lecture 10 - 14 - kuet 1281... · 2019. 2. 5. · lecture 10 - 14: map projections and coordinate...

Lecture 10 - 14: Map Projections and Coordinate System

URP 1281 Surveying and Cartography

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December 27, 2015

Course Teacher: Md. Esraz-Ul-Zannat Assistant Professor

Department of Urban and Regional Planning Khulna University of Engineering & Technology

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These slides are aggregations for better understanding

of Cartography. I acknowledge the contribution of all

the authors and photographers, power point slides

from where I tried to accumulate the info and used for

better presentation.

ACKNOWLEDGEMENT

To introduce with the Map Projections and

Coordinate System in relation to cartography.

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OBJECTIVE OF THE CLASS

Spatial Reference Coordinate System

& Map Projection

Outline

1. Geodesy 2. Datum 3. Coordinate System 4. Projection System 5. Common Projection System in

Bangladesh

“Every map user and maker should have a basic understanding of projections no matter how much computers seem to have automated the process.”

- John P. Snyder

Spatial Reference = Datum +

Projection +

Coordinate system

• For consistent analysis the spatial reference of

data sets should be the same.

• ArcGIS does projection on the fly so can display

data with different spatial references properly if

they are properly specified.

• ArcGIS terminology

– Define projection. Specify the projection for some

data without changing the data.

– Project. Change the data from one projection to

another.

Merriam-Webster: a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and with the description of variations of its gravity field

Geodesy

Shape of the Earth

We think of the earth as a sphere

It is actually a spheroid, slightly larger in radius at the

equator than at the poles

Ellipse

P

F2

O

F1

a

b

X

Z

An ellipse is defined by:

Focal length =

Distance (F1, P, F2) is

constant for all points

on ellipse

When = 0, ellipse =

circle

For the earth:

Major axis, a = 6378 km

Minor axis, b = 6357 km

Flattening ratio, f = (a-b)/a

~ 1/300

Ellipsoid or Spheroid Rotate an ellipse around an axis

O

X

Z

Y a a

b

Rotational axis

Basic Terminology Projections/Coordinate System

Meridian of longitude

Parallel of latitude

X

Y

Z N

E W

P

O R

•

Greenwich

meridian

=0°

•

Equator =0°

•

•

- Geographic longitude - Geographic latitude

R - Mean earth radius

O - Geocenter

Cutting Plane of a Meridian

P

Meridian

Equator

Prime Meridian

Eratosthenes

Egypt about 240 BC

Syene

Alexandri

a

7 º 12’

or

1/50th

of a circle

Eratosthenes had observed

that on the day of the summer

solstice, the midday sun shone

to the bottom of a well in the

Ancient Egyptian city of

Swenet (known in Greek as

Syene).

Sun not directly

overhead

To these observations,

Eratosthenes concluded

that the circumference of

the earth was 50 x 500

miles, or 25000 miles.

The accepted value along the equator is

24,902 miles, but, if you measure the earth

through the poles the value is 24,860 miles

He was within 1% of today’s accepted value

Eratosthenes' conclusions were highly

regarded at the time, and his estimate of the

Earth’s size was accepted for hundreds of

years afterwards.

He knew that at the same time,

the sun was not directly

overhead at Alexandria;

instead, it cast a shadow with

the vertical equal to 1/50th of a

circle (7° 12').

He also knew that

Alexandria and Syene

were 500 miles apart

15/27

P

= the angle between a cutting plane on the prime meridian and the cutting plane on the meridian through the point, P

0°E, W

90°W (-90 °)

180°E, W

90°E (+90 °)

-120°

-30°

-60°

-150°

30°

-60°

120°

150°

l P

Basic Terminology Longitude,

Longitude

West

Longitude

Meridians of longitude 0° longitude Prime Meridian

East

longitude

Grenwich, England

(1) Take a point S on the surface of the ellipsoid and define there the tangent plane, mn (2) Define the line pq through S and normal to the tangent plane (3) Angle pqr which this line makes with the equatorial plane is the latitude f, of point S

O f

S m

n

q

p

r

Basic Terminology Latitude, f

Latitude

Parallels of

latitude

0° latitude

north

latitud

e

south

latitud

e

90°

N

equato

r

Latitude-Longitude

• Not uniform units of measure

• Meridians converge at the Poles

1° longitude at Equator = 111 km at 60° lat. = 55.8 km at 90° lat. = 0 km

1° latitude at Equator = 111 km at 90° lat. = 112 km

Primitive Idea – Fully Sphere

Newton Reasoned – Spheroid (ellipsoid)

Model of Earth’s Shape

A spheroid is defined either by the semi-major axis a,

and the semi-minor axis b, or by the flattening.

The flattening f: f=a-b/a

The flattening usually defined by

1/f

1/f=1/300

The spheroid parameters for World Geodetic System-984 (WGS84) are: a = 6378137.0 meters

b = 6356752.31424

meters

1/f = 298.257223563 The parallels and meridians of latitude and longitude

together mark an invisible three dimensional framework of

reference on the globe known as the graticule.

Graticule

A spheroid approximates the shape of the earth, a datum

defines the position of the spheroid relative to the centre of

the earth.

Two types of Datums are Global Datum and Local Datum

Datum

A point, line, or surface used as a reference, as in

surveying, mapping, or geology.

Datum

Datum

• A Datum is a spheroid, plus the definition of the relationship between the Earth and the coordinates on the spheroid.

• Link a spheroid to a location on the earth

• Define the origin and orientation of the coordinate systems used to map the earth

• There are many datums Local:

NAD 27 Datum, uses Clarke 1866 spheroid NAD 83 Datum, uses GRS 1980 spheroid Everest Bangladesh 1937

Global WGS 84 Datum, uses WGS 1984 spheroid

• In addition to being in the same projection, data themes must also be in the same datum.

• Datum is of two types, Horizontal and Vertical

Coordinate Systems

• There are many different coordinate systems, based on a

variety of geodetic datums, projections, and units in use.

In context of GIS, Coordinate System is of two type…..

• Geographic coordinate systems (no projection): Spheroid

(or Ellipsoid)-based systems, local systems.

• Projected coordinate systems: world, continental, polar,

US National Grids, UTM, state plane.

Types of Coordinate Systems

• (1) Global Cartesian coordinates (x,y,z) for the whole earth

• (2) Geographic coordinates (f, l, z)

• (3) Projected coordinates (x, y, z) on a local area of the earth’s surface

• (4) Polar coordinates ((r,θ)) on a local area of the earth’s surface

• The z-coordinate in (1) and (3) is defined geometrically; in (2) the z-coordinate is defined gravitationally

Global Cartesian Coordinates (x,y,z)

O

X

Z

Y

Greenwich

Meridian

Equator

•

Geographic and Projected Coordinates

(f, ) (x, y) Map Projection

Coordinate Systems vs. Map Projections

• A map projection is a method or a type of equation used to transform three-dimensional coordinates on the earth to two-dimensional coordinates on the map.

• A coordinate system usually includes the specification of a map projection, plus the three dimensional model of the Earth to be used, the distance units to be used on the map, and information about the relative positions of the two dimensional map and the model of the Earth.

Geographic Coordinates (f, l, z)

• Latitude (f) and Longitude () defined using an ellipsoid, an ellipse rotated about an axis

• Elevation (z) defined using geoid, a surface of constant gravitational potential

• Earth datums define standard values of the ellipsoid and geoid

• A reference system using latitude and longitude to define

the location of points on the surface of a sphere or spheroid

– decimal degrees (DD) -92.5

– degrees/minutes/seconds (DMS) 92° 30’ 00” W

Geographic Coordinate System

- Earth is not a sphere - Poles are flattened

- Bulges at equator

Earth is a spheroid……or ellipsoid

An ellipsoid of revolution is the figure

which would be obtained by rotating an

ellipse about its shorter axis. The

GRS80 ellipsoid is used for the NAD83.

a= 6378137.00000 meters

b= 6356752.31414 meters

f= 1/(a-b)/a = 298.2572220972

So we squash the

sphere to fit better at

the poles.

This creates a

spheroid

a = 6,378,137.00000

m

b =

6,3

56,7

52.3

1414

m

Close Fit At The

Equator

But The Poles Are

Out

NAD83 uses the

GRS80 Ellipsoid

GRS80 fits geoid

to about +/- 300’

32/27

GRS80-WGS84 CLARKE 1866

GEOID

Earth Mass

Center

Approximately

236 meters

Local vs. Global Reference Ellipsoid

UNITED STATES

ELLIPSOID DEFINITIONS

CLARKE 1866

a = 6,378,206.4 m 1/f = 294.97869821

GEODETIC REFERENCE SYSTEM 1980 - (GRS 80)

a = 6,378,137 m 1/f = 298.257222101

WORLD GEODETIC SYSTEM 1984 - (WGS 84)

a = 6,378,137 m 1/f = 298.257223563

BESSEL 1841

a = 6,377,397.155 m 1/f = 299.1528128

Local vs. Global

Reference Ellipsoid

Projected Coordinate Systems

• Define locations on a 2-D surface

• Traditional planar coordinates

• Can allow easy measurement, calculation, and/or visual interpretation of distances and areas

• A map projection is the systematic transformation of locations on the earth (latitude/longitude) to planar coordinates

• The basis for this transformation is the geographic coordinate system (which references a datum)

• Map projections are designed for specific purposes

• Projected Coordinate Systems mathematically transform the 3 dimensional earth so that it can be modeled in 2 dimensions.

• This results in distortion

• Different projections are used for different areas and purposes

Projected Coordinate Systems

Vertical Datum

Definition of Elevation

Elevation Z

•

P z = zp

z = 0

Mean Sea level = Geoid

Land Surface

Elevation is measured from the Geoid

Gravity: Local Attraction

Unfortunately, the density of the earth’s crust is not uniformly the same. Heavy

rock, such as an iron ore deposit, will have a stronger attraction than lighter

materials. Therefore, the geoid (or any equipotential surface) will not be a simple

mathematical surface.

Vertical Datums The Geoid

What is the GEOID?

• “The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, global mean sea level.”

• Can’t see the surface or measure it directly.

• Modeled from gravity data.


Equipotential

Surfaces Topography


42/27

Ellipsoid vs. Geoid

• Ellipsoid

– Simple Mathematical Definition

– Described by Two Parameters

– Cannot Be 'Sensed' by Instruments

• Geoid

– Complicated Physical Definition

– Described by Infinite Number of Parameters

– Can Be 'Sensed' by Instruments

Vertical Datums

43/27

Ellipsoid vs. Geoid

Vertical Datums

High

Density

Low

Density

ellipsoid geoid Earth’s

surface

44/27

N = separation between

geoid and ellipsoid

(Geoid03)

h = elevation

relative to

ellipsoid

(GRS80) This is what we reference

elevations to. These are

the elevations you get

from the NGS datasheets

and traditionally were

obtained from geodetic

leveling h = N- H

The geoid is the

equipotential surface

of the earth’s

attraction and rotation

which, on the

average, coincides

with mean sea level in

the open ocean.

They are instead

referenced to the

GRS80 ellipsoid, that

squashed sphere that

best fits the earth and

is used for NAD83

Let’s take a look at the difference

between NAVD88 elevations

(orthometric heights) and the

ellipsoid heights from GPS

GPS heights are not related

to either orthometric or

hydraulic/tidal elevations.

To convert GPS derived

heights to NAVD88 you

must use the latest geoid

model (currently Geoid03)

H = elevation relative to geoid

(orthometric or NAVD88)

46/27

Geoid Model

47/27

H is measured traditionally h is measured with GPS Observations N is modeled using Gravity Models

Vertical Datums

H = h + N

Map Projection

Basics of Map Projections

• A map projection is a mathematical model for conversion of locations from a three-dimensional earth surface to a two-dimensional map representation. This conversion necessarily distorts some aspect of the earth's surface, such as area, shape, distance, or direction.

• Every projection has its own set of advantages and disadvantages. There is no "best" projection. Some distortions of conformality (shape), scale, distance, direction, and area always result from this processes. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties

• The mapmaker must select the one best suited to the needs, reducing distortion of the most important features.

• Mapmakers and mathematicians have devised almost limitless ways to project the image of the globe onto a flat surface (paper).

Map Projections: Distortion

• Converting from 3-D globe to flat surface causes distortion

• Types of distortion

– Shape

– Area

– Distance

– Direction

• No projection can preserve all four of these spatial properties

• If some properties are maintained,

errors in others may be exaggerated

Map Projection

Several map projection methods are available, but all distort one or more of its

properties of the Earth surface:

Shape, Area, Distance, and Direction

For applying an optimal map projection, it depends on the property precision

and the size of the study area.

The projections can be classified into four principal

methodological categories:

• Azimuthal : An azimuthal projection transform

the graticule onto a tangent plane.

• Cylindrical : A cylindrical projection results in a

rectangular-shaped graticule.

• Conic : A conic projection generates a fan-

shaped graticule.

• Pseudo-cylindrical : The pseudo-cylindrical

properties are not truly cylindrical, but are

derived mathematically with certain properties

resembling these.

Map Projection

Common GIS Projections

Mercator- The Mercator projection has straight meridians and parallels that intersect at right

angles. Scale is true at the equator or at two standard parallels equidistant from the equator.

The projection is often used for marine navigation because all straight lines on the map are lines

of constant azimuth.

Transverse Mercator - Transverse Mercator projections result from projecting the sphere onto a

cylinder tangent to a central meridian. Transverse Mercator maps are often used to portray

areas with larger north-south than east-west extent. Distortion of scale, distance, direction and

area increase away from the central meridian.

Universal Transverse Mercator (UTM) – The Universal Transverse Mercator (UTM) projection

is used to define horizontal, positions world-wide by dividing the surface of the Earth into 6

degree zones, each mapped by the Transverse Mercator projection with a central meridian in

the center of the zone. UTM zone numbers designate 6 degree longitudinal strips extending

from 80 degrees South latitude to 84 degrees North latitude. UTM zone characters designate 8

degree zones extending north and south from the equator.

Lambert Conformal Conic – Area, and shape are distorted away from standard parallels.

Directions are true in limited areas. This projection is one of the best for middle latitudes

because distortion is lowest in the band between the standard parallels. It is similar to the Albers

Conic Equal Area projection except that the Lambert Conformal Conic projection portrays shape

more accurately than area.

Classes of Map projections

Physical models:

• Cylindrical projections

(cylinder)

- Tangent case

- Secant case

• Conic Projections (cone)

- Tangent case

- Secant case

• Azimuthal or planar projections (plane)

- Tangent case

- Secant case

Distortion properties:

Conformal (preserves local

angles and shape)

Equal area or equivalent (area)

Equidistant (scale along a center line)

Azimuthal (directions)

Projections Preserve Some Earth Properties

• Area - correct earth surface area (Albers Equal Area) important for mass balances

• Shape - local angles are shown correctly (Lambert Conformal Conic)

• Direction - all directions are shown correctly relative to the center (Lambert Azimuthal Equal Area)

• Distance - preserved along particular lines

• Some projections preserve two properties

Map Projection

Map projections can be divided into three spatial property types:

Equal area projection: preserves the property of area. On an equivalent projection all parts

of the earth's surface are shown with the correct area. However, latitudinal distances are

never accurate.

Conformal projection: preserves equal shape as right angles between lines of latitude and

longitude and are primarily used because they preserve direction. Area is always distorted on

conformal maps.

Equidistant Azimuthal: Only preserves correct distance relationships along a few lines on

the map. These are seldom used in GIS.

The other type of map projection consists of projections that are neither equal-area nor

conformal, but are usually some compromise between these two properties.

Two systems are mostly used in Bangladesh

Bangladesh Transverse Mercator (BTM) Projection

Lambert Conformal Conic (LCC) Projection System

Cylindrical Projections (Mercator)

Transverse

Oblique

The lines where

the cylinder is

tangent or

secant are the

places with the

least distortion.

Panhandle of

Alaska

Conic Projections

(Lambert)

The lines where the

cone is tangent or

secant are the

places with the

least distortion.

Lambert Projection Transverse Mercator Projection

East-West North-South

EARTH

IMAGINARY CYLINDER

A

C

B

D

A

C D

B

IMAGINARY CONE

EARTH

•Conformal (preserve distances and directions within defined limits) 158 miles for 1:10,000

158

miles

wide

Conical & Cylindrical Projections

Cylindrical Transverse Cylindrical Oblique Cylindrical Secant Cylindrical

Conical Secant Conical Planar Secant Planar

Different Map Projection

Common Map Projections Used In GIS

• Lambert Conformal Conic Projection (1772) - Distances true only along standard parallels; reasonably accurate

elsewhere in limited regions. Directions reasonably accurate. Distortion of shapes and areas minimal at, but increases away from standard parallels. Shapes on large-scale maps of small areas essentially true Used for maps of North America. USGS Base Maps for 48 conterminous States with standard parallels 33 N, and 45 N (maximum scale error 2 ½ %). for TOPO maps, standard parallels vary.

- Used for many topographic maps and for State Base Map series.

Lambert Conformal Conic Projection

Lambert Conic Projection (Northern Hemisphere)

North Standard

Parallel

South Standard

Parallel

Parallel of

Grid Origin

(Base Parallel)

Central Meridian Polar Axis

Lines of Contact

If using a two standard parallel case, the two standard parallels.

If using a single standard parallel case, and the scale factor is 1.0, the

standard parallel.

If using a single standard parallel and the scale factor is less than 1.0, the

cone cuts the spheroid along two parallels.

Linear Graticules

All meridians.

Properties

Shape

All graticular intersections are 90°. Small shapes are maintained.

Area

Minimal distortion near the standard parallels. Areal scale is reduced

between standard parallels and increased beyond them.

Direction

Local angles are accurate throughout because of conformality.

Distance

Correct scale along the standard parallels. The scale is reduced between

the parallels and increased beyond them.

Limitations

Best for regions predominantly east–west in extent and located in the

middle north or south latitudes. Total latitude range should not exceed 35°.

Map Projection (LCC)

Map Projection Parameters

Spheroid : Name of the Spheroid

Central Meridian : defines the origin of the x-coordinate

Single Standard Parallel:

If using a single standard parallel case, and the scale factor is 1.0, the standard parallel.

1st standard parallel (Besides Equator) :

for conic projections to define the latitude lines where the scale is 1.0

2nd standard parallel (Besides Pole) :

for conic projections to define the latitude lines where the scale is 1.0

Latitude of Origin : defines the origin of the y coordinates

False Easting : linear value applied to the origin of the x coordinates

False Northing : linear value applied to the origin of the y coordinates

Scale Factor : scale factor be is used by the projection System

Following Projection Parameters are mostly used in different Projection Systems:

Applicable for LCC projection

Map Projection (Mercator)

To eliminate the necessity for using negative

numbers to describe a location, the east-west origin

is placed 500,000 meters west of the central

meridian. This is referred to as the zone’s ‘false

origin’. The zone doesn't extend all the way to the

false origin.

Map Projection (Mercator)

Universal Transverse Mercator (UTM)

• Developed by military

• Grid system

• Earth divided into 60 zones

• Great for small areas

– minimal map distortion

– distortion greater at edge of zones

Universal Transverse Mercator (UTM) Coordinate System

• UTM system is transverse-secant cylindrical projection, dividing the surface of the Earth into 6 degree zones with a central meridian in the center of the zone. each one of zones is a different Transverse Mercator projection that is slightly rotated to use a different meridian. UTM zone numbers designate 6 degree longitudinal strips extending from 80 degrees South latitude to 84 degrees North latitude. UTM is a conformal projection, so small features appear with the correct shape and scale is the same in all directions. (all distances, directions, shapes, and areas are reasonably accurate ). Scale factor is 0.9996 at the central meridian and at most 1.0004 at the edges of the zones.

• UTM coordinates are in meters, making it easy to make accurate calculations of short distances between points (error is less than 0.04%)

• Used in USGS topographic map, and digital elevation models (DEMs)

• Although the distortions of the UTM system are small, they are too great for some accurate surveying. zone boundaries are also a problem in many applications, because they follow arbitrary lines of longitude rather than boundaries between jurisdictions.

UTM Coordinate Systems

Allows projection of a

spherical surface onto a

flat surface

A plane coordinate system to

relate the coordinates of points

on earth’s curved surface with

the coordinates of the same

points on a plane or flat surface

Zone 1

International Date

Line - 180

Equator

Zone 18 o

Universal Transverse Mercator

UTM Zone Numbers

UTM Zone in Bangladesh

UTM 45 84N to 90N

UTM 46 90N to 96N

Projection : Transverse Mercator

False Easting : 500000.000000 (m)

False Northing : 0.000000 (m)

Central Meridian : 87.000000 (dd)

Scale Factor : 0.99960000

Latitude of Origin : 0.000000 N

Linear Unit : Meter (1.000000)

Geographic Coordinate

System

: WGS 84

Angular Unit : Degree (0.017453292519943299)

Prime Meridian : Greenwich (0.000000000000000000)

Datum : WGS 84

Spheroid : WGS 84

Semi major Axis : 6378137.000000000000000000

Semi minor Axis : 6356752.314245179300000000

Inverse Flattening : 298.257223563000030000

UTM Parameters for Zone 45


False Easting : 500000.000000 (m)

False Northing : -2000000.000000 (m)






System

: Everest Bangladesh



Datum : Everest Bangladesh

Spheroid : Everest Bangladesh Adjustment 1937

Semi major Axis : 6377276.344999999700000000

Semi minor Axis : 6356075.413140240100000000


BTM Projection Parameters


False Easting : 500000.000000 (m)







System




Datum : Gulshan 303

Spheroid : Everest Bangladesh Adjustment 1937

Semi major Axis : 6377276.344999999700000000

Semi minor Axis : 6356075.413140240100000000


Gulshan 303/ Bangladesh Transverse Mercator Projection Parameters


False Easting : 500000.000000 (m)







System

: WGS 84



Datum : WGS 84

Spheroid : WGS 84

Semi major Axis : 6378137.000000000000000000

Semi minor Axis : 6356752.314245179300000000


BUTM Projection Parameters

Projection : Lambert Conformal Conic (LCC)

False Easting : 2743185.699 (m)


Central Meridian : 90 00 00 (dd mm ss)

1st standard parallel : 23 09 00 (dd mm ss)

2nd standard parallel : 28 48 00 (dd mm ss)

Latitude of Origin : 26 00 00 (dd mm ss)



System




Datum : Everest Bangladesh

Spheroid : Everest Bangladesh 1937

Semi major Axis : 6377276.344999999700000000

Semi minor Axis : 6356075.413140240100000000


LCC Projection Parameters for Bangladesh

Projection System used in Bangladesh

€ LCC – LGED, SRDI, BARC, RHD

€ UTM – BIWTA, BUET, JU, WARPO

€ BTM – IWM, BADC, BARC, BBS, CEGIS,

Projection System is required to Transform the map from

Geographic Coordinate to Linear Coordinate system

Projection System Used in Bangladesh

Parameters of different projection system

Thank You For being with me

81

lecture 10 - 14 - kuet 1281... · 2019. 2. 5. · lecture 10 - 14: map projections and coordinate...

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