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A SAS UTM PROJECTION FOR GEOGRAPHICAL INFORMATION SYSTEMS APPLICATIONS David J. Cowen, University of South Carolina James S. Roberts, University of South Carolina r f t Introduction The purpose of this

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A SAS UTM PROJECTION FOR GEOGRAPHICAL INFORMATION SYSTEMS APPLICATIONS David J. Cowen, University of South Carolina James S. Roberts, University of South Carolina r f t Introduction The purpose of this paper is to discuss the development and applications of a Universal Transverse Mercator (UTH) map projection algorithm within a SAS system framework. For large scale (small area) applications the UTM 'projection has several advantages over the projections available in the existing SAS software options. By creating a SAS system macro it has been possible to utilize the data base management and mapping capabilities of the SAS software system as an integral part of a statewide geographical information system. The objective of any map' projection is to create a two dimensional representation of a spherical object. Therefore any ma'p projection is a series of equations that converts geodetic coordinates such as latitude and longitude into a cartesian system. These cartesian or X,Y coordinates provide the basis for the placement of geographical entities onto a two dimensional surface such as a piece of paper or a CRT. Any map projection must distort the representation of the Earth's surface. The types of distortion generally relate to area, shape, scale and direction. Since the acceptability of these distortions varies with applications there is no single optimal projection system~ In fact, the United States Geological Survey uses, at least, twenty-one different projections for its various map series. (Syrider, 1984)!!!!. Need for UTK Project.ion The three current map projections available in the SAS system provide good options for maps covering fairly large spatial extents but are not the most 'appropriate for data base applications at larger scales. There is a 'growing interest in computer based systems tha't can integrate several layers of spatial information into such a data base. These geographical information systems are proving to be valuable tools for analysis and planning activities in state and local governments, as well as, Federal natural resource agencies. A detailed comparison of several coordinate systems for use in such systems determined that:... the Universal Transverse Mercator reference system is the best type of projection based plane coordinate reference system for providing the basic requirements of a general reference system. (Beavers, 1978 p.7) The UTM system is widely used in such systems because it provides a world wide reference system, metric cartesian coordinates with minimum distortion and is easily incorporated into any data system. For these reasons UTM coordinates are now included on many large scale maps such as the USGS 7 1/2 minute and county map series. Furthermore, it is used as the basis for the new 1: roo,000 metric map series and is the coordinate system used for many new digital cartographic data files. Construct1.on The UTM projection was developed for military applications during World War II to create a planar global reference system. The system is based on a series of sixty zones centered on meridians spaced at six degree intervals. Therefore, the UTM system actually consists of sixty different map projections that extend north and south rather than the normal Mercator projection that is a single map centered on the Equator. (Fig. 1) In,order to further minimize distortion the UTM system actually moves the proj ection cylinder into a secant position so its radius is smaller than that of the Earth. The resultant projection, therefore, has true scale at the two lines of tangency 180,000 meters east and west of the central meridian. The central meridian is assigned a false easting of 500,000 meters so that any polnt wt-thin the six degree wide zone can be referenced by positive cartesian coordinates. The UTM system is optimal for use in any area that in included within a single zone with distortions only ranging between and from the central meridian to the extents of the zone. (Fig. 2) Application The UTM projection is ideal for states such as South Carolina that do noc extend beyond a single zone. (Fig. 2) In fact, because South Carolina is almost perfectly bisected by the central meridian (81 degrees W) of UTM zone 17 it has been adopted as the basis of a state wide information system. This system is being used to integrate a wide variety of spatial information from a number of different sources. Al though FORTRAN programs are available for conversion of various coordinates into UTM values it was desirable to incorporate the conversion process into a general data management and mapping system. Therefore, using the equations available in Synder's ~ Projections Used..!:!I. the United States Geological Survey a SAS system macro was developed. The UTM macro is used dai ly for a number of applications. In some cases existing digital cartographic data bases such as the census polygonal units are converted from latitude and longitude into UTM coordinates. These coordinates are passed directly to a mapping procedure in the SAS/GRAPH system or are written to a file that is compatible with another mapping system. In a more general context the UTM macro is part of a total l t 968 geographical data processing system. In this framework maps and other spatial data are digitized with a personal computer based system that includes extensive interactive editing capabilities and affine transformation procedures that convert table coordinates into latitude and longitude. These resul tant files are then either uploaded to a mainframe computer or processed with the PC SAS base system. For example, forty-six individual county maps were used to digitize the boundaries of water systems in the state. The individual files were then converted into UTM coordinates and and combined into a single map of the state using PROC CHAP. (Fig. 3) The macro is also used in conjunction with a polygon to grid procedure to create inputs into a grid cell based geographical information system. (Figs. 4 and 5) Input/Output Macro UTH can be easily called with the following statement: %UTM(R,DNAM,XNAM,YNAM,MEAS,ZONE,FORCE); (See program listing below for parameter descriptions.) On input, the unprojected map data set should contain variables which identify the latidute and logitude or radian coordinates. The procedure also allows for the input of the UTM zone or calculates it directly form the coordinates. Furthermore, any unit or polygon segment variables should also be present in the data set. On output, the specified data set will contain all the original information, as well as two new variables named X and Y. These two new variables will contain the UTM coordinates in meters. Progrma Listing NCRO UTM (R,DNAM,XHAM. YNAM.MEAS.ZONE,FDRCC); X-._._._-***._._._..._ _.. _.- _... ***-_._._._*** ***._._********..... *** U TTTTT MM MM U U MMMM U U M M M UUUU U\AJ M......_..._..._...***..._... PROGRAMMER: JAMES S. ROBERTS SOCIAL & BEHAVIORAL SCIENCES LABORATORY UNIVERSITY OF SOUTH CAROLINA THE FORMULAS USED IN THE UTM PROJECTIOH MACRO ARE DOCUMeNTED IN: $MYDER. J. P. (1984),' MAP PROJJ;:CTlONS USEO 8'1' THE u.s. GEOLOGICAL SURVEY GeOLOGICAL SURVEY BULLETIN SECOHD EDITION MACRO UTM MAY BE CALLED AS FOLLOWS: UlTM(R,DNAM.XNAM, YNAM.MEAS,ZONE, FORCE) WHERE: R IS EITHER TNE LETTER 'R' OR 'N'. IF THE LETTER 'R' IS PASSED, THEN THE SIGN OF ALL X COORDINATES WILL BE REVERSED. ON IS THE IWIE OF THE SAS DATA SET CONTAINING THE COOROINATES XNAM IS THE NAME OF THE X COORDIHATE YNAM IS THE NAME OF THE Y COOlNIINATE MEAS IS EITNER THE LETTER 'R' OR 'L'. IF THE LETTER 'R' IS PASSED, THEN THE PROGRAM WILL ASS\JIE THAT THE COORDINATES ARE IN RAOIANS ON INPUT. ZONE IS THE UTM ZONE TO BE USED IN THE PROJECTION. EITHER A NUMBER BETWEEN 1 AND 60 OR TilE LETTER 'U' SHOULD BE PASSED. IF A NUMBER IS PASSED. THEN THE MACRO WILL USE THE SPECIFIED ZONE IN THE PROJECTION. IF THE LETTER 'U' IS PASSED, THEN THE MACRO WILL CHOOSE THE f40st APPROPRIATE UTM ZONE FOR THE DATA USING THE ZONE IN wflich MOST OF THE COOROINATES RESIDE. FORCE IS EITHER TNE LETTER 'Y' OR 'N'. IF A 'Y' IS PASSED. THE MACRO WILL FORCE THE PROJECTION OF ALL (X, Y) COORDINATES USING THE SPECIFIED/CHOSEN UTM ZONE CENTRAL MERIDIAN. IF AN 'N' IS PASSED, TilE MACRO WILL CLIP ALL COORDINATES WIIICH FALL OUTSIDE OF THE CHOSEN/SPECIFIED UTM ZONE.... _...***..._... ***._... ; CREATE THE POINTS FILE AND RENAME THE (X.V) COORDINATES; DATA UTMP; SET &onam; X=&XNAM; Y=&YNAM; REVERSE TItE SIGH OF THE LONGITUDINAL COORDINATES IN NECESSARY; XIF &R R XTIIEN X X XSTRe;); CONVERT POINTS TO LATlTtIlE AND LONGITUDE IF NECESSARY; XI F ~S-R XlHEN XDO; X= *X; Y= S Y; %END;..._... IF TilE USER lias SPECIfIED U FOR THE ZONE PARAMETER, THEN COMPUTE TilE ZONE FOR THIS RUN...._...; XIF &ZONEmU XTHEN XDO; COMPUTe VARIABLE ZONER THE UTM ZONE FOR EACH (X,V) PAIR.; DATA UTMP; SET UTMP;!F X LT 0 THEN DO; IF MOO(X,6)~ THEN ZONER=X/6+31; ELSE ZONER=INT(X/6)+30; IF X LE 180 THEN ZONER '; END; ELSE DO; ZONER=INT(X/6)+31 : IF x GE 180 THEN ZONER;;60; END; FIND THE MODE FOR THE ZONER VARIABLE; PROC UNIVARIATE; VAR ZONER: OUTPUT ctft,.zoned MOOE;ZONER; ~ STORE THE MOOAL UTM ZONE 1M THE MACRO VARIABLE ZONE.; PROC PRINT; OATA ZONED; SET ZONED; CALL SYMPUTC'ZONE',20NER); WRITE A MESSAGE IMDI!=ATlNG WHICH ZONE HAS BEEN PICXED.; FILE PRINT IfOTITLES; IF _ _ EQ 1 THEN DO; PUT *, ; PUT -... THE UTM ZONE CHOSEN IS 20NE ZONER ' _ ; PUT... ***... ** *..., ; ENO; RUN; DATA UTMP; SET UTMP; DROP ZONER; XEND; COMPUTE TilE WESTMOST ANO EASTMOST MERIDIANS IN TilE SPECIFIED ZONE; LZLEFT 180+{(&lONE ' ) 6); L2RIGHT., 180+(&lONE*6); 969 :' * If TilE force PARAMETER IS N (NO), THEN THROW OOT ANY POINTS THAT DO NOT FALL WITIiIN TilE SPECifIED UTN GRID ZONE: IF &FORCE=N %THEN IF.X LT LZLEfT OR X GT LZRIGHT THEN DELETE:; * COMPUTE THE CENTRAL MERIDIAN WITIiIN TilE UTM GRID ZONE: LAMO;LZLEFT' (LZLE FT lzr I GHT) /2: DEfiNE CONSTANTS *********** *******************; * SET ALPHA EQUAL TO THE EQUATORIAL RADIUS FOR THE CLARKE ELlIPSIOO; AlPHA=6378Z06.4; * SET KO EQUAL TO THE SCALE ON THE CENTRAL MERIDIAN OF TilE UTM GRID ZONE; KO=.9996: * SET EZ EQUAL TO THE ECCENTRICITY OF THE CLARKE 1866 ELLipSOID: EZs ; EPZ;E2/(1'E2); ******************************************** *********************** DEFINE VARIABlES MOTi: THAT THE CONSTANT,0174S33 IS USED TO SCALE THE Y AND X VALUES BACK INTO RADIAN MEASURE. *********... *.. ****************.. *****.. **.. ***.. ****.. *.. **.. *.. ***.. **.. ****.. *: N=AlPHA/SQRT(,. E2* {SI N ( ( Y) )**2) ) : T:TAN( (.0174S33*Y) )**2: C ( COS( ( *Y) ) *2)*EP2; A=COS« *Y»*(X LAMO)*.0174S33: VARIABLE If CONTAINS THE TRUE OISTANCE ALONG THE CENTRAL MERIDIAN FROM TilE EQUATOR TO Y. IT IS SIMPLIFiEO USING THE CLARKE 1266 ELLIPSOID. NOTE ALSO THAT THE EQUATOR IS TAKEN AS THE ORIGIN Of OF LATITUDE for ALL CALCULATIONS. -****...**...*...******...***********************._...***...******...***; M= *Y *SIN( (2* '*y» *51 N ( (4* *Y» - 02*51N ( (6* *Y) ) ; *.** * *.*.****._**.*.******** **.* **.********-***--*-*.*** COMPUTE THE UrM CooROINATE VALUES OF X AND Y. TREAT THE POLES DIFFERENTLY *.* **-*-**.****.* ** ** * *.****.*.* * **.************: If ABS(y)= THEN 00; X=O; Y=KO M: END: ELSE 00; X=KO N* (A+( 1 T +C}*(A**3 )16+(5 18 T + 1**2+ n c 58*EPZ)* (A* S) 11Z0); Y=KO*(M+N*T AN ( ( Ot74S33*Y) )* ( (A**2) IZ+( 5 T +9*C+4*C**2) (A *4 )lz4+ (61 SS T+T* Z+60Q*C-330 EPZ) (A *6)1nO» ; END; ADD TO X FOR FALSE EASTINGS.; X=X+SOOOOO; DROP LZlEFT LZRIGHT LAMO ALPHA EPZ EZ KO N T CAM; DATA &DNAM; SET UTMP; %MEND UTM; References Beavers, G. H., Researeh Considerations: Spatial Referencing of Data in a Land Information System, Iowa State University Land Use Analysis Laboratory, Snyder, J. P., Map Projections Used by the U.S. Geologieal Survey, Geological Survey Bulletin 1532, 2nd Ed., SAS and SAS/GRAPH are registered trademarks of SAS Institute Inc., Cary. NC, USA. 970 UTMZONES FOR THE CONTINENTAL UNITED STATES Fig. 1 Six deg ree UTM zones for the continental U.S. Fig. 2 Scale distortions across a UTM zone 971 BASE MAP OF SOUTH CAROLINA WATERUSE AREAS FIliAL TEST - ALL COUll/TIES VAL _ I Fig. 3 Composite map of water ~upply_systems maps generated from 46 county 972 -,~~ E... Il00. COLUMN , !_~~~! C~ OJ ( V!l\ r\. J f', ~... 1\ ~....~ 1\.GT5 y \. II ~ B6QOOO E..no.ooo E S(}(),OOOE 680Il00' BI W REl'ERENCE GRID 1 KM CELlB. UTM COORDINATF.'! Fig. 4 Reference grid for UTM based grid cell system / [: ,54(tOOON L III i Fig. 5 Grid cell map generated from the coordinates transformed with MACRO UTM. 973

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