RAMP: a computer system for mapping regional areas
Bradley B. Nickey PACIFIC SOUTHWEST Forest and Range Experiment Station
FOREST SERVICE lJ S DEPARTMENT OF AGRICULTURE P.O. BOX 245, BERKELEY, CALIFORNIA 94701
USDA FOREST SERVICE GENERAL TECHNICAL REPORT PSW-12 11975 CONTENTS
Page Introduction ...... 1 Individual Fire Reports ...... 1 RAMP ...... 2 Digitization Requirements ...... 2 Accuracy ...... 2 Computer Software ...... 2 Computer Operations ...... 4 Converting Coordinates ...... 4 Aligning Coordinates ...... 4 Mapping Sections ...... 6 Application ...... 8 Literature Cited ...... 9 Nickey, Bradley B. 1975. RAMP: a computer system for mapping regional areas. USDA Forest Serv. Gen. Tech. Rep. PSW-12, 9 p., illus. Pacific Southwest Forest and Range Exp. Stn., Berkeley, Calif. Until 1972, the U.S. Forest Service's Individual Fire Reports recorded locations by the section-township-range system..These earlier fire reports, therefore, lacked congruent locations. RAMP (Regional Area Mapping Pro- cedure) was designed to make the reports more useful for quantitative analysis. This computer-based technique converts locations expressed in section-township-range notations into latitude-longitude coordinates. Two subsystems make up RAMP. The technique can be applied to other types of land-management problems.
Oxford: 439:582:U681.4 Retrieval Terms: fire case histories; burn pattern; mapping systems; coor- dinates; locations; computer programs; RAMP; Regional Area Mapping Procedure.
Tho Anthn~
BRADLEY B. NICKEY is an operations research analyst with the Station's fire management systems research unit, headquartered at the Forest Fire Laboratory, Riverside, Calif. He was graduated from San Diego State College (B.S. degree in general engineering, 1961; M.S. degree in business administration, 1966). Before joining the Forest Service in 1967, he worked as an industrial engineer at Norton Air Force Base, in California. Muchinformation useful for land-use planning re- Oregon, illustrates the complexity of the problem mains untapped by computerized retrieval systems @g. 1). because of the cost of correcting inadequate land 10- Sections are nominally 1 mile square; townships cators. A typical example of this problem is found in are 6 miles by 6 miles and contain 36 sections. The the U. S. Forest Service's Individual Fire Report half townships (T.25 1/2S.)?however, contain six sec- (Form 5 100-29). In 1972, the form was revised to tions, and one of them is much smaller than the record fire locations in degrees and minutes of lati- others (see section 31, fig. I). Irregularities such as tude and longitude. But until then, the section, town- these preclude the use of the existing locator for com- ship, and range in which the fire started were re- puter analysis. corded. This location is appropriate for statistical Spatial analysis of the Individual Fire Reports ar- tabulations, but is not suitable for quantitative ana- chives requires a change to a congruent locator, such lysis. Therefore, much of the information in these as degrees latitude and longitude. Highly accurate earlier reports is not available to the fire manager and computer-based mapping systems that use legal land planner. descriptors, least-square error techniques, and other To tap this reservoir of historical information, a sophisticated methods are available, but are costly computer-based technique called the Regional Area (Swann and others 1970). For many jobs a high de- Mapping Procedure (RAMP) was developed. RAMP is gree of locator accuracy is not critical. designed to provide longitude and latitude values of section corners and midpoints from digitized map 10- cations of townships. This report describes RAMP, its characteristics, digitization requirements, and computer software, and suggests how the system could be used in solving other types of land management problems. Instructions on how to prepare input for the com- puter system are found in the Procedural Guide for the RAMP Quantization and Coding Process. The Guide is available upon request to: Director, Pacific Southwest Forest and Range Experiment Station, P. 0. Box 245, Berkeley, California 94701, Attention: Computer Services Librarian.
INDIVIDUAL FIRE REPORTS
The individual Fire Reports are a primary source of wildfire information used in fire prevention, fuel treatment, and fire planning. Generally, the planning techniques currently used require manual processing of this information. But computer-produced tabu- lations and summary reports are available by using keypunched copies of the form. Analyzing the spatial information in the Individual Fire Reports by advanced quantitative techniques would require a computer. However, such work has been hampered by the format of the report-partic- Figure 1-The township configuration found on the Deschutes National Forest, Oregon, includes half ularly its location of the fire by the use of the sec- townships (6 sections) as well as full ones (36 sec- tion-township-range system. The township and tions). Some of the sections may be much smaller than section pattern of the Deschutes National Forest, in others. RAMP The time required for digitizing is a function of the number of townships within a forest, the amount RAMP (Regional Area Mapping Procedure) accepts of key information required, and the number of non- the errors inherent in a map, and converts the section- rectangular sections it contains. For example, on the corner projections into degrees latitude and longi- Clearwater National Forest, in Idaho, it was necessary tude. Briefly, the system involves digitizing the loca- to digitize 463 records to cover 3646 sections. Many tions of the corners of a few sections in each town- of these records were required to process an extraor- ship. Variations from nominal size are identified and dinarily large number of nonrectangular sections. distributed among the sections, by procedures similar This work took about 3-112 hours. On the other .to the General Land Office survey rules for handling hand, only 116 records were needed to cover 54 1 1 errors. Finally, the locations of all remaining sections sections in the Tonto National Forest in Arizona. In and the centroid of each section are computed. With this case, about 2 hours were needed to digitize the this system, digitizing one township can result in as maps. many as 35 section locations being calculated auto- The average number of sections calculated for each matically by the computer. Locations by lati- digitized record for seven forests is 15.4 (table I). tudellongitude and section/range/township are then However, considerable differences from the average cross-referenced. existed for different forests. RAMP consists of two interrelated subsystems: one converts section corner locations on a map to a digital ACCURACY recording of an x-y coordinate in a form compatible for computer processing; the other provides instruc- Analysis of the magnitude and direction of calcu- tions that take advantage of township surveying prin- lated locations for 53 points, taken from nine dif- ciples and section numbering configurations to mini- ferent forest maps, showed no systematic errors over mize the amount of digitizing. the range of latitude and longitude examined. The computed standard error for latitude was 252 feet DIGITIZATION REQUIREMENTS and 437 feet for longitude (table 2). The scale of all of the maps digitized was % inch Many different characteristics exist on commer- to 1 mile. The smallest line digitized on these maps cially available digitizers. Some of the more critical was clearly legible at a viewing distance of 5 feet. This differences are (a) fixed versus variable length digital would indicate that the lines were at least 0.03 inch records-a record is the unit of data to be transmitted wide (Robinson and Sale 1969). A line of this width to the computer, (b) nu~nberof x-y coordinate points is equivalent to a distance of 316 feet on the maps that can be entered on a record, (c) availability or analyzed. One of the more accurate computer-based limitations or both on keying information into a rec- systems accepts calculated points which have an error ord, and (d) coordinate alignment procedures. Each of less than 200 feet at the latitude/longitude inter- difference affects the digitizing and coding proce- sections (Swann and others 1970). It would appear dures. In turn, each procedure influences the com- from this comparison that the errors associated with puter program used to process the digitized infor- RAMP are reasonable-especially for maps of the mation. scale used in the study. In RAMP, nine different digitized records are used. They provide the essential information for (a) devel- COMPUTER SOFTWARE opment of scale coefficients for conversion of x-y corner locations to degrees latitude and longitude, (b) Many commercially available digitizers have built- alignment of the x axis of the digitizer coordinate in functions to insure the alignment of the coordinate system with the longitude axis of the map, (c) identi- system with a map system that covers a small geo- fication of the latitude and longitude at the origin of graphic area. When this capability is not available, as the digitizer coordinate system, (d) determination of in RAMP, the computer software must perform these the latitude and longitude of the corner points and functions. A closely related item is the ability to in- centroid of a section(s), and (e) comparison of known terrupt a digitized session, remove the map from the map coordinate locations with calculated values. An digitizer, and then later restart the process so that all 80-column punchcard, limited to three sets of digit- new records are adjusted to the original initial origin. ized x-y coordinate points and 41 columns of keyed Somewhat less common is a built-in function for information, provides the means for linking these rec- the conversion of x-y coordinates developed by digit- ords to the computer subsystem. izing map points to coordinates of latitude and longi- Table 1-Efficiency of RAMP, as measured by the average number of sections processed by one digitized record
Forest Digitized Sections Efficiency Unit records processed (sections/record)
Deschutes N.F. Tonto N. F. Pike N. F. Sequoia N. F. Mendocino C.D.F.R.U. Sierra N. F. Clearwater N. F. Total 1 1555 23915 Average 222.1 3416.4 15.4
tude. Within WP, conversion to latitude is A full township consists of 36 sections (fig. 1). achieved by using a constant scale factor for each Less than full townships may occur (T.25 1/2S., map. However, this factor may change between maps. R.6E., for example). In those instances, generally one Because the distance between two latitude lines de- or more of the northern rows or western columns of creases rapidly as they approach the earth's poles, the the township or both are absent. Each digitized rec- conversion to longitude is a variable scale factor de- ord must contain three digitized points-coded infor- pending upon the latitude of the point. mation containing the unique township and range To relate congruent location dimension to a sec- address-and the number of the section which serves tion-township-range locator, three different sets of as the intersection of the most western column and computer instructions are used in WP:(a) one de- the most northern row of the township. termines the latitude and longitude of the four To illustrate, a record for T.25S., R.6E. (fig. 1) corners and the midpoint of a single rectangular would contain the digitized northwest and southeast shaped section; (b) another performs similar calcula- corner points of section 6 and the southeast corner tions for triangular or quadrilateral sections; and (c) point of section 36. It would also contain the codes the third provides latitude and longitude locations for T.25S., R.6E., and 6. Ths information would result each section within a township. Both of the first two in the development of latitude and longitude for each techniques have an efficiency of I; that is, for each corner and midpoint for all 36 sections. If the record digitized record, one section is provided with latitude contained an 8 instead of the section number 6, 25 and longitude locations. The third technique can re- sections would be processed. The section numbers eli- sult in an efficiency of up to 36. Lower efficiencies minated would be 1-7, 18, 19, 30, and 31. In addi- than this are due to the existence of irregular town- tion, any oversized or fractional section dimensions in ships. the northern row or western column of the township
Table 2-Known and calcu~ated coordinates of latitude and longitude for 53 points from nine forest maps (scale: 112 inch - I mile)
1 Latitude Longitude Coordinates Standard Standard 1 Mean 1 deviation 1 Mean 1 deviation I Degrees Known 40.2271 4.6116 111.0928 11-6320 Calculated 1 40.2272 4.6103 1 1 1.0929 11.6311 Error 1 0.0001 -0.001 3 0.0001 -0.0009 or both would be noted by the computer, and appro- from the longitude scale on the top of the map. The priate adjustments made in all other sections within same operation is repeated on the bottom longitude the same row or column or both. scale of the map. The X conversion coefficient, being The RAMP computer program consists of about a variable value, is calculated for every point being 1300 statement lines, written in FORTRAN IV lan- transformed by incorporating Equation I into a con- guage for an IBM 360150 Operating System1, and re- version coefficient function. The number of X digiti- quires approximately 130K of core to execute. Direct zation units within a degree of longitude at the top of transfer of this program to other systems is limited a map will be less than the equivalent degree mea- because of design effects resulting from the interface sured at the bottom of the map. RAMP uses linear with the RSS400 Graphic Quantitizer. interpolation to approximate this change in dimen- sions within a National Forest. COMPUTER OPERATIONS The X conversion coefficient function is Three major categories of calculations are required SCALE(J) = SCALEX(1) - SCALEX(2) (2) by WP.It provides algorithms to (a) determine *(LATTOP - SCALE(3)*LAT(J)) and correct for the nonalignment that may exist be- / (LATTOP-LATBOT) tween the X axis of the digitizer coordinate system and the longitude axis of the map; (b) develop scaling and coefficients for converting digitizer coordinates to spherical coordinates of longitude and latitude; and (c) calculate the latitude and longitude of the corners and the midpoints of sections. in which Converting Coordinates SCALE(J) = X conversion coefficient at Lati- Two scaling operations are used by RAh4P. Ade- tude J. quate precision is achieved by treating the conversion SCALEX(1) = X conversion coefficient at the of Y digitized units to latitude values as a constant top (I=l) and at the bottom (1~2) within a given National Forest, but it may change in longitude scales of the maps. value for a different forest. Two widely separate but LATTOP = Approximate latitude of the top known latitude points, selected from one of the two longitude scale, expressed in deci- latitude scales on either side of a map, are digitized. mal degrees of latitude. The basic FORTRAN equation used to develop the Y LATBOT = Approximate latitude of the bot- conversion coefficient is tom longitude scale, expressed in decimal degrees of latitude. LAT(J) = Y Coordinate of the point (J) in which: being converted to spherical coor- dinates. This variable should be SCALE(3) = Y conversion coefficient expressed in units measured by YDELTA = Difference between the two Y coor- the digitizer. dinates, resulting from the digiti- XDELTA(1) = Difference between the two X co- zation of known latitude values. ordinates, resulting from the IRANGE = Difference between the two known digitization of known latitude latitude coordinates digitized for values at I. YDELTA, JRANGE(1) = Difference between the two known longitude coordinates di- Because latitudes converge quickly at the earth's gitized at I. poles, the conversion of X digitized units to longitude values is treated as a variable, depending upon the Aligning Coordinates latitude of the point being transformed. Two widely separate but known longitude points are digitized If the digitizer coordinate system originated ex- actly at the center of a 36-inch wide map (scale: % '~radenames and commercial enterprises or products are inch = 1 mile), an alignment error of 15 minutes be- mentioned solely for necessary information. No endorsement tween the two coordinate systems would result in a by the U.S. Department of Agriculture is implied. conversion error of about 828 feet for locations near the map edge. And if maps are larger than 36 inches, When the map coordinates at the origin of the they would be subjected to even greater errors. In digitizer are unknown, a much more complex pro- addition, a digitizer operator would be hard pressed blem exists. Finding the angle of rotation and the to keep alignment errors close to 15 minutes. Many longitude and latitude at the origin requires the solu- digitizers allow the operator to establish the origin of tion of two transcendental equations containing three its coordinate system at any convenient map point. A unknowns. Since the number of unknowns exceeds seldom used but more universal requirement is the the number of available expressions, an iterative pro- ability to perform rectangular coordinate axis trans- cess for finding the solution is required. Fortunately, lation or rotations, or both. This procedure would the range over which the iteration must be performed allow the interruption of a digitization process, re- is small. Most "unassisted" digitizer operators can moval of the map from the equipment, and continu- align the two coordinate systems within a range of ation of the digitization with all measures trans- several degrees. The two equations that need to be formed to the initial coordinate system. The RAMP solved are computer program provides for all of these pro- cedures. XFUN = ABS(L0NE-LTWO) (6) The most simple alignment correction problem -ABS((SCALE(2)*XX2 exists when the longitude and latitude at the origin of -SCALE(l)*XXl)*COS(ARG) the rectangular coordinate system is known. The angle -(SCALE(l )*YY 1 of rotation between the X axis and the longitude axis -SCALE(2)* YY2)*SIN(ARG) is found by and THETA = ARSIN(D/(SCALE(l)*SCALE(2) (4) YFUN = ABS(LAT0NE -LATWO)-ABS (7) *(YY 1*XX2-W2*XX1))) (((YY2-YY I )*COS(ARG) and -(XX2-XXl)*SIN(ARG)*SCALE(3))) D = XX2*SCALE(2)*(LZERO-LONE) (5) in which + XXl *SCALE(l)*(LTWO-LZERO) XFUN, YFUN = Conditional transcendental in which equations containing the un- THETA = Angle separating the X axis of the known angle of rotation. digitizer with a longitude line on the ARG = An assumed angle of rota- map. tion between the X axis of LZERO = Longitude at the origin of the rec- the digitizer coordinate tangular coordinate system, ex- system and a longitude line pressed in decimal degrees of longi- on the map. tude. LATONE, LATWO = Known latitudes at LONE LONE = Longitude at a known point on the and LTWO respectively, ex- map. This point should be located to pressed in decimal degrees the right of LZERO and have a of latitude. known value less than LZERO, and be expressed in decimal degrees of If the two coordinate axes have been closely longitude. aligned before digitizations, only one angle of rota- LTWO = Longitude at a known point on the tion will exist between 510 degrees that will yield map which has a value greater than equivalent solutions for Equations 6 and 7. If both LZERO, expressed in decimal de- equations are equal, ARG is nearly equal to THETA. grees of longitude. The map coordinates at the origin of the rectangular XXI ,YY I = X and Y digitization value of LONE, coordinate system are now found by: expressed in rectangular coordinate LZERO = LONE + XX 1*SCALE( I) units. (8) XX2,YY2 = X and Y digitization value of LTWO, and expressed in rectangular coordinate units. LATO = LATONE - YY I *SCALE(3) (9) SCALE(K) = Equation 2 solved for point YYl (K=l) and YY2 (K=2), respectively. in which LATO = Latitude at the origin of the rectan- Mapping Sections gular coordinate system, expressed in decimal degrees of longitude. A section is considered mapped when all corners of the boundary and the centroid of the area within An interrupted digitization effort-one that re- the boundary are described by longitude and latitude quires establishment of a new origin-will normally coordinates. Attachment of the section-township- require both a translation and rotation trans- range label to the coordinates creates a suitable cross- formation to align the new origin with the initial ori- reference index record for the individual Fire Re- gin. This allows all the digitized records of a map to ports. be .processed during a single computer run. Two Three methods exist within RAMP for mapping flagged points digitized during the initial effort are sections: (a) one provides latitude and longitude loca- redigitized. The angle of rotation between the old and tions of the four corners and midpoint of each sec- the new is found by tion within a township; (b) another performs similar calculations for a triangular or quadrilateral section; THETAN = ARCOS((C*C - A*A - B*B) (10) and (c) the last procedure determines the latitude and (-2.*A*B) / longitude for a single rectangular section. in which The first method reduces the number of digitized points required to process a township by taking ad- vantage of the surveying and identity coding stand- ards of sections within a township. Three sets of digitized points, the township and range codes, and at least one but not more than two and section numbers are needed to process a township. C = (X2NEW + XlOLD - X20LD)**2 (13) The northwest corner of the section that serves as the + (Y2NEW + YIOLD - Y20LD)**2 intersection of the top row and leftmost column of the township is digitized and referred to as X1 and in which Y 1. The southeast corner of this same section is digit- ized and referred to as X2 and Y2. The number of THETAN = Rotation angle required to this section, (ISECT) is also recorded. The last point align the current rectan- digitized-X3, Y3-is the southeast corner of the sec- gular coordinate system of tion that occupies the intersection of the rightmost the digitizer to the original column and bottom row of the township. If any rectangular coordinate righthand columns or southern rows of the township system. are missing, the section number (JSECT) is also Rectangular coordinates recorded. from the initial digiti- In RAMP, all townships are initially assumed to be zation effort. Each point made up of 36 sections. Each row and column in a was previously marked as a full township also has a reference number associated potential future reference with it. For example, section number 6 is defined as a location. member of column 1, row 1. Section number 5 is a XINEW, YINEW Rectangular coordinates member of column 2, row 1. The intersection of col- {XINEW, Y2NEW) = from the new digitization umn 1, row 2 would then be occupied by section effort of the above flagged number 7. Thus, the origin of the reference system is locations. considered to be section number 6. Columns moving The translation constants for X and Y axes are, re- to the east increase in number as they move away spectively from the origin. Rows increase as they move south from the origin. With this reference system, the actual XADJ = XlOLD and YADJ = Y 1OLD (14),(15) number of sections and their configuration in the township can be determined from values of ISECT and JSECT. Methods to perform the actual translation or rota- The reference number of the most northern row of tion, or both, utilizing the results from Equations 4 the township can be found by to 15 are available in most mathematical handbooks (Selby and others 1965). LY = (ISECT - 1) / 6 + 1 (1 6) and the most western column is inwhichLY+2
Xi.L = XL and Xi.LX+ I = X2 (2% (23) A quadrilateral section containing one 90-degree internal angle can have two "basic" shapes (fig. 2). It and for the remaining columns of the matrix are is always possible to partition such a section into an Xi,j = Xi,j-, + XDELTA (24) oblique triangle and a right triangle. Location of the centroid in this section requires identifying a fifth in which, LY 5 i 5 LLY-I and LX+2 5 j 5 LXX point, called X5 and Y5. The coordinates of the un- -1. known point are located on a straight line passing In a similar manner, the coordinates of the first through the points XI, Y1 and X3, Y3. The equation two rows of the Y matrix are of this line is
and for the remaining rows in which
YiJ = Yi., ,j - YDELTA (27) A=Y2-Y3,B=X1 -X3 (33),(34) and
The point X5,Y5 is also a member of a straight line passing through point X2,Y2. By requiring this line to be perpendicular to Equation 32, the coordi- nates of the point X5,Y5 can be found by the fol- lowing expression
Figure 2-A quadrilateral section that contains an in- ternal 90-degree angle can have two "basic" shapes. and Dashed lines illustrate how the section can be viewed as an oblique triangle added (A) or subtracted (B) from a right triangle.
The centroid of the quadrilateral section can now A modification of the above process is used to be obtained by the use of the principle of moments digitize a right-triangular section. In this situation, the (Higdon and others 1955). Logical check of the third digitized point (X3,Y3) is the corner of the in- points X5,Y5 and X2,Y2, along with the quadrant ternal 90-degree angle. Equations 28 to 37 are not position of the section will determine if the area of required in this situation. RAMP uses a logical com- the oblique triangle, called A2, must be removed or parison of the three digitized points to differentiate a added to the area of the right triangle (Al). Thus right triangle from a quadrilateral section. Infor- mation on the quadrant position of the section will Quadrant 1 or 4, and X2 < X5 = - A2 determine the equations to use for solution of XBAR Quadrant 2 or 3, and X2 > X5 = - A2 and YBAR. When A2 is given a zero value, Equations The moments of the areas around the X and Y 38 to 41 are then applicable for locating the midpoint of the section. axes for sections located in quadrants 1 or 3 are The third method is used to map a single rectan- XBAR = (A1 *X3 + A2*(X3 + X2)) (38) gular section. Only two digitized points are required. / (3 .*(A1 + A2)) The problem is easily solved by RAMP. and APPLICATION YEAR = (A1 *Y 1 + A2*(Y 1 + Y2)) (39) / (3.*(Al + A2)) RAMP was designed originally to provide a useful respectively. For sections located in quadrants 2 and spatial variable that could be associated with data 4, the moments of the areas around the X and Y axes from the Individual Fire Reports for the FOCUS pro- are gram. FOCUS (Fire Operational Characteristics Using Simulation) is a model being developed at the Pacific XBAR = (A1 *X1 + A2*(X1 + X2)) (40) Southwest Forest and Range Experiment Station's / (3.*(Al + A2)) Forest Fire Laboratory, Riverside, California, to sirrt- ulate the probable consequences of available alterna- and tives in fire planning (Storey 1972). To date, a cross- reference catalogue has been produced within the YBAR = (A1 *Y3 + A2*(Y3 + Y2)) (41) (3.*(Al +A2)) computer for 12 National Forests and one California Division of Forestry Ranger Unit by RAMP. respectively. The intersection of the XBAR and The techniques and procedures used in RAMP can YEAR is the location of the midpoint of the quadri- be applied by land-use planners to tap many other lateral section, expressed in the rectangular coordi- sources of useful spatial information. As an example, nates of the digitizer. Equations 1 and 3 can be used a brief investigation shows that it could be applied to to develop the latitude and longitude of corners of the following U. S. Forest Service reports: (a) Bridge the section and its midpoint. Inventory, R5-7700-24; (b) Report of Suspected Timber Trespass, R5-6500-129; (c) Record of Sale, Robinson, Arthur H., and Randall D. Sale. Land or Easement, R5-5400-11; (d) Animal Damage 1969. Elements of cartography. p. 251-252. John Wiley Survey, R5-5200-39; (e) Prescribed Bum Report, and Sons, New York. R5-5100-199; (0Archaelogical Site Survey Record, Selby, Samuel M., and Brian Girling. RS-2700-3 1; and (g) Tree Seed Crop Condition Re- 1965. Standard mathematical tables. p. 515. The Chem- port, R5-2400-58. ical Rubber Co., Cleveland. Storey, Theodore G. 1972. FOCUS: a computer simulation model for fie LITERATURE CITED control planning. Fire Tech. 8(2):91-103. Swann, D. H., P. B. DuMontelle, R. F. Mast, and L. H. Van Higdon, Archie, and William B. Stiles. Dyke. 1955. Engineering mechanics. p. 12-14, 62-77. Prentice- 1970. ILLIMAP-a computer-based mapping system for Hall Inc., New York Illinois. 111. State Geol. Sum. Circ. 45 1:1-24.