GPS and GIS

6/29/2015 BasicConcepts(GPSandGIS)Part5

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BasicConcepts(GPSandGIS)Part5

SetYourWatch

{_}TheGPSreceiversclockhasbeencorrectlysetbytheexposuretothesatellites.Itnowhasaveryaccurateideaofthetime.Soyoumaysetyourwatchbyitandbecorrecttothenearestsecond.21Withtherecordingofthegeographiccoordinatesandthesettingofyourwatch,youhaveusedGPStopositionyourselfinfourdimensional(4D)space.

TimeontheGeo3,assumingthatithasbeenproperlyconfiguredforthelocaltime,isfoundbyFn&OPTION~Chart.Ifthetimedoesntshowup,pressOPTION~Infowindows.Putacheckby"Currenttime"withtheENTERkey,(Youmighthavetounchecksomethingelsetomakeroomforthetimewindow.)PressCLOSE.

(Asyoumayormaynotknow,Einsteinsgeneraltheoryofrelativitypredictsthattimerunsmoreslowlythegreaterthegravitationalfieldasomewhatamazingclaimthathasbeenverified.Thatis,aclockwouldrunfasterfaroutinspace,awayfromanylargemasses,thanitwouldhereonearth.Ananimalwouldagemorequickly.Itturnsoutthat,whiletheeffectistinyforGPSsatellites,theirclocksarefarenoughawayfromEarthsothattheydorunatadifferentratethanthosehere,andthisdifferencehasbeencompensatedfor.)

DidtheEarthMove?

{_}Gotothe"Navigation"itemontheMainMenu.Whenyouselectityouwillfindfivemenuitems,asshownbelow:

1.StartNavigate

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2.ToWaypoint

3.FromWaypoint

4.WaypointSetup

5.DisplayFormat

{__}Select"DisplayFormat."Select"Velocity/Time."Thedisplayreturnstothe"Navigation"menu.Select"StartNavigate."Scrollthescreenuntil"Vel:"(forVelocity)appears.Anumber,representingkilometersperhour(kph),isdisplayed.Thenumberwillbebetweenzeroandaround0.4.

AnynumbergreaterthanzeroindicatesthattheantennaismovingatsomenumberofkilometersperhourwithrespecttotheEarth.Thatsodd.Youseethattheantennaisvirtuallymotionless.Whyshouldthereceiver



berecordingmovement?Theansweristhat,withanyphysicalsystem,thereareerrors.YourGPSreceiveriscalculatingpositionsattherateofaboutthreeeverytwoseconds.Sinceeachpositiondiffers,slightly,fromtheonebeforeit,thereceiverbelievesthatitsantennaismoving.

{_}Nowbegintowalkwiththeunitheldoutinfrontofyou.

Calloutthevelocityreadingstoyourpartner.Heorsheshould"mentally"averageyourreadingsandrecordsomevalues.Acomfortablewalkingspeedisaboutfivekph(threemilesperhour).Isthatwhattheunitindicates?

{_}Continuetowalk.Escapefromthecurrentscreenandselect"DisplayFormat"again.Thistimepick"Dist~Bearing."Select"StartNavigate"again.Scrollthescreenuntil"Heading:"appears.Thenumberindicatesyourdirectionoftravel,relativetoTrueNorth("Tn"),indegrees.Again,callthereadingsouttoyourpartner.Dotheytendtoaveragetotheapproximatedirectionyouarewalking?

OnewaytonavigatewiththeGeo3:Fn&OPTION~Compass~OPTIONInfoWindows.WiththeupanddownarrowkeysandtheENTERkey,turnonHeading,Velocity,andCurrenttime.Scrolldowntobesureeverythingelseisturnedoff,Thenbegintowalk.

{_}Walkbacktotheoriginallocationwhereyourecordedthepositionfixes.Afteraminuteorso,shuttheunitoffandreturntoyourlab,room,oroffice.Becertainthescreenisblank,sothattheunitisnotcollectingnewpositionfixes.Disconnectthepowercordfromthebattery(notfromtheGPSunit).Donotturntheunitonagainuntilyouareinsideabuilding,becauseinthenextProjectwewillwanttousethelastpositionthatwasrecordedbythereceiver.Thecoordinatesofthatpositionwillberememberedbythereceiver.

Ifyouturnitoff,theGeoSlosesthelastposition,soyoucannotdoProject1C.Therefore,leavetheGeo3turnedon(besurethebacklightisoffsoastosavethebattery).Tapethesquareofaluminumfoiloverthetopoftheunitwheretheantennaissoitcantcontinuetotakedata.Backinyourroom,office,orlabbegintheProjectbelowimmediately.

PROJECT1C

BackInside

Yoursessioninthefieldmayhaveraisedasmanyquestionsasitanswered.Wewilllookattheanswerstothosequestionsinlatertopics.First,letsverifythatGPSreallyworks.(SomeoneistellingyouthatyoucanfindyourpositiononEarthtowithinafewfeetfromfourobjectsinspace,morethan12,000milesaway,battingalongat2.4milespersecond.Wouldyoubelievethemwithoutchecking?Iwouldnt.)

{_}Usingacalculator,obtaintheaverageofeachofthe15latitudes,15longitudes,and15altitudesyourecorded.

AverageLatitude_

AverageLongitude_

AverageAltitude_

Plotthepointonyourtopomap.Doesthepointrepresentwhereyouwere?

TheaveragealtitudeindicateddevelopedbyGPSislikelytobesomewhatdifferentfromthatshownbythemap.Thehorizontalaccuracyofasinglepointisusuallywithin10meters,orroughly33feet.Verticalaccuracyisabouthalforathirdthatgood.Soyouraltitudefixthatyourreceiverrecordedatanygivenpointcouldbeoffby70to100feet.Theaverageofthe15altitudesshouldbesomewhatbetter.



TheShapeoftheEarthFindingElevations

Intermsoftryingtofindamathematicalortextualdescriptionofitsshape,Earthisamess.Evennotconsideringitsobviousbumpinessclearlyevidenttoyouifyouonlylookoutawindowtheoverallshapedefiesanyattemptatneatdescription.ThewonderfulideathatEarthwasthesimplestofallthreedimensionalfiguresthespherebitthedustin1687whenNewtonproposedthatanellipsoidwasabetterapproximation.ThustheEarthwasconsideredtomoreresembleaball,compressedslightlyatthepoles,withgreatergirthattheequator.

Thediameterthroughthepolesissome43kilometerslessthanadiameteracrosstheplaneoftheequator.

Inthelatterpartofthetwentiethcenturyitwasdeterminedthattheshapedepartedfromellipsoidalaswell.Aslightdepressionatthesouthpolecomplementsalittleprotuberanceatthenorthpole,andjustsouthoftheequatorwefindabulge.Sohowcanacohesivedescriptionbemade?Bycarefulmathematicalwork,basedongravityandwater.

Adefinition:Thegeoidisasurface,likeaneggshell.Itisequipotential(thatis,everywhereonthesurfacethestrengthofgravityisthesame)and(almost)coincideswithmeansealevel.Imaginethatallseasarecalm,andmeansealevelextendsthroughthelandformsthroughanetworkofcanals.(Inreality,meansealevel,itself,canvarybyameterortwo,dependingonwhereitismeasured.)Thegeoidsurface,bydefinition,isperpendiculartotheforceofgravity,nomatteratwhatpointitisconsidered.BecausethevalueofgravityvariesoverthesurfaceoftheEarth,thesurfaceofthegeoidissmoothandcontinuous,butnotregularasasphereorellipsoidwouldbe.Ithasdepressionsandbulges.

Satellitesarekeptintheirorbitsbygravity.GravitycanbeconsideredaforcebetweenthesatelliteandthecenterofmassoftheEarth.TheGPSsatellitesarenotaffectedbytheshapeoftheEarthnorvariationsinitsdensity.Theyorbitarounditscenterofmassandarealongwayaway.ThisprovidestheopportunitytodefineasimplemathematicalsurfacethatapproximatesthesurfaceoftheEarth.Thereferenceellipsoidisthissurfacecreatedbyrotatinganellipsearoundtheaxisconnectingthepoles.Thecenteroftheellipse,andhencethecenteroftheellipsoid,isthecenterofmassoftheEarth.Thesurfaceoftheellipseismeanttoapproximatethegeoid.Someplacesthereferenceellipsoidsurfaceisbelowthegeoidandsomeplacesitisabove.

ComparetheTwoAltitudeReferencingSystems

Forallbutthelastfewyears,mostpeoplemeasuredaltitudefromtheaverageleveloftheoceans.Thetwoprimarymethodsoftakingmeasurementswereverticallengthmeasurementfromabeach(inconvenientifnooceanwerenearby)andmeasurementofairpressure.Ofcourse,airpressureisvariablefromhourtohoursotherearecomplicationsusingthismethodaswell.

Aspreviouslymentioned,anewdefinitionofaltitudehasbeendeveloped,usingnotsealevelasthezerobutthegravitationalsurfacecalledthereferenceellipsoid.AsIjustsaid,thereferenceellipsoidapproximatesmeansealevel,butisslightlydifferentfromitalmosteverywhere.Sincethesatellitesareslavestogravity,theGeoExplorer"thinks"ofaltitudeandelevationintermsofheightabovethereferenceellipsoid(HAE).

Ofcoursealmostalldatarelatedtoaltitude,garneredoverseveralhundredyears,isexpressedinaltitudeabovemeansealevel(MSL).SoformulasandtableshavebeendevelopedthatindicatethedifferencebetweenMSLandHAE.TheseareincorporatedintotheGeoExplorerreceiverssotheymaydisplayaltitudeinMSL.YouwillexamineHAEandMSLinyourareabydoingthefollowing:

{_}ReconnectthebatterytothepowercordtotheGPSunit.

TurntheGPSuniton.Thereceiverkeptinitsmemorythecoordinatesofthelastdatapointyoutookinthefieldthecoordinatesofthispointcanbedisplayedfromthe"2.Position"menuitemintheMainMenu.Thescreenheadingwillbe"OldPosition."NowdeterminetheapproximatedifferencebetweenMeanSeaLeveland



theHeightAboveEllipsoidinyourarea.(Themanufacturerofthereceivercodedtheinformationinyourreceiverforalllocationsontheearthssurface.)TheideaisthatyouwillfirstdisplaytheOldPositioninMSL,thendisplayitinHAE.

First,writedowntheelevationofthelastpoint(theOLDposition)fromthe"Position"screen.Thiswillbeaheightabovesealevelinfeetormeters,dependingonhowyousettheunits.NowunderConfiguration~UnitsCustomSetup~AltReferenceselect"Ellipsoid(HAE)."Returntothe"Position"screen.Adifferentnumberwillbeshownforelevation.ThisnewnumberistheheightoftheOLDpositionabovethereferenceellipsoid.Fromthesetwonumbersyoucancalculatethedifferenceinheightbetweenthereferenceellipsoidandmeansealevel.Whatisitandinwhatunits?_.Whichishigher?_.

ToseethedifferenceinMSLmidHAEaltitudesusingtheGeo3:Firstrecordthealtitudeshownonthescreenthatshowsyouthelatitudeandlongitudecoordinates(Fn&OPTION~GPSusingtheStandardscreen).Thealtitudewillappearatthebottomofthescreen,alternatingwithacoupleofmessages.YouwillbewritingdownthealtitudeaboveMeanSealLevel(MSL),TodeterminetheHeight

AboveEllipsoid:Fn&OPTION~Setup~Configurations~CoordinatesAltitudereference~HAE.(MakesurethealtitudeunitsandcoordinateunitsaresettoMeters.)ReturntothescreenfromwhichyoufoundtheMSLaltitudeearlier.

{_}TurntheGPSunitoff.Readthefollowingsectioncarefully!

Twice![IfyouareusingtheGeo3,don'tturntheunitoff.]

TheDatumMakesaDifference

Itisabsolutelyvital,whenintegratingGPSdatawithGISdata,thatyourdatasetsmatchwithrespecttogeodeticdatum,22coordinatesystem,units,andprojection.YouwillsoonprovetoyourselfhowimportantthisisbyfillingouttheLatitudeandLongitudeComputationTablesattheendofthistopicandnotingthedifferencesbetweendifferentsystems.Youwillneedtousethefollowingfourpointsofinformationtodeterminethedifferencesinpositiondesignationfromonedatumtoanother,andfromonecoordinatesystemtoanother:

Onedegreeoflatitudecorrespondstoapproximately111kilometers(km)thereforeoneminuteoflatitudecorrespondstothatnumberdividedby60,orapproximately1,845meters.

Thelengthofaminuteoflongitude,measuredalongaparallel,dependsuponthelatitudeofthatparallel.Thelengthvariesfromapproximately1,855metersattheequatortozerometersatthepoles.Sosomecomputationisneeded:atthelatitudeatwhichyoutookdata(whatisit?_),oneminuteoflongitudecorrespondstoapproximately1,855metersmultipliedbythecosineofthatlatitude.Forexample,ifyourlatitudewere30thevalueofthecosinewouldbeapproximately0.866.Thereforeaminuteoflongitudewouldcorrespondto1,601meters(thats1,855times0.866=1,601).Nowdothecalculationsforyourlatitude:Atthepositionofyourfix,aminuteoflongitudecorrespondsto_meters.

OntheTrimbledisplay,thepositioninformationinUniversalTransverseMercator(UTM)isgivenwitheasting(thexcoordinate)first,andnorthing(theycoordinate)second.Notethatthisisoppositethe"latitudefirst"conventionof"Deg&Min."

IntheUTMcoordinatesystem,inagivenzone,agreaternumberofmetersindicatesamoreeasterlypositioninlongitude,oramorenortherlypositioninlatitude.Thatis,"x"and"y"increase"totheright"and"up,"respectively,inaccordancewithstandardCartesianconvention.

{_}TurntheGPSuniton.Makecertainthereceiverisnottakingdatafromsatellites.FillouttheLatitudeandLongitudeComputationTablesbelow.Todothis,youwillhavetoobtaineightnumbersfromtheGPSunitwhenitisnottakingdatafromsatellites(e.g.,whileinsideorwithacoupleoflayersofaluminumfoiltaped



overtheantenna).Thereceiverkeptinitsmemorythecoordinatesofthelastdatapointyoutookinthefieldasbefore(withthealtitudecomputationyoudid),thesecanbedisplayedastheOldPosition.Letmesaythatagain:ThereceiverkeptinitsmemorythecoordinatesofthelastdatapointyoutookinthefieldthesecanbedisplayedastheOldPosition.

TheGeo3willonlydisplaythelastpositionittookifitisleftonfromthelasttimeittookdatafromthesatellites.Ifyouhaveturneditoffinthemeantimeyouneedtotakeitbackoutsideandhaveitcalculateaposition.

Youcanviewbothcoordinatesofthatpointinseveralways,usingwhateverdatumyouwantandinwhatevercoordinatesystemyouwant.Youmayobtainthefirsttwooftheeightnumbersbysettingtheconfigurationto,say,latitude&longitudeandNAD27,thenswitchingtothePositionscreenandwritingdownthenumbersintheappropriatespacesontheappropriatetablesattheendofthetopic.ThenchangethedatumtoWGS84,gotothePositionscreenandwritedownthosenumbers.NextdoUTMandWGS84.FinallydoUTMandNAD27.Whenyouhavefinishedwritingdownthecoordinatesanddoingthecalculationsontheforms,comebackandanswerthequestionbelow:

{_}DoesthedifferenceinmetersfromWGS84toNAD27usingtheUTMcoordinatesystemcorrespondtothedifferenceinmetersyoucalculatedbasedonlatitudeandlongitudedegreesandminutes?_.Whatconclusionscanyoudrawfromyourobservationsandcalculations?

WiththeGeo3,thescreenyouneedtousetowritedowntherequirednumbersisFn&OPTION~GPS,inStandardmode.TogettothedifferentcoordinatesystemsandtowhereyoucansettheDatumyouuse:

Fn&OPTION~Setup~Configurations~Coordinates~SystemtosetLatitudeandLongitude,Fn&OPTION~Setup~Configurations~Coordinates~SystemtosetUniversalTransverseMercator,afterwhichyoumustsettheZonetoyourUTMzone,e.g.,16North(availablefromthetopomap),andFn&OPTION~Setup~Configurations~Coordinates~Datum.

Latitude



Latitude

Longitude



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