# 量 說 Explanatory Notes on Geodetic Datums in Hong Kong

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 量 說 Explanatory Notes on Geodetic Datums in Hong Kong Survey & Mapping Office Lands Department 1995 All Right Reserved by Hong Kong Government 留

2 CONTENTS INTRODUCTION A1 HISTORICAL BACKGROUND A1 GEODETIC DATUMS A2 Hong Kong 1980 Geodetic Datum (HK80) World Geodetic System (WGS84) MAP PROJECTION AND GRID SYSTEM A3 Universal Transverse Mercator Grid (UTM Grid) Hong Kong 1980 Grid (HK1980 Grid) VERTICAL DATUMS A4 Hong Kong Principal Datum (HKPD), Chart Datum (CD). WGS84 Heights and HKPD Heights CONVERSION OF CO-ORDINATES A5 Latitude, longitude on HK80 and WGS84 Datums UTM Grid co-ordinates on HK80 and WGS84 Datums Latitude, longitude and UTM co-ordinates Latitude, longitude and HK1980 Grid co-ordinates APPENDICES Diagrams Illustrating Geodetic Datums in Hong Kong C1 Transverse Mercator Projection C2 Vertical Datums C2 Evolution of Hong Kong Geodetic Datums and Map Projections C3 Schematic Diagrams showing Transformation of Co-ordinates between Datums C4 UTM Zones in Hong Kong C5 Contour Map showing Difference between WGS84 and HKPD Heightings C6 Definitions of Terms C7 Conversion Formulae C8 Parameters and Reference Examples C9

3 INTRODUCTION With the advent of technologies, fixing position to 5 to 100 metres accuracy is no longer difficult by using Global Positioning System (GPS) receivers. Higher accuracy in position fixing by GPS can also be obtained by longer observation time, applying differential corrections and computing the co-ordinates by post-processing method. However, users are very often confused by various geodetic datums and grid systems presented on maps and plans. This booklet introduces the particulars of various geodetic datums and grid systems being used in Hong Kong without going into technical aspects deeply. Conversion formulae and parameters are also given in appendices to facilitate users to convert the co-ordinates of a point between various datums. Users should be aware that these conversion information will only give the computed co-ordinates to an accuracy specified of 2 to 5 meters or less than that of the original co-ordinates. HISTORICAL BACKGROUND Triangulation stations first appeared on the map of Hong Kong produced in A map was produced by Mr. Tate in 1899/1900 and another one was compiled by Mr. W. J. Newland in 1903/1904. Although triangulation stations are shown on these maps, there is no survey record found for the triangulation. In 1928/29 a military map of scale 1/20,000 was produced from air photographs taken in 1924/25 by the R.A.F. with ground controls provided by the 2nd Colonical Survey Section R.E. These ground controls were adjusted by the Geographical Section in and were later re-adjusted by the Crown Lands and Survey Office in It was adopted as the Main Triangulation of Hong Kong on which all surveys were based up to In 1963, a re-triangulation was carried out because the network of that time could not meet the requirements for large scale mapping and cadastral surveys. The Hong Kong (1963) Datum was established using Clarke (1858) as the reference ellipsoid and Patridge Hill as origin of the local Datum. A plane rectangular grid system was developed using Cassini" projection with gird origin in the southwest of Lantau Island to enable the co-ordinates in the Hong Kong territory were all positive values. In line with the metrication policy in the 1970s, the Imperial grid was converted to metric unit of measure in with the grid origin further shifted 3550 meters to the west. With the introduction of electro- magnetic distance measuring instrument, the distances between hilltop triangulation control points were resurveyed in to improve the consistence and accuracy of the control network. In this re-survey, a new geodetic datum, HK80 Geodetic Datum using International Hayford (1910) as the reference ellipsoid and the same projection origin was adopted. In the same time, Transverse Mercator projection was used for the rectangular grid system which was known as the Hong Kong 1980 Grid. A1

4 In 1990, the Survey & Mapping Office, Lands Department started to apply the GPS technique for fixing position of survey control points. A territory wide observation on a network of fifteen stations (twelve of which are at existing trig stations) was carried out by the No. 512 Specialist Team, Engineers of the U.K. Military Survey using GPS and Doppler satellite techniques. The network was adjusted with the results of high accuracy order. This survey provided a rigid link between the local HK80 Geodetic Datum and the global WGS84 Datum. Since position of a point can be easily fixed by small GPS receivers on WGS84 Datum, the latitude, longitude and Universal Transverse Mercator projection (UTM) co-ordinates shown on the small maps are now based on this global datum to facilitate general users for hiking, boating, rescue, navigation purpose. GEODETIC DATUMS An ellipsoid defined with orientation and position as well as size and shape is known as geodetic datum. A geodetic datum can be a local datum for an area by defining the geodetic position and azimuth of a point as the origin in that area. The datum can also be a global datum if it is defined by the geocentre of the Earth mass. There are two geodetic datums currently in use for horizontal control in Hong Kong. They are the local datum Hong Kong 1980 Geodetic Datum (HK80), and the global datum the World Geodetic System (WGS84). Details of these datums are described in the following sections and illustrated in the diagrams at appendix C1. Hong Kong 1980 Geodetic datum (HK80) The reference ellipsoid for HK80 is the International Ellipsoid (Hayford 1910). The origin is at the old Trig Zero" (now gone), which was 38.4 feet due south along the Transit Circle of the Hong Kong Observatory in Kowloon. As the latitude of the Hong Kong Observatory determined by astronomical observations was " N, the latitude of the Trig Zero" was thus "N. The Longitude of the Trig Zero" was "E which was determined in 1924 from simultaneous observations of Bordeaux signals made at Greenwich and Hong Kong. The Azimuth adopted was the line from Trig 67.2 to Trig 94 (i.e. Tai Mo Shan to Au Tau) at " which corresponded with the azimuth from old Trig 67 (now lost) to Trig 94 at ". The latter value was determined by astronomical observations in February 1960 by a team of visiting Geodesists who assessed the accuracy to be ± 0.2. World Geodetic System (WGS84) WGS 84 is an earth-centred, earth-fixed Cartesian coordinate system. The origin of the system is at the geometric centre of the WGS84 Ellipsoid which also coincides with the Earth s centre of mass. The X-axis of this datum passes through the Greenwich meridian and the equator. The Y-axis forms a right-handed orthogonal plane on the equatorial plane. The Z- axis goes through the North Pole. A2

5 Due to different definitions of the two datums, the geodetic positions (i.e. latitude and longitude) and the UTM co-ordinates of a point will be slightly different. Details of the above datums are illustrated in the following tables and diagrams. Datum Parameters Datum Ellipsoid Origin Azimuth Hong Kong 1980 Geodetic Datum (HK80) International Hayford (1910) Semi-major axis (a) = m Flattening (f) = 1 / Old trig Zero"at Hong Kong Observatory Latitude " N Longitude " E Trig 67.2 to Trig " World Geodetic System (WGS84) WGS84 Semi-major axis (a) = m Flattening (f) = 1 / Centre of Earth mass Not applicable MAP PROJECTION and GRID SYSTEM A map projection is a representation of the latitude and longitude of the ellipsoidal Earth surface by a planar surface according to certain mathematical functions. As the projected graticules are not rectangular, a rectangular grid system will be further developed to facilitate large scale mapping, cadastral and engineering survey. The Transverse Mercator is a conformal cylindrical projection which can be considered as a cylinder wrapping the Earth with its axis passes through the plane of equator. The Universal Transverse Mercator projection is a universal projection by rotating the cylinder around the earth with 6 interval in longitude. Refer appendix page C2. Universal Transverse Mercator Grid (UTM Grid) Hong Kong is in the Zone 49Q and Zone 50 Q of the UTM with 111 E and 117 E as the central meridians respectively. This Grid system can be found in all small scale maps in Hong Kong. To distinguish positions in different UTM Zones, each position is prefixed with its unique zone name. The UTM zones in Hong Kong using HK80 Datum are Zone 49Q GQ, HQ and Zone 50Q JV, KV. These prefixes are changed to Zone 49Q GE, HE and Zone 50Q JK and KK respectively under WGS84 Datum. (see appendix C5). Hong Kong 1980 Grid (HK 1980 Grid) The HK1980 Grid is a local rectangular grid system based on the HK80 Datum and Transverse Mercator projection. It is used in cadastral, engineering surveying and large scale mapping in Hong Kong. The origin of projection is at the old Trig 2 (now gone) and the scale factor is unity (1.0) along the central meridian. A3

6 This is a local rectangular grid system and is still in used for the above purposes. The latitude and longitude, and UTM graticule on WGS84 Datum is adopted in small scale maps for users convenience. The projection parameters are illustrated in the table below. Projection Parameters Grid System Universal Transverse Mercator Grid Hong Kong 1980 Grid System (UTM) (HK 1980 Grid) Projection Transverse Mercator Transverse Mercator Geodetic Datum HK80 WGS84 HK80 Reference International Ellipsoid Hayford (1910) WGS84 Ellipsoid International Hayford (1910) Zone 49Q Zone 50Q Old Trig 2 Patridge Hill" Origin of Latitude Equator Equator Latitude " N Projection Longitude 111 E 117 E Longitude " E Grid Coord. of 0 mn 0 mn mn Origin me me me Scale Factor at the central meridian Unity (1.0) along the central meridian at old Trig 2 VERTICAL DATUM There are two vertical datum currently in use for vertical control in Hong Kong. They are the Principal Datum (HKPD) and the Chart Datum. Hong Kong Principal Datum (HKPD) In Hong Kong all heights and levels on land refer to the Principal Datum which is formerly known as Ordnance Datum. A vertical datum is usually determined with certain relationship to the mean sea level. The HKPD was previously determined as 1.125m below Mean Sea Level"by Dr. Doberck for the years This figure is superseded by the updated determination by Hong Kong Observatory derived using 19 years ( ) observation records of the Automatic Tide Gauge situated at North Point, Victoria Harbour. It was then determined that the Mean Sea Level" is approximately 1.23m above HKPD. The original monument Rifleman s Bolt", is a copper bolt fixed in Hong Kong Naval Dockyard. The level of the Bolt" was determined by H.M. Surveying Vessel Rifleman" in 1866 as 5.435m above HKPD. Since then, the Rifleman s Bolt" was used as a datum for all levelling. The bolt was latter removed from the original store house to the eastern wall of Blake Block in H.M.S. Tamar. The survey in May 1984 revealed that the level of the Bolt" is 5.420m above HKPD. This monument is being preserved for its historical value and not to be used as a bench mark. A4

7 The Chart Datum (CD) The Chart Datum, formerly known as Admiralty Datum, is approximately the level of Lowest Astronomical Tide and is adopted as the zero point for Tide Tables since All depths, heights above mean high water mark and submarine contours on Admiralty Charts and sounding plans refer to the Chart Datum. The Chart Datum is approximately 1.38m below Mean Sea Level" or 0.146m below the Hong Kong Principle Datum. The relationship among different datums are summarized at page C2. WGS84 Heights and HKPD Heights The heights fixed by GPS are the ellipsoidal heights with reference to the WGS84 Datum. To convert the ellipsoidal heights to the heights above HKPD, the difference between these two vertical datums must be known. From the survey by UK Military 512 STRE in 1991, a rough relationship was deduced. It is noted that the WGS84 heights are generally higher than the HKPD heights with the magnitude of 2.4m in the west and 0.4m in the east of Hong Kong. The differences of these two datums are illustrated in the map at page C6. It is estimated that this relationship will give the height conversion to an accuracy of better than ±0.15m. CONVERSION OF CO-ORDINATES Users are reminded to confirm the geodetic datum of the co-ordinates input for the conversion. The information given below only serve as an approximate conversion to the accuracy generally 2m to 5m or that of the original co-ordinates whichever the less. For precise conversion, users may approach the Survey and Mapping Office for assistance. The flow chart, formulae and parameters for the conversion of co-ordinates are shown on the pages C4, C7 to C9. Latitude, longitude on HK80 Datum and WGS84 Datum Due to the change of reference ellipsoid, the latitude, longitude on HK80 and WGS84 of a point are slightly different. As Hong Kong is a small area, additive constants for the geographic co-ordinates shown below are sufficient to attain the general accuracy. longitude HK80 = longitude WGS84 8.8" (corrected to nearest 0.1") latitude HK80 = latitude WGS " (corrected to nearest 0.1") UTM Grid co-ordinates on HK80 Datum and WGS84 Datum Similarly, the UTM co-ordinates of a point on the two Datums are also slightly different. The conversion factors given below should be applied in the specified zone only. The conversion of UTM zones prefix can be referred to the map on appendix C5. The accuracy of these conversion factor should be about 5m. Zone 49Q UTM Easting HK80 = UTM Easting WGS84 245m UTM Northing HK80 = UTM Northing WGS m Zone 50Q UTM Easting HK80 = UTM Easting WGS84 260m UTM Northing HK80 = UTM Northing WGS m A5

8 Latitude, longitude and UTM co-ordinates The conversion between the latitude, longitude and UTM Grid co-ordinates on either HK80 Datum or WGS84 Datum can be performed by using the projection formulae 1 to 3 or 3 to 5 and appropriate parameters. Users should be aware to apply appropriate parameters for different datums and check with the worked examples at page C9 to ensure the correctness of the conversion. Latitude, longitude and HK1980 Grid co-ordinates The conversion between the latitude, longitude (on HK80 Datum) and the HK 1980 Grid co-ordinates can be performed by the same projection formulae 1 to 3 or 3 to 5 with the projection origin at old Trig 2 and HK80 Datum parameters. WGS84 latitude, longitude can be computed by further applying the additive constants. A6

9 DIAGRAMS ILLUSTRATING GEODETIC DATUMS North Pole Greenwich Meridian Latitude 22º N Origin : Trig Zero Equator Longitude 114º E HK80 Geodetic Datum Reference Ellipsoid : International Hayford (1910) North Pole Greenwich Meridian Origin λ Ø Hong Kong Equator WGS84 Datum Reference Ellipsoid: WGS 84 C1

10 Rifleman s Bolt 5.42 m Mean Sea Level 1.230m 0.146m HKPD Chart Datum Chart depth Vertical Datum Central Meridian N Earth Longitude Latitude 3 3 S The Transverse Mercator Projection C2

11 Evolution of Hong Kong Geodetic Datums and Map Projections Stage Geodetic Datum Projection and Local Grid System Pre 1963 Reference Ellipsoid: Clark 1880 Origin: Trig Zero 38.4 feet south of Hong Kong Observatory 1963 Reference Ellipsoid: Clark 1858 Re-triangulation Origin: Trig Zero 1976 Reference Ellipsoid: Clark 1858 Metrication and Origin: Trig Zero co-ordinates transformation 1980 Reference Ellipsoid: International Hayford (1910) Trilateration Origin: Trig Zero 1990 No change in definitions of the local geodetic datum. GPS observation Latitude, longitude and UTM Grid on WGS84 Datum are added to small scale maps for users convenience. Projection : Cassini Origin : Victoria Peak Co-ord : 5.18 ft N 0.38 ft E Grid Origin : Trig No. 1 Projection : Cassini Origin : Victoria Peak Co-ord : ft N ft E False Grid Origin : southwest Lantau Island Projection : Cassini Origin : Victoria Peak Co-ord : mn me False Grid Origin : 3550m east of false origin of HK 1963 Grid Projection : Transverse Mercator Origin : Trig No. 2 at Patridge Hill Co-ord : mn me False Grid Origin : Same as HK1976 Grid No change of map projection, projection origin and grid origin for local rectangular grid system. C3

12 SCHEMATIC DIAGRAM SHOWING TRANSFORMATION OF CO-ORDINATES OF GEODETIC DATUMS UTM Grid N WGS84, E WGS84 Projection Formulae equation (1) to (3) equation (3) to (5) Geographic Co-ordinate Φ WGS84, λ WGS84 WGS 84 DATUM Shifting Longitude Latitude Longitude Latitude Shifting Zone49Q +245mE -195mN Zone 50Q +260mE -205mN Zone49Q -245mE +195mN Zone50Q -260mE +205mN UTM Grid N HK80, E HK80 Projection Formulae equation (1) to (3) Geographic Co-ordinate Φ HK80, λ HK80 HK80 DATUM equation (3) to (5) Projection Formulae Equation (3) to (5) Equation (1) to (3) Transformation Accuracy UTM WGS UTM HK80 ± 5m Φ, λ WGS Φ, λ HK80 ± 0.2 UTM Φ, λ ± 5m/ 0.2 N, E Φ, λ HK80 ± 5m/ 0.2 HK1980 GRID N, E HK80 DATUM C4

13 UTM Grid Zone in Hong Kong ( WGS84 Datum SHENZHEN Zone 49Q SCALE 例 Zone 50Q KM Geodetic Datum HK80 WGS84 GQ GE HQ HE JV JK KV KK m to 117 E LANTAU ISLAND NEW TERRITORIES KOWLOON Zone 50Q HONG KONG m to 111 E utm gridzone destination 49Q GE HE Zone 49Q JK KK - C5 -

14 Contour Map Showing the Difference between Heights of WGS84 and Principal Datum N H WGS 84 = m H HKPD = m -0.5 Conversion of Heights -0.5 HWGS84 = H HKPD + diff - C6 -

15 DEFINITIONS OF TERMS Let P be the point to be converted. Central Meridian Projection origin N, E = Northing, Easting of P N 0, E 0 = Northing, Easting of projection origin O Φ, λ = Latitude, Longitude of P Φ 0, λ 0 = Latitude, Longitude of projection origin O m 0 = scale factor on the central meridian λ = longitude of P measured from central meridian in radian (i.e. λ λ 0 ) t = tan Φ M = meridian distance measured from the Equator to P M 0 = meridian distance measured from the Equator to origin of projection υ s = radius of curvature in the prime vertical = a / (1-e 2 sin 2 φ) 1/2 ρ s = radius of curvature in the meridian = a(1 - e 2 )/(1 - e 2 sin 2 φ) 3/2 ψ s = isometric latitude = υ s / ρ s a = semi-major axis of the reference ellipsoid f = flattening of the reference ellipsoid e 2 = first eccentricity of the reference ellipsoid = 2f - f 2 C7

16 Projection Formulae Φ, λ to Grid co-ordinates 2 λ N = N 0 + m 0 {(M M 0 ) + υ s (sin Φ) ( )(cos Φ)} --(Eq. 1) 2 3 λ E = E 0 + m 0 {υ s λ cos Φ + υ s 6 (cos 3 Φ)(ψ s t 2 ) } --(Eq. 2) Meridian distance, M M = a [A 0 Φ A 2 sin (2Φ) + A 4 sin (4Φ)] --(Eq. 3) 2 e 3e 4 where A 0 = A 2 = (e 2 4 e + ) A 4 = e Notes: 1. M 0 is computed using Eq. 3 by putting Φ=Φ 0 (Latitude of the projection origin.) 2. λ, Φ are in radian. Grid Co-ordinates to Φ, λ λ = λ 0 + secφ ρ ( E m 0 ν ρ 3 E ) - secφ ρ ( )(ψ 3 3 ρ + 2t 2 ρ ) --(Eq. 4) m ν 6 0 ρ 2 t ρ E Φ = Φ ρ ( ) ( ) --(Eq. 5) m 0 ρ ρ 2m0ν ρ where N = N N 0 E = E E 0 and Φ p is the latitude for which M = ( N + M 0 ) / m 0 Notes: 1. Φ p must be computed by iteration using Eq All other quantities, such as t p, ρ p, υ p, ψ p have their usual meanings but are computed usingφ p. C8

17 Parameters for Projection Formulae Para. WGS84 Datum (UTM Φ, λ) HK80 Datum (UTM Φ, λ) HK80 Datum (HK1980 Grid Φ, λ) N 0 0m N 0m N m N E m E m E m E Φ 0 Zone 49Q: 0 Zone 50Q: 0 λ 0 Zone 49Q: 111 E Zone 50Q: 117 E Zone 49Q: 0 Zone 50Q: 0 Zone 49Q: 111 E Zone 50Q: 117 E N E m M 0 0m 0m m υ s m m m ρ s m m m ψ s a m m m e x x x10-3 Notes: υ s, ρ s, ψ s are parameters of a point near the centroid of Hong Kong and given to simplify the transformation. Reference Example Datum Input Data Result Φ N UTM m N WGS84 λ UTM E m N Φ m E N m E λ E Φ N UTM m N λ E m E Φ N HK m N HK80 λ UTM E m N GRID Φ m E N m E λ E HK m N Φ N GRID m E λ E C9

### 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

### 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)

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### A guide to coordinate systems in Great Britain

A guide to coordinate systems in Great Britain An introduction to mapping coordinate systems and the use of GPS datasets with Ordnance Survey mapping D00659 v2.3 Mar 2015 Crown copyright Page 1 of 43 Contents

### Surveying & Positioning Guidance note 5

Surveying & Positioning Guidance note 5 Coordinate reference system definition recommended practice Revision history Version Date Amendments 2.1 January 2009 In example c corrected value for inverse flattening

### 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,

### 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

### 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

### 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,

### 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

### 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)

### The Chief Directorate: National

Surveying The South African Coordinate Reference System (Part 1) by Aslam Parker, Chief Directorate: National Geo-spatial Information This article will define the various elements of the South African

### CHAPTER 9 SURVEYING TERMS AND ABBREVIATIONS

CHAPTER 9 SURVEYING TERMS AND ABBREVIATIONS Surveying Terms 9-2 Standard Abbreviations 9-6 9-1 A) SURVEYING TERMS Accuracy - The degree of conformity with a standard, or the degree of perfection attained

### 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

### 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

### GEOGRAPHIC INFORMATION SYSTEMS CERTIFICATION

GEOGRAPHIC INFORMATION SYSTEMS CERTIFICATION GIS Syllabus - Version 1.2 January 2007 Copyright AICA-CEPIS 2009 1 Version 1 January 2007 GIS Certification Programme 1. Target The GIS certification is aimed

### 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

### 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

### 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

### 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

### 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)

### Maintaining High Accuracy in Modern Geospatial Data

Maintaining High Accuracy in Modern Geospatial Data Patrick Cunningham President info@bluemarblegeo.com www.bluemarblegeo.com +1 (207) 582 6747 Copyright 2010 Blue Marble Geographics Concepts Geodesy -

### 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

### 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

### 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

### 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

### 1. GLOBAL NAVIGATION SATELLITE SYSTEMS

1. GLOBAL NAVIGATION SATELLITE SYSTEMS The Global Navigation Satellite System (GNSS) is a constellation of satellites, transmitting signals for use in navigation and positioning applications, anywhere

### 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

### Math 215 Project (25 pts) : Using Linear Algebra to solve GPS problem

Due Thursday March 1, 2012 NAME(S): Math 215 Project (25 pts) : Using Linear Algebra to solve GPS problem 0.1 Introduction The age old question, Where in the world am I? can easily be solved nowadays by

### Beacon to Beacon Northern & Southern Maps

Beacon to Beacon Northern & Southern Maps Disclaimer: When using the Beacon to Beacon Guide booklets and/or the maps contained therein for commercial or non-commercial purposes, the Department of Transport

### GPS ALIGNMENT SURVEYS AND MERIDIAN CONVERGENCE

GPS ALIGNMENT SURVEYS AND MERIDIAN CONVERGENCE By Tomás Soler, 1 Member, ASCE, and Rudolf J. Fury 2 ABSTRACT: Since the advent of the Global Positioning System (GPS), geodetic azimuths can be accurately

### 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

### A guide to coordinate systems in Great Britain

A guide to coordinate systems in Great Britain An introduction to mapping coordinate systems and the use of GPS datasets with Ordnance Survey mapping Contents Section Page no 1 Introduction...3 1.1 Who

### 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

### 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

### 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

### 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

### ELEMENTS OF SURVEYING FOR CADASTRAL MAPPING

ELEMENTS OF SURVEYING FOR CADASTRAL MAPPING Chapter 4 2015 Cadastral Mapping Manual 4-0 Elements of Surveying and Mapping Utah's system of land surveying is the rectangular survey system as set forth on

### GPS LOCATIONS FOR GIS: GETTING THEM RIGHT THE FIRST TIME

GPS LOCATIONS FOR GIS: GETTING THEM RIGHT THE FIRST TIME Caroline Erickson and Pierre Héroux Geodetic Survey Division, Geomatics Canada Natural Resources Canada 615 Booth Street Ottawa, Ontario K1A 0E9

Plotting and Adjusting Your Course: Using Vectors and Trigonometry in Navigation ED 5661 Mathematics & Navigation Teacher Institute August 2011 By Serena Gay Target: Precalculus (grades 11 or 12) Lesson

### SESSION 8: GEOGRAPHIC INFORMATION SYSTEMS AND MAP PROJECTIONS

SESSION 8: GEOGRAPHIC INFORMATION SYSTEMS AND MAP PROJECTIONS KEY CONCEPTS: In this session we will look at: Geographic information systems and Map projections. Content that needs to be covered for examination

### Chapter 2. Mission Analysis. 2.1 Mission Geometry

Chapter 2 Mission Analysis As noted in Chapter 1, orbital and attitude dynamics must be considered as coupled. That is to say, the orbital motion of a spacecraft affects the attitude motion, and the attitude

### 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

### 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

### Understanding Map Projections

Understanding Map Projections Melita Kennedy ArcInfo 8 Copyright 1994, 1997, 1999, 2000 Environmental Systems Research Institute, Inc. All Rights Reserved. Printed in the United States of America. The

### 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

### Used by New Zealand. Emergency Services. Map Reading Guide 1:50 000. How to use a Topographic map

Used by New Zealand Emergency Services Map Reading Guide How to use a Topographic map 1:50 000 This guide provides information on: datums projections the New Zealand topographic map series Topo50 (and

### Land Information Management in Southern Africa Focus on technology management training in Surveying and Mapping in Namibia

Land Information Management in Southern Africa Focus on technology management training in Surveying and Mapping in Namibia Chris Paresi, Urban and Regional Planning and Geo-Information Management Department,

### Objectives After completing this section, you should be able to:

Chapter 5 Section 1 Lesson Angle Measure Objectives After completing this section, you should be able to: Use the most common conventions to position and measure angles on the plane. Demonstrate an understanding

### 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

### Geodetic Survey. LSD PQSL Series Download me: 10 October 2014 Sr Kenny CHAN

Download me: http://goo.gl/sm1dj1 LSD PQSL Series 2014 Geodetic Survey 10 October 2014 Sr Kenny CHAN BSc(Hons), MSc, MHKIS, MRICS, RPS(LS) Land Surveying Division The Hong Kong Institute of Surveyors APC

### 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,

### 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

### Calculation of Azimuth, Elevation and Polarization for non-horizontal aligned Antennas

Calculation of Azimuth, Elevation and Polarization for non-horizontal aligned Antennas Algorithm Description Technical Document TD-1205-a Version 1.1 23.10.2012 In Co-operation with 1 Objective Many SatCom

The Basics of Navigation Knowledge of map reading and the use of the compass is an indispensable skill of bushcraft. Without this skill, a walker is a passenger and mere follower on a trip. To become a

### GPS. Essentials of Satellite Navigation. Compendium. locate, communicate, accelerate. Abstract

GPS Essentials of Satellite Navigation Compendium locate, communicate, accelerate Abstract Theory and Principles of Satellite Navigation. Overview of GPS/GNSS Systems and Applications. www.u-blox.com Document

### GNSS and Heighting, Practical Considerations. A Parker National Geo-spatial Information Department of Rural Development and Land Reform

GNSS and Heighting, Practical Considerations A Parker National Geo-spatial Information Department of Rural Development and Land Reform GNSS Global Navigation Satellite Systems (GNSS) Global Positioning

### NC General Statutes - Chapter 102 1

Chapter 102. Official Survey Base. 102-1. Name and description. The official survey base for the State of North Carolina shall be a system of plane coordinates to be known as the "North Carolina Coordinate

### Caribbean datums and the integration of geographical data

Caribbean Journal of Earth Science, 37 (2003), 1-10. Geological Society of Jamaica. Caribbean datums and the integration of geographical data KEITH M. MILLER Department of Surveying and Land Information,

### COVER VERSION 10.4.12

COVER VERSION 10.4.12 P a g e 1 Copyright notice This ebook is provided, and may be used, free of charge. Selling this ebook in its entirety, or extracts from it, is prohibited. Obtain permission from

### 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

### 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

### North American Horizontal Datums. Jan Van Sickle

North American Horizontal Datums Jan Van Sickle http://www.holoscenes.com/cgi-bin/moin.cgi/easternobliquearc The New England Datum 1879 was the first geodetic datum of this type in the United States. The

APPENDIX D: SOLAR RADIATION The sun is the source of most energy on the earth and is a primary factor in determining the thermal environment of a locality. It is important for engineers to have a working

### 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

### Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis

Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis 2. Polar coordinates A point P in a polar coordinate system is represented by an ordered pair of numbers (r, θ). If r >

### ESTIMATION USABILITY OF THE FREE SOFTWARE FOR TRANSFORMATION OF GEODETIC COORDINATES BETWEEB LOCAL AND GLOBAL DATUMS-EXAMPLE OF THE ADRIATIC SEA

ESTIMATION USABILITY OF THE FREE SOFTWARE FOR TRANSFORMATION OF GEODETIC COORDINATES BETWEEB LOCAL AND GLOBAL DATUMS-EXAMPLE OF THE ADRIATIC SEA Duplančić Leder, Tea; Faculty of Civil Engineering and Architecture,

### 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

### 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,

### 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

### 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

CHAPTER 7 DEAD RECKONING DEFINITION AND PURPOSE 700. Definition and Use Dead reckoning is the process of determining one s present position by projecting course(s) and speed(s) from a known past position,

### 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

### 6. The greatest atmospheric pressure occurs in the 1) troposphere 3) mesosphere 2) stratosphere 4) thermosphere

1. The best evidence of the Earth's nearly spherical shape is obtained through telescopic observations of other planets photographs of the Earth from an orbiting satellite observations of the Sun's altitude

### 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

### 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

### THE FINNISH COORDINATE REFERENCE SYSTEMS

THE FINNISH COORDINATE REFERENCE SYSTEMS Published by the Finnish Geodetic Institute and the National Land Survey of Finland Editors: Marko Ollikainen, National Land Survey of Finland Matti Ollikainen,

### ALBERTA SURVEY CONTROL PRODUCTS MANUAL

ALBERTA SURVEY CONTROL PRODUCTS MANUAL Lands Division Land Dispositions Branch Geodetic Control Unit Edmonton 2007 Pub. No.: Ref. 85 ISBN: 0-7732-1298-1 For copies of this document, please contact: Geodetic

### 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

### Flight and Orbital Mechanics

Flight and Orbital Mechanics Lecture slides Challenge the future 1 Material for exam: this presentation (i.e., no material from text book). Sun-synchronous orbit: used for a variety of earth-observing

### 4.03 Vertical Control Surveys: 4-1

4. HORIZONTAL AND VERTICAL CONTROL 4.01 General: Sufficient horizontal and, if applicable, vertical control surveys shall be established by the Contractor for all photogrammetric mapping purposes. Prior