on w&ic& o$a6ue eart& features are $(aced.

-&en $roject t&e feature out(ines onto a two,dimensiona( f(at $iece of $a$er.9ifferent ways of $rojecting can be $roduced by surrounding t&e g(obe in a

cylindricalfas&ion" as a cone" or even as a flat surface. Eac& of t&esemet&ods $roduces w&at is ca((ed a map projection family. -&erefore" t&ere isa fami(y of planar projections" a fami(y of cylindrical projections" andanot&er ca((ed conical projectionssee I((ustration 2!

-oday" of course" t&e $rocess of $rojecting t&e s$&erica( eart& onto a f(at $iece

of $a$er is done using t&e mat&ematica( $rinci$(es of geometry andtrigonometry. -&is recreates t&e $&ysica( $rojection of (ig&t t&roug& t&e g(obe.

ccuracy of map projections

#a$ $rojections are never abso(ute(y accurate re$resentations of t&e s$&erica(eart&. +s a resu(t of t&e ma$ $rojection $rocess" every ma$ s&ows distortionsof angular conformity! distance and area. + ma$ $rojection may combinesevera( of t&ese c&aracteristics" or may be a com$romise t&at distorts a(( t&e$ro$erties of area" distance and angu(ar conformity" wit&in some acce$tab(e(imit. Eam$(es of com$romise $rojections are t&e"in#el Tripel projectionand t&e $o%inson projectionsee I((ustration 4be(ow!" w&ic& are often used

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Illustration 1: The three families of map projections. They can be representedby a) cylindrical projections, b) conical projections or c) planar projections.


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for wor(d ma$s.

It is usua((y im$ossib(e to $reserve a(( c&aracteristics at t&e same time in a ma$$rojection. -&is means t&at w&en you want to carry out accurate ana(ytica(o$erations" you need to use a ma$ $rojection t&at $rovides t&e bestc&aracteristics for your ana(yses. 'or eam$(e" if you need to measuredistances on your ma$" you s&ou(d try to use a ma$ $rojection for your datat&at $rovides &ig& accuracy for distances.

Map projections with angular conformity

7&en wor/ing wit& a g(obe" t&e main directions of t&e com$ass rose *ort&"East" Sout& and 7est! wi(( a(ways occur at 3 degrees to one anot&er. In ot&erwords" East wi(( a(ways occur at a 3 degree ang(e to *ort&. #aintainingcorrect angular propertiescan be $reserved on a ma$ $rojection as we((. +ma$ $rojection t&at retains t&is $ro$erty of angu(ar conformity is ca((ed aconformal or orthomorphic projection.

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Illustration 2: The Robinson projection is a compromisewhere distortions of area, angular conformity anddistance are acceptable.

Illustration : The !ercator projection, for e"ample, is used where angular

relationships are important, but the relationship of areas are distorted.


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-&ese $rojections are used w&en t&e preservation of angular relationshipsis im$ortant. -&ey are common(y used for navigationa( or meteoro(ogica( tas/s.It is im$ortant to remember t&at maintaining true ang(es on a ma$ is difficu(tfor (arge areas and s&ou(d be attem$ted on(y for sma(( $ortions of t&e eart&.

-&e conforma( ty$e of $rojection resu(ts in distortions of areas" meaning t&at ifarea measurements are made on t&e ma$" t&ey wi(( be incorrect. -&e (arger t&e

area t&e (ess accurate t&e area measurements wi(( be. Eam$(es are t&eMercator projectionas s&own in I((ustration ;above! and t&e &am%ert'onformal 'onic projection. -&e U.S. Geo(ogica( Survey uses a conforma($rojection for many of its to$ogra$&ic ma$s.

Map projections with eual distance

If your goa( in $rojecting a ma$ is to accurate(y measure distances" you s&ou(dse(ect a $rojection t&at is designed to $reserve distances we((. Suc&$rojections" ca((ed euidistant projections" re6uire t&at t&e sca(e of t&e ma$is #eptconstant. + ma$ is e6uidistant w&en it correct(y re$resents distancesfrom t&e centre of t&e $rojection to any ot&er $(ace on t&e ma$. uidistantprojectionsmaintain accurate distances from t&e centre of t&e $rojection ora(ong given (ines. -&ese $rojections are used for radio and seismic ma$$ing"and for navigation. -&e Plate 'arree uidistant 'ylindricalseeI((ustration 5be(ow! and t&e uirectangular projectionare two goodeam$(es of e6uidistant $rojections. -&e *imuthal uidistant projectionis t&e $rojection used for t&e emb(em of t&e United *ations see I((ustration


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Projections with eual areas

7&en a ma$ $ortrays areas over t&e entire ma$" so t&at a(( ma$$ed areas &avet&e same $ro$ortiona( re(ations&i$ to t&e areas on t&e Eart& t&at t&eyre$resent" t&e ma$ is an eual area map. In $ractice" genera( reference andeducationa( ma$s most often re6uire t&e use of eual area projections. +st&e name im$(ies" t&ese ma$s are best used w&en ca(cu(ations of area are t&edominant ca(cu(ations you wi(( $erform. If" for eam$(e" you are trying toana(yse a $articu(ar area in your town to find out w&et&er it is (arge enoug& fora new s&o$$ing ma((" e6ua( area $rojections are t&e best c&oice. On t&e one&and" t&e (arger t&e area you are ana(ysing" t&e more $recise your areameasures wi(( be" if you use an e6ua( area $rojection rat&er t&an anot&er ty$e.On t&e ot&er &and" an e6ua( area $rojection resu(ts indistortions of angularconformityw&en dea(ing wit& (arge areas. Sma(( areas wi(( be far (ess $rone to&aving t&eir ang(es distorted w&en you use an e6ua( area $rojection. l%er+seual area" &am%ert+s eual areaand Mollweide ual rea 'ylindricalprojectionss&own in I((ustration =be(ow! are ty$es of e6ua( area $rojectionst&at are often encountered in GIS wor/.

Kee$ in mind t&at ma$ $rojection is a very com$(e to$ic. -&ere are &undreds

of different $rojections avai(ab(e wor(d wide eac& trying to $ortray a certain$ortion of t&e eart&0s surface as fait&fu((y as $ossib(e on a f(at $iece of $a$er. Inrea(ity" t&e c&oice of w&ic& $rojection to use" wi(( often be made for you. #ostcountries &ave common(y used $rojections and w&en data is ec&anged $eo$(ewi(( fo((ow t&e national trend.

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Illustration +: The late -arree *uidistant -ylindrical projection, for e"ample,is used when accurate distance measurement is important.


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'oordinate $eference ,ystem ('$,) in detail

7it& t&e &e($ of coordinate reference systems CRS! every $(ace on t&e eart&can be s$ecified by a set of t&ree numbers" ca((ed coordinates. In genera( CRScan be divided into projected coordinate reference systemsa(so ca((edCartesian or rectangu(ar coordinate reference systems! and geographiccoordinate reference systems.

eographic 'oordinate ,ystems

-&e use of Geogra$&ic Coordinate Reference Systems is very common. -&eyuse degrees of (atitude and (ongitude and sometimes a(so a &eig&t va(ue todescribe a (ocation on t&e eart&>s surface. -&e most $o$u(ar is ca((ed ", ./.

&ines of latituderun $ara((e( to t&e e6uator and divide t&e eart& into 2?3e6ua((y s$aced sections from *ort& to Sout& or Sout& to *ort&!. -&e reference(ine for (atitude is t&e e6uator and eac& hemisphereis divided into ninetysections" eac& re$resenting one degree of (atitude. In t&e nort&ern &emis$&ere"degrees of (atitude are measured from 1ero at t&e e6uator to ninety at t&e

nort& $o(e. In t&e sout&ern &emis$&ere" degrees of (atitude are measured from1ero at t&e e6uator to ninety degrees at t&e sout& $o(e. -o sim$(ify t&edigitisation of ma$s" degrees of (atitude in t&e sout&ern &emis$&ere are oftenassigned negative va(ues 3 to ,3@!. 7&erever you are on t&e eart&>s surface"t&e distance between t&e (ines of (atitude is t&e same =3 nautica( mi(es!. SeeI((ustration Abe(owfor a $ictoria( view.

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Illustration : The !ollweide *ual 'rea -ylindrical projection, for e"ample,ensures that all mapped areas ha/e the same proportional relationship to theareas on the arth.


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&ines of longitude" on t&e ot&er &and" do not stand u$ so we(( to t&e standardof uniformity. )ines of (ongitude run $er$endicu(ar to t&e e6uator and convergeat t&e $o(es. -&e reference (ine for (ongitude t&e $rime meridian! runs fromt&e *ort& $o(e to t&e Sout& $o(e t&roug& Greenwic&" Eng(and. Subse6uent (inesof (ongitude are measured from 1ero to 2?3 degrees East or 7est of t&e $rimemeridian. *ote t&at va(ues 7est of t&e $rime meridian are assigned negativeva(ues for use in digita( ma$$ing a$$(ications. See I((ustration AError:

Reference source not foundfor a $ictoria( view.

+t t&e e6uator" and on(y at t&e e6uator" t&e distance re$resented by one (ine of(ongitude is e6ua( to t&e distance re$resented by one degree of (atitude. +s youmove towards t&e $o(es" t&e distance between (ines of (ongitude becomes$rogressive(y (ess" unti(" at t&e eact (ocation of t&e $o(e" a(( ;=3@ of (ongitudeare re$resented by a sing(e $oint t&at you cou(d $ut your finger on you$robab(y wou(d want to wear g(oves t&oug&!. Using t&e geogra$&ic coordinatesystem" we &ave a grid of (ines dividing t&e eart& into s6uares t&at covera$$roimate(y 24;=;.;=5 s6uare /i(ometres at t&e e6uatorBa good start" but

not very usefu( for determining t&e (ocation of anyt&ing wit&in t&at s6uare.-o be tru(y usefu(" a ma$ grid must be divided into sma(( enoug& sections sot&at t&ey can be used to describe wit& an acce$tab(e (eve( of accuracy! t&e(ocation of a $oint on t&e ma$. -o accom$(is& t&is" degrees are divided intominutes (+)and seconds (0). -&ere are sity minutes in a degree" and sityseconds in a minute ;=33 seconds in a degree!. So" at t&e e6uator" onesecond of (atitude or (ongitude ;3.?A=4< meters.

A

Illustration 0: eographic coordinate system with lines of latitude parallel to

the e*uator and lines of longitude with the prime meridian throughreenwich.


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Projected coordinate reference systems

+ two,dimensiona( coordinate reference system is common(y defined by twoaes. +t rig&t ang(es to eac& ot&er" t&ey form a so ca((ed 12,$(ane seeI((ustration ?on t&e (eft side!. -&e &ori1onta( ais is norma((y (abe((ed 1" andt&e vertica( ais is norma((y (abe((ed2. In a t&ree,dimensiona( coordinate

reference system" anot&er ais" norma((y (abe((ed 3" is added. It is a(so at rig&tang(es to t&e 1and2aes. -&e 3ais $rovides t&e t&ird dimension of s$acesee I((ustration ?on t&e rig&t side!. Every $oint t&at is e$ressed in s$&erica(coordinates can be e$ressed as an 1 2 3coordinate.

+ $rojected coordinate reference system in t&e sout&ern &emis$&ere sout& oft&e e6uator! norma((y &as its origin on t&e e6uator at a s$ecific &ongitude.

-&is means t&at t&e D,va(ues increase sout&wards and t&e ,va(ues increase tot&e 7est. In t&e nort&ern &emis$&ere nort& of t&e e6uator! t&e origin is a(sot&e e6uator at a s$ecific &ongitude48owever" now t&e D,va(ues increasenort&wards and t&e ,va(ues increase to t&e East. In t&e fo((owing section" wedescribe a $rojected coordinate reference system" ca((ed 5niversalTransverse Mercator (5TM)often used for Sout& +frica.

5niversal Transverse Mercator (5TM) '$, in detail:

-&e Universa( -ransverse #ercator U-#! coordinate reference system &as itsorigin on t&e euatorat a s$ecific &ongitude4 *ow t&e D-va(ues increaseSout&wards and t&e 1,va(ues increase to t&e 7est. -&e U-# CRS is a g(oba(ma$ $rojection. -&is means" it is genera((y used a(( over t&e wor(d. Fut asa(ready described in t&e section accuracy of ma$ $rojectionsH above" t&e(arger t&e area for eam$(e Sout& +frica! t&e more distortion of angu(arconformity" distance and area occur. -o avoid too muc& distortion" t&e wor(d isdivided into 6 eual *onest&at are a(( 6 degreeswide in (ongitude from

East to 7est. -&e 5TM *onesare numbered 8 to 6" starting at t&e

?

Illustration : rojected coordinate reference systems. Two3dimensionalwith 4 and 5 coordinates 6left) and three3dimensional with 4, 5 and 7

coordinates 6right).


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international date line*one 8at 2?3 degrees 7est (ongitude! and$rogressing East bac/ to t&e international date line*one 6at 2?3degrees East (ongitude! as s&own in I((ustration be(ow.

+s you can see in I((ustration above and I((ustration 23be(ow" Sout& +frica iscovered by four 5TM*onesto minimi1e distortion. -&e *onesare ca((ed 5TM99,! 5TM 9/,! 5TM 9,and 5TM 96,. -&e,after t&e 1one means t&at t&e

U-# 1ones are (ocated south of the euator.

Say" for eam$(e" t&at we want to define a two,dimensiona( coordinate wit&in

t&e rea of ;nterest (O;)mar/ed wit& a red cross in I((ustration 23above

Illustration 8: The $ni/ersal Trans/erse !ercator (ones. 9or outh'frica $T! (ones , #, +, and are used.

Illustration 1;: $T! (ones , #, +, and with theircentral longitudes 6meridians) used to project outh 'frica withhigh accuracy. The red cross shows an 'rea of Interest 6'


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Dou can see" t&at t&e area is (ocated wit&in t&e 5TM *one 9,. -&is means" tominimi1e distortion and to get accurate ana(ysis resu(ts" we s&ou(d use 5TM*one 9,as t&e coordinate reference system.

-&e $osition of a coordinate in U-# sout& of t&e e6uator must be indicated wit&t&e *one num%er;5! and wit& its northing (y) valueand easting (


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window" because t&ey &ave different $rojections.

-o so(ve t&is $rob(em" many GIS inc(ude a functiona(ity ca((ed On-the-fly$rojection. It means" t&at you can definea certain $rojection w&en you startt&e GIS and a(( (ayers t&at you t&en (oad" no matter w&at coordinate referencesystem t&ey &ave" wi(( be automatica((y dis$(ayed in t&e $rojection you defined.

-&is functiona(ity a((ows you to over(ay (ayers wit&in t&e ma$ window of yourGIS" even t&oug& t&ey may be in differentreference systems.

'ommon pro%lems > things to %e aware of:

-&e to$ic map projectionis very com$(e and even $rofessiona(s w&o &avestudied geogra$&y" geodetics or any ot&er GIS re(ated science" often &ave$rob(ems wit& t&e correct definition of ma$ $rojections and coordinatereference systems. Usua((y w&en you wor/ wit& GIS" you a(ready &ave$rojected data to start wit&. In most cases t&ese data wi(( be $rojected in acertain CRS" so you don0t &ave to create a new CRS or even re $roject t&e datafrom one CRS to anot&er. -&at said" it is a(ways usefu( to &ave an idea aboutw&at ma$ $rojection and CRS means.

"hat have we learnedA

)et0s wra$ u$ w&at we covered in t&is wor/s&eet:

Map projections$ortray t&e surface of t&e eart& on a two,dimensiona("f(at $iece of $a$er or com$uter screen.

-&ere are g(oba( ma$ $rojections" but most ma$ $rojections are created

and optimi*ed to project smaller areasof t&e eart&0s surface. #a$ $rojections are never abso(ute(y accurate re$resentations of t&e

s$&erica( eart&. -&ey s&ow distortions of angular conformity!distance and area4It is im$ossib(e to $reserve a(( t&ese c&aracteristicsat t&e same time in a ma$ $rojection.

'oordinate reference system CRS! defines" wit& t&e &e($ ofcoordinates" &ow t&e two,dimensiona(" $rojected ma$ is re(ated to rea((ocations on t&e eart&.

-&ere are two different ty$es of coordinate reference systems:eographic 'oordinate ,ystemsand Projected 'oordinate,ystems.

On the @ly projectionis a functiona(ity in GIS t&at a((ows us to over(ay(ayers" even if t&ey are $rojected in different coordinate referencesystems.

?ow you tryB

8ere are some ideas for you to try wit& your (earners:

Start LGIS and (oad two (ayers of t&e same area but wit& different$rojections and (et your $u$i(s find t&e coordinates of severa( $(aces on

t&e two (ayers. Dou can s&ow t&em t&at it is not $ossib(e to over(ay t&etwo (ayers. -&en define t&e coordinate reference system as Geogra$&icM

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7GS ?< inside t&e %roject %ro$erties 9ia(og and activate t&e c&ec/ bo0enab(e On,t&e,f(y CRS transformation0. )oad t&e two (ayers of t&e samearea again and (et your $u$i(s see &ow On,t&e,f(y $rojection wor/s.

Dou can o$en t&e %roject %ro$erties 9ia(og in LGIS and s&ow your $u$i(st&e many different Coordinate Reference Systems so t&ey get an idea oft&e com$(eity of t&is to$ic. 7it& 0On,t&e,f(y CRS transformation0 enab(ed

you can se(ect different CRS to dis$(ay t&e same (ayer in different$rojections.

,omething to thin# a%out:

If you don0t &ave a com$uter avai(ab(e" you can s&ow your $u$i(s t&e $rinci$(esof t&e t&ree ma$ $rojection fami(ies. Get a g(obe and $a$er and demonstrate&ow cy(indrica(" conica( and $(anar $rojections wor/ in genera(. 7it& t&e &e($ ofa trans$arency s&eet you can draw a two,dimensiona( coordinate referencesystem s&owing aes and D aes. -&en" (et your $u$i(s define coordinates and y va(ues! for different $(aces.

@urther reading:

Coo#s:

C&ang" Kang,-sung 433=!: Introduction to Geogra$&ic InformationSystems. ;rdEdition. #cGraw 8i((. ISF* 33A3=5??=!

9e#ers" #ic&ae( *. 4335!: 'undamenta(s of Geogra$&ic InformationSystems. ;rdEdition. 7i(ey. ISF* ?2

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