# UTM and UPS James R. Clynch 2003

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 UTM and UPS James R. Clynch 2003 I. Introduction The Universal Transverse Mercator (UTM) projection coordinates occur on most topographic maps. This is the Northing and Easting coordinates discussed below. In addition the projection is used on many charts and maps. It forms the basis for the Military Grid Reference System (MGRS) for US DoD maps in non-polar regions. North of 84 N and south of 80 S the Universal Stereographic Projection (UPS) is used for the MGRS. Note that as with all projections, the map is not specified until the ellipsoid and datum are specified. You have to check the map legend. II. Universal Transverse Mercator (UTM) A. Basic Geometry of a UTM Zone This is a Mercator based on a cylinder that is turned on its side so that the tangent line would be a meridian of longitude. In fact the cylinder is slightly depressed into the earth. The amount is defined by specifying the scale value on the central meridian is Because it is a Mercator projection, it is conformal. (Rotating the cylinder just rotates Tissot's Indicatrix, which is a circle and remains a circle if you rotate it.) The meridians are now curved lines. The parallels are straight lines. The meridians bow in. This means that azimuths will be in error for points not on the central meridian. The scale error will be zero on the meridians that cut the earth. These are standard lines. The scale error is, of course ( ) along the central meridian. It grows as you go east or west of the standard lines. The maximum scale error is controlled by only using the projection +/- 3 degrees of longitude of the central meridian. This is a zoned map. There are 60 separate projections, one for each 6 degree band of longitude beginning at 180E. This controls the error. The green line in the distortion graph above is in fact the maximum error for the UTM projection. The first zone covers 180E to 186 E, the second 186 E to 172 E and so forth. Technically the UTM only is defined from 84 N to 80 S. This is a windowed projection. What is seen on a map, is a part of the projection for the whole zone. Adjacent maps within one zone will line up on the edges. The error is controlled by depressing the cylinder into the earth and by limiting the width of the zone. No point is more than 3 degrees from the central meridian. You can plot the entire earth as a Transverse Mercator projection. This is done on the following figure with the central meridian through the US. Notice that the zone does not extend to the poles. It cuts off at 80 degrees south, but goes to 84 north for the convenience of map makers. 1

2 The first zone, numbered 1, is between longitudes of 180 E and 186 E, or 180 W and 177 W. This means that the area to the east of the prime meridian is zone 31. The official zone map is above. Zone 10 has been colored. In addition the few irregular zones in Scandinavia are also colored. (These 2

3 are often incorrectly computed by computer programs.) The horizontal lines every 8 degrees are used in the Military Grid Reference System (MGRS) discussed below. Zone West Longitude Zone West Longitude Zone West Longitude Zone West Longitude W W 31 0 E E W W 32 6 E E W W E E W W E E W W E E W W E E W W E E W W E E W W E E W W E E W W E E W W E E W W E E W W E E W 30 6 W E E B. Scale Value The construction of a Mercator, and hence also a transverse Mercator can be done geometrically. It was done that way originally. Today we us formulas for the map x and y in terms of the latitude, φ, longitude λ and the radius of the globe R. (R is the nominal scale factor times the radius of the earth.) As with the Mercator, the projection is conformal and hence h = k everywhere. Normally only the formula for k are therefore given. The formulas for a sphere are tractable. For the ellipsoid they become quite complex. They are usually written as an expansion in the eccentricity of the earth. Here the formulas for the sphere will be given. The formula for the scale factor is, where k k o = 2, 1 B B 0 = cosφ sin( λ λ ). The central meridian is at longitude 0 λ and where the scale factor is k 0. Of course for the UTM k 0 is the value The maximum value of the longitude difference within a zone is 3 degrees. The sine factor in B is therefore small, having a maximum absolute value of B is always small. Note also that B has a latitude dependence. 3

4 The scale value is the most important of these values to understand. It is shown below for four latitudes. On the left is the independent values is the longitude difference. However the distance of a degree of longitude is a function of latitude as the meridians converge at the poles. On the right the same data is plotted as a function of distance from the center. The whole zone width is plotted. The curves overlay in terms of distance. At the center the value is as set by the standard. This means that distances will be 0.40 m short for every kilometer there. At the edge at the equator, about 330 km from the center, the distances will be 0.98 m / km long. C. Eastings and Northings The formula for the x and y coordinates are usually written in terms of B. x y = = Rk Rk B ln 2 1 B tan φ arctan cos( λ λ 0 ). Here x is the horizontal map coordinate, the one in the east-west direction. If the real radius of the earth is used, then the value is a distance called Easting, usually expressed in meters. Easting is zero on the central meridian using the above equation for x. Easting would be both plus and minus. At the time UTM was first used, negative numbers were not well know. To avoid them, an offset was added. The value 500,000 was chosen. This keeps the left or western edge of all points in a zone positive. (The minimum distance on the plot of distortions above is -330 km.) The values in the north-south direction are also handled to avoid negative numbers. These are called Northings. For points north of the equator there is no need for an offset. However south of the equator an offset is needed. The value of ten million meters (10,000,000 m) is added to northings for points south of the equator. 4

5 A diagram is shown below of a UTM zone and the Northings. Notice that there will be the same value used in both the north and south hemisphere. There are multiple conventions on how to handle this. On maps you usually attach a "N" or "S" to the values to designate hemisphere. On computers the zone number is set to the negative of its correct value south of the equator for several implementations. You just have to read the documentation with computer programs. Notice that at high latitudes the cylinder does not break the surface at the zone boundary. This means that the scale error will always be negative at those latitudes. The standard lines do not enter the zone there. This is one of the reasons that the UTM system is not used at high latitudes. There a stereographic projection (UPS) is used. Both UTM and UPS were chosen in part because they are conformal projections. 5

6 A table of the UTM coordinates at a few points throughout the zone follow. These were computed on the WGS84 ellipsoid and datum. Latitude Zone Location Northing m Easting m Error m/km +84 Center Center Center Center Center Center Notice that the Easting at the center is always 500,000 and the scale error 0.4 m / km there. Notice also that the Northings are always increasing as you go north, but jump back 10,000,000 m at the equator. By convention the 0 value is normally used for the equator. The values of the UTM Northings and Eastings at the edges of the zone are shown in the table below. Notice that the scale error is now larger. It is positive on the zone boundaries for most of the zone. Also notice that the Northings are the same on the edge, but slightly different from the center value in the table above. This is due to the projection. Keeping it conformal has some consequences, even close to the central meridian. Latitude Zone Location Northing m Easting m Error m/km +84 West Edge East " West Edge East " West Edge East " West Edge East " West Edge East " West Edge East "

7 D. UTM Grids on Maps On many topographic maps and some charts a UTM grid of eastings and northings is overlaid. On USGS topographic maps only edge tic marks are present. This is done despite the fact that the projection of the map is not UTM. The above image of the map that covers Monterey CA shows the UTM tics. These are indicated in a large/small print format. The large number is multiplied by 100,000 m and the small by 10,000 m. Therefore the easting value of the tic is 590,000 m E. This is just bigger than the 500,000 value of the central meridian. The northing value shown is 4,040,000 m N. Thus this point is just over 4 million meters ( 4000 km ) north of the equator along an arc of the ellipsoid. E. Azimuth Error Convergence It is obvious from the above diagram showing the zone boundaries and the cylinder edges that the Northing lines do not line up with the true north, except on the equator. This leads to an azimuth error if the differences of Eastings and Northings are used in an inverse tangent function. This difference is called convergence. The convergence is defined as the angle from the true north to the grid north. Here grid north is the vertical lines or the northing axis. It is approximately given by the equation c λ sin φ where the longitude difference is taken in east longitude. It will be positive to the east of the central meridian and negative to the west of the central meridian. This is in line with the bowing in of the true north lines on a UTM map. This equation is approximate even for a spherical earth model. There are corrections for the spherical formula. In either case, the above is in error by times the approximate value at maximum. The largest azimuth errors are close to 3 degrees in the polar regions. The grid convergence is usually given in the legend of a navigation chart or topographic map. 7

8 8

9 III. Universal Stereographic Polar In the polar regions the UTM system suffers greatly from convergence. Therefore the standard map used there is a stereographic projection. This is chosen because it has reasonable distortion and it is conformal. It is important that a conformal projection be chosen for any projection used for navigation. The Universal Polar Stereographic projection is defined for latitudes north of 84 N and south of 80 S. The asymmetry is due to boundaries of important land masses. The plane of projection is depressed into the earth. The scale factor at the center is This means the place cuts the earth at about degrees. The above figure shows the diagram of the UPS projection in the northern polar region. As in all stereographic projections, the perspective point is at the point across the earth from the central point. Here this is the south pole. For the UPS southern projection the images in inverted and the north pole is the projection point. As with the UTM, the coordinates are expressed in Easting and Northing meters. However the definition of these values differs from the UTM. In concept the are the same, meters from the center point. There is also a false easting and northing added. In this case they both are 2 million meters. Thus the coordinates of the pole are 2,000,000 N and 2,000,000 E. The azimuth becomes less meaningful in polar regions. Therefore the grid north and grid azimuth are commonly used. These differ greatly from true azimuths on UPS maps. The reference line for the grid, in both hemispheres, is the line from the south pole to the north pole along the prime meridian. 9

10 The above diagrams show the coordinates in both polar regions to the same scale. Notice that there are nowhere negative numbers given this chose of offsets. The formulas for the easting (x) and northing (y) are fairly simple for the polar case. x y = = Rk cos φsin λ Rk cos φ k = 2k 0 1± sin φ where the upper sign is used in the northern hemisphere and the lower sign in the southern hemisphere. Of course, these become much more complex for the ellipsoidal model of the earth. 10

11 IV. Military Grid Reference System (MGRS) The Military Grid Reference System is just a re-labeling of the UTM (or UPS) easting and northings to avoid large numbers. It makes use of the fact that a map or operational area will usually only cover a small fraction of a UTM zone. It assigns letters to boxes in a hierarchical system. (It is easier and less error prone to send letters in Morse code, a common method of communication when this system was developed.) Only a summary of the system will be given here. A complete description is in reference 4. The zones define the longitude belts or zones. They use the standard UTM zone numbers. The longitude zones are identified by numbers, the latitude zones by letters. The latitude is broken into 20 zones, 8 degrees tall except the last. These are lettered from south (80 S to 72 S) to north with the letters C to X omitting O and I. These are given in the table below. Notice that the north most segment, X, is wider. Latitude Limits MGRS Letter Latitude Limits MGRS Letter 80 S to 72 S C 0 to 8 N N 72 S to 64 S D 8 N to 16 N P 64 S to 56 S E 16 N to 24 N Q 56 S to 48 S F 24 N to 32 N R 48 S to 40 S G 32 N to 40 N S 40 S to 32 S H 40 N to 48 N T 32 S to 24 S J 48 N to 56 N U 24 S to 16 S K 56 N to 64 N V 16 S to 8 S L 64 N to 72 N W 8 S to 0 N/S M 72 N to 84 N X North Polar Y and Z South Polar A and B The Naval Postgraduate School, in Monterey CA is at about N and W. This puts it in zone 10. The above latitude nomenclature means that NPS is in MGRS location 10S. Of course this is a huge area. In order to further specify locations squares 100,000 m by 100,000 m ( 100 km by 100 km) are given letter two labels. The first letter specifies the east-west location and the second the north-south location. (This is in the same order as x, y used to plot the map.) The 100,000 meter square for this point is FF. There are 6 sets of 100 km box designators which cycle with the UTM zone numbers. This keeps the same Box Identification from being confusing if the UTM zone is left off. At this point I need to point out that there are two MGRS s. The old MGRS and new MGRS. The most important difference is the 100 km square letter assignment. The ellipsoid is also different. While most MGRS coordinates in use today should be the new version, there can be some confusion. In order to help, the square identification places the locations 1000 km apart for the same designation. 11

12 It is common to truncate the MGRS locations to the accuracy needed. So the location of NPS would be reported with different number of values in different situations. Here is an example. The east value is first because this is the order for MGRS. Notice in the meter level MGRS that the numbers on the end are just the UTM coordinates leaving off the values beyond 100,000 s. These are taken care of with the latitude code S and the 100,000 m square code FF. Coordinate Type East-West Value / MGRS North-South Value Geographic W N UTM Zone ,653 E 4,050,535 N MGRS to Meter 10SFF MGRS to 100 m 10SFF References 1. NIMA Geodesy and Geophysics Online Reference Material 2. USGS Map Information Page 3. Snyder, John P., Map Projections, A Working Manual, US Geological Survey Professional Paper 1365, 1987, US Government Printing Office. 12

13 4. Datums, Ellipsoids, Grids, and Grid Reference Systems. Edition 1. US National Imagery and Mapping Agency (NIMA). TM , Washington, D.C., NIMA, 20 September (Available at reference 1 website as a PDF file.) 5. The Universal Grids: Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS). Edition 1. US National Imagery and Mapping Agency (NIMA). TM Washington, D.C., NIMA, 18 September (Available at reference 1 website as a PDF file.) 13

### Map Projection, Datum and Plane Coordinate Systems

Map Projection, Datum and Plane Coordinate Systems Geodetic Control Network Horizontal Control Network Datum A datum is a set of parameters defining a coordinate system, and a set of control points whose

### GEOGRAPHIC INFORMATION SYSTEMS Lecture 11: Projected Coordinate Systems

UTM Coordinate System GEOGRAPHIC INFORMATION SYSTEMS Lecture 11: Projected Coordinate Systems Why do we need the UTM coordinate system? - in a rectangular (Cartesian) coordinate system, with linear x and

### Map Projections & Coordinates. M. Helper 09-01-15 GEO327G/386G, UT Austin 1

Map Projections & Coordinates 09-01-15 GEO327G/386G, UT Austin 1 Laying the earth flat Why? Need convenient means of measuring and comparing distances, directions, areas, shapes. Traditional surveying

### Ellipsoid and Datum, Projection, Coordinate system, and Map Scale

Ellipsoid and Datum, Projection, Coordinate system, and Map Scale Lectures 4 Sept 14, 2006 Why we need it? Earth Shape Models Flat earth models are still used for plane surveying, over distances short

### It is a little challenging suppose you are to describe a point on the surface of a basketball.

Coordinate Systems 1. Geographic coordinate system To locate a point on a piece of white paper, we usually use the distances of the point to the left/right edge (x) and top/bottom edge (y). Therefore the

### Latitude and Longitudes in Geodesy James R. Clynch February 2006

Latitude and Longitudes in Geodesy James R. Clynch February 2006 I. Latitude and Longitude on Spherical Earth Latitude and longitude are the grid lines you see on globes. For a spherical earth these are

### Welcome to Lesson 3. It is important for a GIS analyst to have a thorough understanding of map projections and coordinate systems.

Welcome to Lesson 3. It is important for a GIS analyst to have a thorough understanding of map projections and coordinate systems. A GIS without coordinates would simply be a database like Microsoft Excel

### SPATIAL REFERENCE SYSTEMS

SPATIAL REFERENCE SYSTEMS We will begin today with the first of two classes on aspects of cartography. Cartography is both an art and a science, but we will focus on the scientific aspects. Geographical

### GIS for Educators. Coordinate Reference System. Understanding of Coordinate Reference Systems.

GIS for Educators Topic 7: Coordinate Reference Systems Objectives: Understanding of Coordinate Reference Systems. Keywords: Coordinate Reference System (CRS), Map Projection, On the Fly Projection, Latitude,

### THE UNIVERSAL GRID SYSTEM

NGA Office of GEOINT Sciences Coordinate Systems Analysis (CSAT) Phone: 314-676-9124 Unclassified Email: coordsys@nga.mil March 2007 THE UNIVERSAL GRID SYSTEM Universal Transverse Mercator (UTM) Military

### Earth Coordinates & Grid Coordinate Systems

Earth Coordinates & Grid Coordinate Systems How do we model the earth? Datums Datums mathematically describe the surface of the Earth. Accounts for mean sea level, topography, and gravity models. Projections

### Lecture 4. Map Projections & Coordinate System in GIS

Lecture 4 Map Projections & Coordinate System in GIS GIS in Water Resources Spring 2015 Geodesy, Map Projections and Coordinate Systems Geodesy - the shape of the earth and definition of earth datums Map

### The Map Grid of Australia 1994 A Simplified Computational Manual

The Map Grid of Australia 1994 A Simplified Computational Manual The Map Grid of Australia 1994 A Simplified Computational Manual 'What's the good of Mercator's North Poles and Equators, Tropics, Zones

### Registered map layers

Registered map layers Coordinate map systems Coordinate map systems 1. The Earth's Graticule Latitude and Longitude The graticule is the imaginary grid of lines running east-west lines of latitude (parallels)

### Geographic Coordinates. Measurement: Just use GPS. Geographic Coordinates 1/17/2013

Geographic Coordinates Analytical and Computer Cartography Lecture 3: Review: Coordinate Systems Geographic Coordinates Geographic coordinates are the earth's latitude and longitude system, ranging from

### Implementation Practice Web Mercator Map Projection

NGA.SIG.0011_1.0.0_WEBMERC NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY (NGA) STANDARDIZATION DOCUMENT Implementation Practice Web Mercator Map Projection 2014-02-18 Version 1.0.0 OFFICE OF GEOMATICS NGA.SIG.0011_1.0.0_WEBMERC

### Projections. Shape (angles) Distance Direction Area. Only a sphere can retain all four properties

Projections Projections Map projections are attempts to portray the surface of the earth (or a portion of the earth) on a flat surface. Four spatial relationships (or properties) between locations can

### 4 The Rhumb Line and the Great Circle in Navigation

4 The Rhumb Line and the Great Circle in Navigation 4.1 Details on Great Circles In fig. GN 4.1 two Great Circle/Rhumb Line cases are shown, one in each hemisphere. In each case the shorter distance between

### GIS s s Roots in Cartography

Following up on the last lecture GIS s s Roots in Cartography Getting Started With GIS Chapter 2 Information ordering: Lists and indexes Organizing data and information Information can be organized as

### World Geography Unit 1 - Test Introduction to World of Geography

Name World Geography Unit 1 - Test Introduction to World of Geography Term Identification Directions: Pick a word from the box that best completes the sentences below. distortion longitude Equator geography

### Earth Coordinates & Grid Coordinate Systems

Earth Coordinates & Grid Coordinate Systems You will always find parallels and meridians on largescale maps This is done to make the map a very close approximation to the size and shape of the piece of

### Lecture 2. Map Projections and GIS Coordinate Systems. Tomislav Sapic GIS Technologist Faculty of Natural Resources Management Lakehead University

Lecture 2 Map Projections and GIS Coordinate Systems Tomislav Sapic GIS Technologist Faculty of Natural Resources Management Lakehead University Map Projections Map projections are mathematical formulas

### 1.7 Cylindrical and Spherical Coordinates

56 CHAPTER 1. VECTORS AND THE GEOMETRY OF SPACE 1.7 Cylindrical and Spherical Coordinates 1.7.1 Review: Polar Coordinates The polar coordinate system is a two-dimensional coordinate system in which the

### GEOGRAPHIC INFORMNATION SYSTEMS Lecture 10: State Plane Coordinate System

State Plane Coordinate System GEOGRAPHIC INFORMNATION SYSTEMS Lecture 10: State Plane Coordinate System Why do we need the State Plane Coordinate System? - the SPCS was designed as a state by state rectangular

### Geographic Datums & Coordinates

Geographic Datums & Coordinates What is the shape of the earth? Why is it relevant for GIS? 9-04-2012 GEO327G/386G, UT Austin 2-1 From Conceptual to Pragmatic Dividing a sphere into a stack of pancakes

### An Introduction to GIS using ArcGIS Spring Lab Workshop 5 March S.P.Harish PhD Candidate Department of Politics New York University

An Introduction to GIS using ArcGIS Spring Lab Workshop 5 March 2013 S.P.Harish PhD Candidate Department of Politics New York University Agenda What is GIS? Basic GIS Concepts Introduction to ArcGIS Coordinates

### Measuring the Earth Using a GPS M. Scott Wilkerson & M. Beth Wilkerson, DePauw University, May 10, 2007

Measuring the Earth Using a GPS M. Scott Wilkerson & M. Beth Wilkerson, DePauw University, May 10, 2007 Modified from: Kerski, J.J., 2007, Measuring the Earth s Circumference with GPS, Copyright ESRI,

### Section 2.6 Cylindrical and Spherical Coordinates A) Review on the Polar Coordinates

Section.6 Cylindrical and Spherical Coordinates A) Review on the Polar Coordinates The polar coordinate system consists of the origin O,the rotating ray or half line from O with unit tick. A point P in

### State Plane Coordinate Systems & GIS

State Plane Coordinate Systems & GIS An overview of SPCS with emphasis on Grid vs. Ground coordinates. New Jersey Geospatial Forum Meeting Friday, March 18 th 2005 Jesse Kozlowski NJ PLS History of SPCS

### The Globe Latitudes and Longitudes

INDIAN SCHOOL MUSCAT MIDDLE SECTION DEPARTMENT OF SOCIAL SCIENCE The Globe Latitudes and Longitudes NAME: CLASS VI SEC: ROLL NO: DATE:.04.2015 I NAME THE FOLLOWING: 1. A small spherical model of the Earth:

### PEOPLE & SITES PEOPLE BIOGRAPHIES

16 PEOPLE & SITES The People & Sites sections contain fields to help you provide contextual information for your collections. Artifacts, archival materials, photographs, and publications reveal something

### Appendix B: Geographic Coordinates Systems & Map Projections. B.1 Approximating the Earth's Shape

The following is an appendix from: Strindberg, S. In prep. Optimized Automated Survey Design in Wildlife Population Assessment. Unpublished PhD Thesis. University of St. Andrews. Appendix B: Geographic

### WHAT YOU NEED TO USE THE STATE PLANE COORDINATE SYSTEMS

WHAT YOU NEED TO USE THE STATE PLANE COORDINATE SYSTEMS N & E State Plane Coordinates for Control Points AZIMUTHS - True, Geodetic, or Grid - Conversion from Astronomic to Geodetic (LaPlace Correction)

### Projections & GIS Data Collection: An Overview

Projections & GIS Data Collection: An Overview Projections Primary data capture Secondary data capture Data transfer Capturing attribute data Managing a data capture project Geodesy Basics for Geospatial

### SECOND GRADE 1 WEEK LESSON PLANS AND ACTIVITIES

SECOND GRADE 1 WEEK LESSON PLANS AND ACTIVITIES UNIVERSE CYCLE OVERVIEW OF SECOND GRADE UNIVERSE WEEK 1. PRE: Discovering stars. LAB: Analyzing the geometric pattern of constellations. POST: Exploring

### An Introduction to Coordinate Systems in South Africa

An Introduction to Coordinate Systems in South Africa Centuries ago people believed that the earth was flat and notwithstanding that if this had been true it would have produced serious problems for mariners

### Massachusetts Institute of Technology Department of Urban Studies and Planning

Massachusetts Institute of Technology Department of Urban Studies and Planning 11.520: A Workshop on Geographic Information Systems 11.188: Urban Planning and Social Science Laboratory Lecture 3: More

### NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY (NGA) STANDARDIZATION DOCUMENT

NGA.STND.0037_2.0.0_GRIDS NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY (NGA) STANDARDIZATION DOCUMENT UNIVERSAL GRIDS AND GRID REFERENCE SYSTEMS 2014-02-28 Version 2.0.0 OFFICE OF GEOMATICS CONTENTS LIST OF

### NGA GRID GUIDE HOW TO USE ArcGIS 8.x ANS 9.x TO GENERATE MGRS AND OTHER MAP GRIDS

GEOSPATIAL SCIENCES DIVISION COORDINATE SYSTEMS ANALYSIS TEAM (CSAT) SEPTEMBER 2005 Minor Revisions March 2006 POC Kurt Schulz NGA GRID GUIDE HOW TO USE ArcGIS 8.x ANS 9.x TO GENERATE MGRS AND OTHER MAP

### Map Coordinates, GIS, and GPS for Enhanced 9-1-1

Map Coordinates, GIS, and GPS for Enhanced 9-1-1 Keith W. Cunningham, Ph.D. 14 East Eighth Street Lawrence, KS 66044 800/238-1911 Maps and coordinates are used to describe features and their locations

### GEOGRAPHIC INFORMATION SYSTEMS Lecture 09: Map Projections

GEOGRAPHIC INFORMATION SYSTEMS Lecture 09: Map Projections Earth Ellipsoid and Horizontal Datums (cont d) Components of a Geographic Coordinate System Recognize that there are three components to a geographic

### OBJECTIVES. Identify the means by which latitude and longitude were created and the science upon which they are based.

Name: Key OBJECTIVES Correctly define: isolines, gradient, topographic map, contour interval, hachured lines, profile, latitude, longitude, hydrosphere, lithosphere, atmosphere, elevation, model EARTH

### 量 說 Explanatory Notes on Geodetic Datums in Hong Kong

量 說 Explanatory Notes on Geodetic Datums in Hong Kong Survey & Mapping Office Lands Department 1995 All Right Reserved by Hong Kong Government 留 CONTENTS INTRODUCTION............... A1 HISTORICAL BACKGROUND............

### WGS AGD GDA: Selecting the correct datum, coordinate system and projection for north Australian applications

internal report WGS AGD GDA: Selecting the correct datum, coordinate system and projection for north Australian applications JBC Lowry Hydrological and Ecological Processes Program Environmental Research

### Coordinate Systems. Orbits and Rotation

Coordinate Systems Orbits and Rotation Earth orbit. The earth s orbit around the sun is nearly circular but not quite. It s actually an ellipse whose average distance from the sun is one AU (150 million

### UTM: Universal Transverse Mercator Coordinate System

Practical Cartographer s Reference #01 UTM: Universal Transverse Mercator Coordinate System 180 174w 168w 162w 156w 150w 144w 138w 132w 126w 120w 114w 108w 102w 96w 90w 84w 78w 72w 66w 60w 54w 48w 42w

### Learning about GPS and GIS

Learning about GPS and GIS Standards 4.4 Understand geographic information systems (G.I.S.). B12.1 Understand common surveying techniques used in agriculture (e.g., leveling, land measurement, building

### UTM Zones for the US UTM UTM. Uniform strips Scalable coordinates

UTM UTM Uniform strips Scalable coordinates Globally consistent, most popular projection/coordinate system for regional to global scale geospatial data (i.e. satellite images global scale datasets USGS/EDC)

### TOPOGRAPHIC MAPS. RELIEF (brown) Hills, valleys, mountains, plains, etc. WATER. land boundaries, etc. CULTURAL

TOPOGRAPHIC MAPS MAP 2-D REPRESENTATION OF THE EARTH S SURFACE TOPOGRAPHIC MAP A graphic representation of the 3-D configuration of the earth s surface. This is it shows elevations (third dimension). It

### EPSG. Coordinate Reference System Definition - Recommended Practice. Guidance Note Number 5

European Petroleum Survey Group EPSG Guidance Note Number 5 Coordinate Reference System Definition - Recommended Practice Revision history: Version Date Amendments 1.0 April 1997 First release. 1.1 June

### Geography I Pre Test #1

Geography I Pre Test #1 1. The sun is a star in the galaxy. a) Orion b) Milky Way c) Proxima Centauri d) Alpha Centauri e) Betelgeuse 2. The response to earth's rotation is a) an equatorial bulge b) polar

### CONTROL POINT SURVEYING AND TOPOGRAPHIC MAPPING

CONTROL POINT SURVEYING AND TOPOGRAPHIC MAPPING Shoichi Oki Land Bureau, National Land Agency, Japan Keywords: control point, survey, topography, mapping, geodesy Contents 1. Introduction 2. Geometric

### 100 Math Facts 6 th Grade

100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

### P-153. NICA D.C. Al. I. Cuza University, IASI, ROMANIA

P-153 CONVERSION OF COORDINATES BETWEEN THE GAUSS-KRÜGER AND UTM CARTOGRAPHIC PROJECTION SYSTEMS ON TOPOGRAPHIC MAPS IN ROMANIA AND REPUBLIC OF MOLDAVIA FOR GIS USE NICA D.C. Al. I. Cuza University, IASI,

### Section 3 Mapping Earth s Surface

Section 3 Mapping Earth s Surface Key Concept Maps are tools that are used to display data about a given area of a physical body. What You Will Learn Maps can be used to find locations on Earth and to

### Geographic Grid. Locations Feature 1 Feature 2 Feature 3

Geographic Grid Name The geographic grid refers to the internationally-recognized system of latitude and longitude used to location positions on Earth's surface. Accurate use of this coordinate system

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### Geodesy and Datums. Ellipsoid and Geoid Geographic Coordinate system

Geodesy and Datums Ellipsoid and Geoid Geographic Coordinate system Defining the Ellipsoid The Earth is not perfectly round Fatter around the waist (equator) Flattened at the Poles To define this unique

### Module 1 : A Crash Course in Vectors Lecture 2 : Coordinate Systems

Module 1 : A Crash Course in Vectors Lecture 2 : Coordinate Systems Objectives In this lecture you will learn the following Define different coordinate systems like spherical polar and cylindrical coordinates

### Sun Earth Relationships

1 ESCI-61 Introduction to Photovoltaic Technology Sun Earth Relationships Ridha Hamidi, Ph.D. Spring (sun aims directly at equator) Winter (northern hemisphere tilts away from sun) 23.5 2 Solar radiation

### Keywords: coordinate systems, latitude, longitude, georeferencing, global positioning system, GPS, geodetic datum, ellipsoid, geocoding, postal code

Core Curriculum-Geographic Information Science (1997-2000) UCSB Peer Reviewed Title: Units 012-017 - Position on the Earth Book Title: Core Curriculum in Geographic Information Science Author: 012-017,

### ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES

ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES The purpose of this lab session is to experimentally investigate the relation between electric field lines of force and equipotential surfaces in two dimensions.

### Structural Geology. Practical 1. Introduction to Stereographic Projection

Structural Geology Practical 1 Introduction to Stereographic Projection Lecture Practical Course Homepage Contact Staff 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 71 8 9 10 STEREONETS 1 INTRODUCTION TO STEREOGRAPHIC

### Mathematical Procedures

CHAPTER 6 Mathematical Procedures 168 CHAPTER 6 Mathematical Procedures The multidisciplinary approach to medicine has incorporated a wide variety of mathematical procedures from the fields of physics,

### Solution Guide for Chapter 6: The Geometry of Right Triangles

Solution Guide for Chapter 6: The Geometry of Right Triangles 6. THE THEOREM OF PYTHAGORAS E-. Another demonstration: (a) Each triangle has area ( ). ab, so the sum of the areas of the triangles is 4 ab

### Example 1. Example 1 Plot the points whose polar coordinates are given by

Polar Co-ordinates A polar coordinate system, gives the co-ordinates of a point with reference to a point O and a half line or ray starting at the point O. We will look at polar coordinates for points

### Maps and Globes. By Kennedy s Korner

Maps and Globes By Kennedy s Korner Table of Contents Words to Know What are Maps and Globes Map Key or Symbols Cardinal Directions Intermediate Directions Equator Prime Meridian Hemispheres Coordinate

### Project 1: Plotting Coordinates and Projections

1 of 6 8/3/2007 1:54 PM Project 1: Plotting Coordinates and Projections Dan Uhrhan dfu101@psu.edu 2 of 6 8/3/2007 1:54 PM 3 of 6 8/3/2007 1:54 PM 4 of 6 8/3/2007 1:54 PM 5 of 6 8/3/2007 1:54 PM [Replace

### Surveying on NAD83 State Plane Coordinate System

Surveying on NAD83 State Plane Coordinate System By Dr. Joshua Greenfeld Surveying Program Coordinator NJ Institute of Technology Objective Modern surveying operations which involves working with GIS/LIS

### INTERNATIONAL INDIAN SCHOOL, RIYADH SA I 2016-17

INTERNATIONAL INDIAN SCHOOL, RIYADH SA I 2016-17 STD V WORKSHEET Page 1 of 7 SOCIAL STUDIES LESSON - 1. KNOW YOUR PLANET Fill in the blanks: 1. A book containing maps is called an. 2. A Flemish map maker,

### Gravitational potential

Gravitational potential Let s assume: A particle of unit mass moving freely A body of mass M The particle is attracted by M and moves toward it by a small quantity dr. This displacement is the result of

### Lines of Latitude and Longitude

ED 5661 Mathematics & Navigation Teacher Institute Keith Johnson Lesson Plan Lines of Latitude and Longitude Lesson Overview: This lesson plan will introduce students to latitude and longitude along with

### Graphs of Polar Equations

Graphs of Polar Equations In the last section, we learned how to graph a point with polar coordinates (r, θ). We will now look at graphing polar equations. Just as a quick review, the polar coordinate

### Exemplar Problems Physics

Chapter Eight GRAVITATION MCQ I 8.1 The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration

### Celestial Observations

Celestial Observations Earth experiences two basic motions: Rotation West-to-East spinning of Earth on its axis (v rot = 1770 km/hr) (v rot Revolution orbit of Earth around the Sun (v orb = 108,000 km/hr)

### This function is symmetric with respect to the y-axis, so I will let - /2 /2 and multiply the area by 2.

INTEGRATION IN POLAR COORDINATES One of the main reasons why we study polar coordinates is to help us to find the area of a region that cannot easily be integrated in terms of x. In this set of notes,

### Coordinate Conversions and Transformations including Formulas

Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas Revised - April 2015 Page 1 of 145 Index Preface 4 Revision history 5 1 MAP PROJECTIONS AND THEIR

### Ampere's Law. Introduction. times the current enclosed in that loop: Ampere's Law states that the line integral of B and dl over a closed path is 0

1 Ampere's Law Purpose: To investigate Ampere's Law by measuring how magnetic field varies over a closed path; to examine how magnetic field depends upon current. Apparatus: Solenoid and path integral

### POLAR COORDINATES DEFINITION OF POLAR COORDINATES

POLAR COORDINATES DEFINITION OF POLAR COORDINATES Before we can start working with polar coordinates, we must define what we will be talking about. So let us first set us a diagram that will help us understand

### Map Projections And State Plane Coordinate Systems. Thomas Maxell Beer, PLS

Map Projections And State Plane Coordinate Systems By Thomas Maxell Beer, PLS Introduction The origin for the modern State Plane Coordinate System in the United States began with two highway engineers

### Chapter 8 Geometry We will discuss following concepts in this chapter.

Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

### PLOTTING SURVEYING DATA IN GOOGLE EARTH

PLOTTING SURVEYING DATA IN GOOGLE EARTH D M STILLMAN Abstract Detail surveys measured with a total station use local coordinate systems. To make the data obtained from such surveys compatible with Google

### The Sphere of the Earth Description and Technical Manual

The Sphere of the Earth Description and Technical Manual December 20, 2012 Daniel Ramos MMACA (Museu de Matemàtiques de Catalunya) 1 The exhibit The exhibit we are presenting explores the science of cartography

### Oregon Geographic Information Council (OGIC) GIS Program Leaders Cartographic Elements Best Practices Version 1.0.7

Oregon Geographic Information Council (OGIC) GIS Program Leaders Cartographic Elements Best Practices Version 1.0.7 Introduction The purpose of this document is to serve as a set of Oregon best practices

### Centroid: The point of intersection of the three medians of a triangle. Centroid

Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

### Basic Coordinates & Seasons Student Guide

Name: Basic Coordinates & Seasons Student Guide There are three main sections to this module: terrestrial coordinates, celestial equatorial coordinates, and understanding how the ecliptic is related to

### How do we predict Weather and Climate?

Explanation and follow-on work Introduction and aim of activity In this activity, students were asked to imagine themselves as human computers in a vast forecast factory. This idea was originally conceived

### The Earth Really is Flat! The Globe and Coordinate Systems. Long History of Mapping. The Earth is Flat. Long History of Mapping

The Earth Really is Flat! The Globe and Coordinate Systems Intro to Mapping & GIS The Earth is Flat Day to day, we live life in a flat world sun rises in east, sets in west sky is above, ground is below

### An ArcGIS Tutorial Concerning Transformations of Geographic Coordinate Systems, with a Concentration on the Systems Used in Lao PDR.

An ArcGIS Tutorial Concerning Transformations of Geographic Coordinate Systems, with a Concentration on the Systems Used in Lao PDR. Introduction...3 PART 1, A Theoretical Background about Coordinate Systems...3

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

### Geomatics Guidance Note 3

Geomatics Guidance Note 3 Contract area description Revision history Version Date Amendments 5.1 December 2014 Revised to improve clarity. Heading changed to Geomatics. 4 April 2006 References to EPSG

### What are map projections?

Page 1 of 155 What are map projections? ArcGIS 10 Within ArcGIS, every dataset has a coordinate system, which is used to integrate it with other geographic data layers within a common coordinate framework

### 3D Visualization of Seismic Activity Associated with the Nazca and South American Plate Subduction Zone (Along Southwestern Chile) Using RockWorks

3D Visualization of Seismic Activity Associated with the Nazca and South American Plate Subduction Zone (Along Southwestern Chile) Using RockWorks Table of Contents Figure 1: Top of Nazca plate relative

### Calculating Astronomical Unit from Venus Transit

Calculating Astronomical Unit from Venus Transit A) Background 1) Parallaxes of the Sun (the horizontal parallaxes) By definition the parallaxes of the Sun is the angle β shown below: By trigonometry,

### Geographic Coordinates

Geographic Coordinates At A Glance Established Goals Robotics/GPS/GIS Skill: Obtain geographic coordinates from a given positioning device. Life Skills: Performing as a Team Member; Organizing Information

### 2 GIS concepts. 2.1 General GIS principles

2 GIS concepts To use GIS effectively, it is important to understand the basic GIS terminology and functionality. While each GIS software has slightly different naming conventions, there are certain principles

### Topo Grabber Help. 2010 Fountain Computer Products

Topo Grabber Help Topo Grabber Help All rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping,