Terrain Mapping and Analysis

Transcription

1 Trrain Mapping and Analysis Data for Trrain Mapping and Analysis Digital Trrain Modl (DEM) DEM rprsnts an array of lvation points. Th quality of DEM influncs th accuracy of trrain masurs such as slop and aspct. Triangulatd Irrgular Ntwork (TIN) TIN approximats land surfac with a sris of nonovrlapping triangls. Elvation valus (z valus) along with x, y coordinats ar stord at th nods that mak up th triangls. Th input data to a TIN com from: DEM, Survyd lvation points,contour lins, Braklins: lin faturs that rprsnt changs of th land surfac such as strams, shorlins, ridgs, and roads. (Figur 1.)

2 Not vry points in DEM ar usd to crat TIN. Slctd points ar slctd using algorithms.g., VIP, z-tolranc. VIP (vry important points) Usd by Arc/info. Convrt DEM into grid and thn valuat th important of ach point (ach cll in th valuation grid) by how wll its valu can b stimatd from th nighboring clls). S Figur 1.1 VIP uss th avrag valu of four offst distanc s, of ach pair of nighbors around th point of intrst, P in Figur 1.1 as indicator of significanc for P.

3 VIP computs th significant valus for ach cll in th lvation grid. Th slction of points by VIP can b basd on ithr a dsird numbr or a spcifid significant lvl. Maximum z-tolranc Algorithm Slct th points from th lvation grid such that th diffrnc btwn th original lvation and th stimatd lvation from a TIN is within th spcifid maximum z- tolranc. Th algorithm uss an itrativ procss.

4 Trrain Mapping Contouring Most common mthod for trrain mapping. Contour lins connct points of qual lvation. Contour intrval rprsnts th vrtical distanc btwn contour lins. Automatd contouring follows two basic stps: (1) Dtcting a contour lin intrscting a grid cll or a triangl. () Drawing th contour lin through th grid cll or triangl. Givn a contour lin, vry triangl dg is xamind to dtrmin if th contour lin should pass through th dg. If it dos dtrmin contour position by a linar intrpolation. (Figur 1.3) Th straight lin sgmnt can b smoothd by splining (fitting a mathmatical function to a point).

5 Vrtical Profiling A vrtical profil shows changs in lvation along a lin, such as a stram or a road. Stps: Draw a lin on a contour map. Mark ach intrsction btwn a contour and th profil lin and rcords its lvation. Rais ach intrsction point to a hight proportional to its lvation, and Plot th vrtical profil by conncting th points. (Figur 1.5)

6 Hill Shading (Shadd Rlif) Simulat how th trrain looks with th intraction btwn th sunlight and surfac faturs. (Figur 1.6) Four factors control th visual ffcts of hill shading: Sun azimuth: th dirction of th incoming light, ranging from 0 to dgr in a clockwis dirction.

7 Th sun s altitud: Th angl of th incoming sunlight masurd abov th horizon btwn 0 0 to Th surfac slop: rangs from 0 0 to Th aspct: rangs from 0 0 to Us th following quation to comput th rlativ radianc for vry cll in th lvation grid or for vry triangl in a TIN.

8 R f ( Af As ) sin H f cos H s cos H f sin H s = cos Whr R f = th rlativ radianc valu of a fact (grid cll or a triangl). A f = th fact s aspct. A s = th sun s azimuth. H f = th fact s slop. H s = th sun s altitud. R f rangs in th valu from 0 to 1.0 I f = R f x 55, th I f valu of 55 would rsults in whit and 0 rsults in black. Prspctiv Viw 3-D viw of th trrain (Figur 1.7). Four paramtrs can control th apparanc of a 3-D viw. (Figur 1.8) Viwing azimuth: th dirction from th obsrvr to th surfac, rang from 0 0 and in a clockwis dirction.

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10 Viwing angl: Th angl masurd from th horizon to th altitud of th obsrvr, ranging btwn 0 to mans viwing dirctly from abov. 0 0 mans viwing surfac dirctly ahad. Viwing distanc: th distanc btwn th viwr and th surfac. Z-scal (xaggration factor): th ratio btwn th vrtical scal and th horizontal scal. Usful for highlighting minor faturs. GIS usrs can rotat th surfac, navigat th surfac, or tak a clos-up viw of th surfac. Th usrs can suprimpos thmatic layrs such as land covr, or roads in a 3-D draping procss. (Figur 1.9)

11 Trrain Analysis Slop and Aspct Slop masurs th rat of chang of lvation at th surfac location. (Figur 1.10) S = ( z / x) ( z / y) ) 0. 5 Whr s = slop xprssd as prcnt or dgr z = lvation at x, y location

12 Aspct is th dirctional masur of slop. (Figur 1.11) A = arctan (( z / y) /( z / x) ) Whr A = aspct = dirctional masur in dgr starts with 0 0 at th north and nds with 360 0

13 Aspct is th circular masur, th usrs oftn transform aspct masurs bfor thy can us in numrical analysis. Th common mthod is to transform into four or ight principal dirctions, and trat aspcts as catgorical data or principal dirction. (Figur 1.1) Slop and aspcts ar usd for studis landform, watrshd units, soil rosion, habitat suitability, sit analysis, and many othr filds.

14 Computing Algorithms for Slop and Aspct Using Grid W can masur th slop and aspct for a cll in th lvation grid by th quantity and dirction of th tilt of th cll s normal vctor. Givn a normal vctor (n x, n y, n z ), s Figur 1.13) s = ( n x n A = arctan y ) 0.5 ( n / n ) y / n x z

15 Approximation Mthods Rittr s Algorithm Us 3x3 moving windows Th slop of th cntr cll can b stimatd by th four immdiat mmbrs. S Figur 1.14 S = ( ) ( ) ) / d D = arctan (( ) /( )) 4 1 3

16 S is slop gradint if multiply S by 100, th unit is in prcnt slop. D is masurd in radian with rspct to x- axis, can b convrtd into dgr from a north bas of 0 0 using algorithm (s txt in Chang s Chaptr 1, pag 8). Horn s Algorithm Usd in Arc/Info and ArcViw. Us 8 nighboring clls and applis wight of 1 to 4 cornr clls. S Figur 1.15.

17 ( ) d S / 8 ) )) ( ) (( )) ( ) (( = ))) ( ) (( )) / ( ) arctan((( D = Horn s Algorithm Usd in Arc/Info and ArcViw. Us 8 nighboring clls and applis wight of 1 to 4 cornr clls. S Figur 1.15.

18 Computing Algorithms using TIN Us bi-dirctional normal vctor (vctor prpndicular to th triangular surfac). Suppos a triangl is mad of th thr nods: A(x 1, y 1, z 1 ), B (x, y, z ),and C (x 3, y 3, z 3 )

19 Th normal vctor ar: AB,(x -x 1 ), (y -y 1 ), (z -z 1 ) and AC,(x 3 -x 1 ), (y 3 -y 1 ), (z 3 -z 1 ). Th thr componnts of th normal vctor ar: n x : (y -y 1 )(z 3 -z 1 ) (y 3 -y 1 )(z -z 1 ) n y : (z -z 1 )(x 3 -x 1 ) (z 3 -z 1 )(x -x 1 ) n z : (x -x 1 )(y 3 -y 1 ) (x 3 -x 1 )(y -y 1 ) slop = ( n x n y ) 0.5 aspct = arctan( n y / n / n x z )

20 Surfac Curvatur Dtrmin if th surfac is upwardly convx or concav. Us 3x3 widows with a quadratic polynomial quation. z = Ax y Bx y Cx y Dx Ey Fxy Gx Hy I Cofficints A to I can b stimatd using th lvation valus in 3x3 window and th grid cll siz. S Box 1.6

21 Thr curvatur masurs can b computd from th cofficints: Profil curvatur = - ((DG EH FGH)/ (G H )) Plan Curvatur = ((DH EG -FGH)/(G H ) Curvatur = (DE) Profil curvatur stimats along th dirction of maximum slop. Plan curvatur stimats across th dirction of maximum slop. Th curvatur is (profil curvatur plan curvatur).

22 Viwshd Analysis Viwshd is th aras of th land surfac that ar visibl from an obsrvation point(s). Applications: Siting forst lookout station, Slcting location for rsort ara dvlopmnt, Evaluat scnic quality along th highway. Hlp locat antnnas for wirlss communication. S Figur 1.71a,b

23 Watrshd Analysis A watrshd is an ara that drains watr and othr substanc to a common outlt. Also calld basin or catchmnt. Watrshd analysis rquirs 3 datasts: A filld lvation grid A flow dirction grid (Figur 1.18) A flow accumulation grid (Figur 1.19). Watrshds can b dlinatd for slctd points or for an ntir grid (Figur 1.19b).

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25 Grid vrsus TIN Main Advantag of TIN Flxibility with input data sourcs DEM, braklins, contour lins, GPS data, or survy data Usr can add lvation point to TIN at thir prcis locations, or add faturs such as ridglins, strams or shorlins to dfin surfac discontinuity. TIN is an xcllnt data modl for 3-D display, bttr dfin land surfac than lvation grid. Main Advantags of Elvation Grid Computational fficincy TIN mad of sampld points from a DEM is lss accurat than th full DEM.