GIS and REMOTE SENSING

5) Selecting a suitable Map Projection

Matter and Photos are Credits of:

References

Knippers, R.A. (1998). Coordinate systems and Map projections. Non-published notes, Enschede, ITC.

Knippers, R.A. (1999). Geometric Aspects of Mapping. Non-published notes, Enschede, ITC.

Stefanovic, P. (1996) Georeferencing and Coordinate Transformations. Non-published notes. Enschede, ITC.

Every map must begin, either consciously or unconsciously, with the choice of a map projection and its parameters. The cartographer's task is to ensure that the right type of projection is used for any particular map. A well choosen map projection takes care that scale distortions remain within certain limits and that map properties match to the purpose of the map.

The selection of a map projection has to be made on the basis of:

shape and size of the area
position of the area
purpose of the map

The choice of the class of a map projection should be made on the basis of the shape and size of the geographical area to be mapped. Ideally, the general shape of a geographical area should match with the distortion pattern of a specific projection. For example, if an area is small and approximately circular it is possible to create a map that minimises distortion for that area on the basis of an Azimuthal projection. The Cylindrical projection should be the basis for a large rectangular area and a Conic projection for a triangular area.

The position of the geographical area determines the aspect of a projection. Optimal is when the projection centre coincides with centre of the area, or when the projection plane is located along the main axis of the area to be mapped (see example figure below).

Choice of position and orientation of the projection plane for a map of Alaska

Once the class and aspect of a map projection have been selected, the choice of the property of a map projection has to be made on the basis of the purpose of the map.

In the 15th, 16th and 17th centuries, during the time of great transoceanic voyaging, there was a need for conformal navigation charts. Mercator's projection -conformal cylindrical- met a real need, and is still in use today when a simple,straight course is needed for navigation.

Because conformal projections show angles correctly, they are suitable for sea, air, and meteorological charts. This is useful for displaying the flow of oceanic or atmospheric currents, for instance.

For topographic and large-scale maps, conformality and equidistance are important properties. The equidistant property, possible only in a limited sense, however, can be improved by using secant projection planes.

The Universal Transverse Mercator (UTM) projection is a conformal cylindrical projection using a secant cylinder so it meets conformality and reasonable equidistance for topographic mapping.

Other projections currently used for topographic and large-scale maps are the Transverse Mercator ( the countries of . Argentina, Colombia, Australia, Ghana, S-Africa, Egypt use it ) and the Lambert Conformal Conic (in use for France , Spain, Morocco, Algeria ). Also in use are the stereographic (the Netherlands ) and even non-conformal projections such as Cassini or the Polyconic (India).

Suitable equal-area projections for distribution maps include those developed by Lambert, whether azimuthal, cylindrical, or conical. These do, however, have rather noticeable shape distortions. A better projection is the Albers equal-area conic projection, which is nearly conformal. In the polar aspect, they are excellent for mid-latitude distribution maps and do not contain the noticeable distortions of the Lambert projections.

An equidistant map, in which the scale is correct along a certain direction, is seldom desired. However, an equidistant map is a useful compromise between the conformal and equal-area maps. Shape and area distortions are moderate.

The projection which best fits a given country is always the minimum-error projection of the selected class. The use of minimum-error projections is however exceptional. Their mathematical theory is difficult and the equidistant projections of the same class will provide a very similar map.

In conclusion, the ideal map projection for any country would either be an azimuthal, cylindrical, or conic projection, depending on the shape of the area, with a secant projection plane located along the main axis of the country or the area of interest.The selected property of the map projection depends on the map purpose.

Nevertheless for each country to use its own projection would make international co-operation in data exchange difficult. There are strong arguments in favour of using an international standard projection for mapping.

Activity You have been asked to produce a small-scale thematic map of your country showing the distribution of the population. Which projection class, aspect and property would you choose considering the location, size and shape of the country and the purpose of the map? Justify your answer!

The classification ... <<<<< >>>>>Map Projections in .....

Technorati Tags: stereographic,equidistance for topographic mapping,Transverse Mercator,aspect of a projection,class of a map

About Map Projection-Properties of Map Projections

2008-02-29T20:18:00.001-08:00

Navigation:

Scale distortions on...<<< >>>The classification of .....

Matter and Photos are Credits of:

References

Knippers, R.A. (1998). Coordinate systems and Map projections. Non-published notes, Enschede, ITC.

Knippers, R.A. (1999). Geometric Aspects of Mapping. Non-published notes, Enschede, ITC.

Stefanovic, P. (1996) Georeferencing and Coordinate Transformations. Non-published notes. Enschede, ITC.

The following properties would be present on a map projection without any scale distortions:

Areas are everywhere correctly represented
All distances are correctly represented.
All directions on the map are the same as on Earth
All angles are correctly represented.
The shape of any area is correctly represented

It is, unfortunately, impossible to have all these properties together in one map projection.

An equivalent map projection, also known as an equal-area map projection, correctly represents areas sizes of the sphere on the map. When this type of projection is used for small-scale maps showing large regions, the distortion of angles and shapes is considerable. The Lambert cylindrical equal-area projection is an example of an equivalent map projection.

The Lambert cylindrical equal-area projection as an example of an equivalent, cylindrical projection

An equidistant map projection correctly represents distances. An equidistant map projection is possible only in a limited sense. That is, distances can be shown at the nominal map scale -the given map scale- only from one or two points to any other point on the map or in certain directions. If the scale on a map is correct along all meridians, the map is equidistant along the meridians (e.g. the Plate Carree projection). If the scale on a map is correct along all parallels, the map is equidistant along the parallels.

The Plate Carree projection as an example of an equidistant, cylindrical projection

A conformal map projection represents angles and shapes correctly at infinitely small locations. Shapes and angles are only slightly distorted, as the region becomes larger. At any point the scale is the same in every direction. On a conformal map projection meridians and parallels intersect at right angles (e.g. Mercator projection).

The Mercator as an example of a conformal, cylindrical projection

Note A map projection may possess one of the three properties, but can never have all three properties. It can be proved that conformality and equivalence are mutually exclusive of each other and that a projection can only be equidistant (true to scale) in certain places or directions.

There are map projections with rather special properties:

On a minimum-error map projection the scale errors everywhere on the map as a whole are a minimum value (e.g. the Airy projection ).

On the Mercator projection, all rumb lines, or lines of constant direction, are shown as straight lines. A compass course or a compass bearing plotted on to a Mercator projection is a straight line, even though the shortest distance between two points on a Mercator projection - the great circle path - is not a straight line.

All rumb lines, or lines of constant direction, are shown as straight lines.

On the Gnomonic projection, all great circle paths - the shortest routes between points on a sphere - are shown as straight lines.

all great circles - the shortest routes between points on a sphere - are shown as straight lines

Technorati Tags: Gnomonic projection,minimum-error map projection,conformality,equidistant,equivalent,equal-area

About Map Projection-The Classification of Map Projection

2008-02-29T19:53:00.001-08:00

Navigation:

1) What is a Map Projection?
2) Scale distortions on a Map
3) Properties of Map Projections
4) The classification of Map Projections
5) Selecting a suitable Map Projection
6) Map Projections in common use

Matter and Photos are Credits of:

References
Knippers, R.A. (1998). Coordinate systems and Map projections. Non-published notes, Enschede, ITC.
Knippers, R.A. (1999). Geometric Aspects of Mapping. Non-published notes, Enschede, ITC.
Stefanovic, P. (1996) Georeferencing and Coordinate Transformations. Non-published notes. Enschede, ITC.
Read more »

About Map Projection-Scale Distortions on A Map

2008-02-29T19:26:00.001-08:00

Navigation:

Matter and Photos are Credits of:

References

Knippers, R.A. (1998). Coordinate systems and Map projections. Non-published notes, Enschede, ITC.

Knippers, R.A. (1999). Geometric Aspects of Mapping. Non-published notes, Enschede, ITC.

Stefanovic, P. (1996) Georeferencing and Coordinate Transformations. Non-published notes. Enschede, ITC.

2) Scale distortions on a Map

The transformation from the curved reference surface of the earth to the flat plane of the map is never completely successful. Look at the diagram below. By flattening the curved surface of the sphere onto the map the curved surface is stretched in a non-uniform manner.

It appears that it is impossible to project the Earth on a flat piece of paper without any locational distortions, therefore without any scale distortions.

Projection plane tangent to the reference surface

The distortions increase as the distance from the central point of the projection increases. Placing the map plane so that it intersects the reference surface will reduce and mean out the scale errors.

Since no map projection maintains correct scale throughout the map, it may be important to know the extent to which the scale varies on a map.

On a world map, the distortions are evident where landmasses are wrongly sized or out of shape and the meridians and parallels do not intersect at right angles or are not spaced uniformly. Some maps have a scale reduction diagram, which indicates the map scale at different locations, helping the map-reader to become aware of the distortions.

On maps at larger scales, maps of countries or even city maps, the distortions are not evident to the eye. However, the map user should be aware of the distortions if he or she computes distances, areas or angles on the basis of measurements taken from these maps.

Scale distortions can be measured and shown on a map by ellipses of distortion. The ellipse of distortion, which is also known as Tissot's Indicatrix, shows the shape of an infinitesimally small circle with a fixed scale on the earth as it appears when plotted on the map. Every circle is plotted as circle or an ellipse or, in extreme cases, as a straight line.

The size and shape of the ellipse shows how much the scale is changed and in what direction. On map projections where all indicatrices remain circles, but the sizes change, the scale change is the same in all directions at each location. These conformal projections represent angles correctly and have no local shape distortion ( e.g. the Mercator projection ).

The indicatrices on the diagram below are circles along the equator. There are no scale distortions along the equator. The indicatrices elsewhere are ellipses with varying degrees of flattening. The projection represents areas correctly - all ellipses have the same area - but angles and, consequently, shapes are not represented correctly.

Lambert Cylindrical equal-area projection with ellipses of distortion

Scale distortions can also be shown on a map by a scale factor. A scale factor smaller than 1 indicates that the scale is smaller than the nominal scale, the scale given on the map. A scale factor larger than one indicates that the scale is larger than the nominal scale.

For example, on the UTM projection a scale factor of 0.99960 has been given to the central meridian of a UTM zone. This means that 1000m measured on the ground becomes 999.6m on the map surface along the central meridian. E.g. the actual map scale along the central meridian will be 1:10,004 (10000 / 0.9996) at a nominal map scale of 1:10,000, so smaller than the nominal scale.

Note Scale distortions can remain within certain limits by choosing the right map projection

What is a Map Projection? <<<< >>>> Properties of Map Projections

Technorati Tags: Mercator,Projection plane tangent,Scale distortions on a Map,scale errors,Tissot's Indicatrix,ellipse,equator,Lambert Cylindrical,scale factor,UTM projection

About Map Projection-What is a Map Projection?

2008-02-29T19:21:00.001-08:00

This article consists of six parts matter that are;

READ FULL THIS ARTICLE HERE

Matter and Photos are Credits of:

References

Knippers, R.A. (1998). Coordinate systems and Map projections. Non-published notes, Enschede, ITC.

Knippers, R.A. (1999). Geometric Aspects of Mapping. Non-published notes, Enschede, ITC.

Stefanovic, P. (1996) Georeferencing and Coordinate Transformations. Non-published notes. Enschede, ITC.

1) What is a Map Projection?

To produce a map of the world in a convenient way we make use of map projections. A map projection is any transformation between the curved reference surface of the earth and the flat plane of the map.

We can as well define a map projection as a set of equations which allows us to transform a set of Ellipsoidal Geographic Coordinates (j, l) representing positions on the reference surface of the earth to a set of Cartesian Coordinates (x, y) representing positions on the two-dimensional surface of the map (see figure above) .

For each map projection the following equations are available:

X,Y = f ( j, l ) Forward equation

j, l = f ( X,Y ) Inverse equation

The forward equations are used to transform geographic coordinates - latitude (j) and longitude (l) - into Cartesian coordinates (X,Y), while the inverse equations of a map projection are used to transform Cartesian coordinates into geographic coordinates. These equations have a significant role in projection change (see section on Coordinate transformations ).

Some examples of map projection equations are given below:

Map projection equations can be considerably more complicated than those introduced here, for example, when an ellipsoid is introduced as reference surface. J. P. Snyder gives an overview of map projection equations in his book entitled 'Map Projections used by the U.S. Geological Survey'. A number of equations are given at World of Mathematics.

Map projection equations have a number of parameters such as

radius of the sphere (R) or equatorial (a) and polar radius (b) of the reference ellipsoid;
geodetic datum;
origin of the coordinate system;
false easting and northings;
central meridian ( lo ), standard parallels ( j1, j2 ) or centre of projection ( j1, lo ) ;
scale factor at the central meridian or standard parallels.

Information about the projection parameters is required to define a countries spatial reference system.

Activity A point P is located on the Stereographic projection at 60o N and 130o E . The sphere is taken as the reference surface of the earth. Use the equations given above to obtain the Cartesian coordinates for point P. The origin of the coordinate system is located on the North Pole (Radius (R) = 6371000 m, Central Meridian (lo) = 0o , equal to the Greenwich meridian).

NEXT>>>>Scale distortions on a Map

Technorati Tags: World of Mathematics,Central Meridian,Map Projection,J.P. Snyder,Ellipsoidal Geographic Coordinates,Cartesian Coordinates,U.S Geological Survey,Spatial Reference System

Implementation of cellular automata models in a raster GIS dynamic modeling environment: an example using the Clarke Urban Growth Model

2008-02-19T03:22:00.001-08:00

Author:

Matthew J. Ungerer

Abstract

This paper discusses some of the issues involved in implementing a cellular automaton (CA) model of urban growth in a fully-integrated raster Geographic Information System (GIS) dynamic modeling environment. CA models are dynamic spatial models in which the basic unit is the cell, situated in a two dimensional plane. CA models are thus very similar to raster GIS in many respects. Work by Batty, White and others has shown that cellular automata (CA) models are simple and effective means for creating portable models of urban growth. The Clarke Urban Growth model is a CA model which has been calibrated and used to predict the urban growth in several urban areas. Using only the built-in functions of the PCRaster GIS package, an approximation of the Clarke Urban Growth Model can be implemented using only about 200 lines of code. The GIS model has the same input maps and growth parameters, very similar growth rules and produces the same output files as the original C-code version. Thus the output files from the two models can be compared to examine if the models are functionally equivalent. The C-code version and the PCRaster version of the Clarke Urban Growth model were each run ten times using the same input maps and model parameters, for a period of 20 years. The last output file (i.e. year 20) from each of the ten runs of the C-code version was compared to the last output file from each of the ten runs of the PCRaster version. The results of the comparison indicate that the output files from the two versions of the model do differ statistically. However, it is also apparent from a visual comparison of the output files in animation format that the output files are remarkably similar. Modeling using a dynamic modeling language in a GIS does not give the modeler the same degree of control as an ordinary computer language, but has several advantages including a reduced development time, enhanced ease of use, and access to the functionality of the GIS for display and file management. A dynamic modeling language tightly coupled with a raster GIS offers an integrated environment that makes it relatively simple to implement cellular automata models, as well as other models of continuous phenomena which vary in time as well as space.

images credit: colorado.edu

Technorati Tags: Cellular automata,human-environment interactions,urban development impacts,GIS,dynamic model,integrated modeling

The application of a cellular automaton model for predicting deforestation: patterns and processes of LULCC in the Ecuadorian, Amazon

2008-02-19T03:10:00.001-08:00

Abstract

Global change research includes an extensive body of literature covering population-environment interactions focusing on the central issues of migration and demography, environmental site and situation, and socioeconomic structures addressed within a spatially-explicit but temporally dependent form. Quite often this is simply because neither the data nor the modeling methodology combine well to effectively address uncertainty and spatially defined time-series data within a nonlinear context. In this research, a cellular automaton model is proposed as an effective framework for the predictive modeling of landuse/landcover change (LULCC) associated with the spatial pattern and rates of deforestation and agricultural extensification in the Ecuadorian Amazon. The model employs user-defined rules based upon spatially explicit probabilities of LULCC derived from remotely sensed time-series data and both biophysical and socioeconomic regional characteristics to produce an output image of the "anthropomorphized" landscape over time and space.

Author: Joseph P. Messina, Stephen J. Walsh

VIEW THE COMPLETE ARTICLE HERE

Technorati Tags: Cellular automata,landscape dynamics,Amazon,deforestation,agricultural extensification,tropical forests,remote sensing

About Map Projection-Map Projection in Common Use

2008-02-12T00:13:00.001-08:00

Navigation: