# How to detect coordinate reference system (CRS)? - I cannot display two vector layers in QGIS at the same time!

When I in QGIS try to display layer (a) together with another layer (b) that differ in their CRS it doesn't work. Both are vector shapefiles. I have tried both with using QGIS 'on the fly' CRS transformation and by saving the two different layers in the CRS- format of the other layer. How do I display both layers at the same time?

**About layer (a)**

I have gotten a .shp file sent to me (together with .dbf,.sbn, .shx, and in addition .sbx, .TAB, .idm and .ind files - which I don't really know what it is). There is no documentation, but I really want to use the map! QGIS displays it nicely as CRS: WGS 84, EPSG:4326. It maps Sweden. It's metainfo is:

xMin,yMin 4062955.57,3164156.34 : xMax,yMax 4646582.49,4704921.56

**About layer (b)**

I trust the other layer (b) more- it is documented to be SWEREF99 TM, EPSG:3006 with metainfo:

xMin,yMin 269616.42,6137945.67 : xMax,yMax 749134.54,6908654.00

**More on what happens**

I cannot convert layer (a) to EPSG:3006 since I get an error message. When I convert layer (b) to EPSG:4326 it becomes weirdly squeezed, and QGIS don't want to display the layers at the same time. Their coordinates differ heavily, so I guess it is not strange that QGIS don't want to display them at the same time. I'm using QGIS 2.8.2 on Mac.

**Speculation on "what's wrong?"**

My first guess is that I have not selected the right CRS for layer (a)- but how do I know what it is? I am completely new to all this.

To clarify some things, you shouldn't need to convert a layer. QGIS should be able to transform them on-the-fly for visualization purposes. So you should be able to do the tests on-the-fly and once you find out the true EPSG of each layer then you can save the transformation into a file.

Layer (a) cannot be in 4326 if it's boundaries are those you indicate (xMin,yMin 4062955.57,3164156.34 : xMax,yMax 4646582.49,4704921.56). These are metric values and 4326 is not metric. The boundaries feel more like a UTM projection.

I suggest you check http://epsg.io. You can search by country and filter the results. Check the filter "Projected" to skip unneeded CRS.

http://epsg.io/?q=sweden%20kind%3APROJCRS

If there is a small offset it is probably due to some small differences between the real projection of the layer and the one you used. For instance, the datum. 3034 uses the datum ETRS89 and maybe you need a projection that uses the WGS84 datum.

PS: WGS84 is not a CRS, it's a datum. The datum is the theoretical shape of the earth where the CRS is mapped into.

## Chapter 3 Coordinate Reference System

After reading and practicing the first two chapters that you can do everything in GIS or QGIS. But, many things are still to know. We might want to know how QGIS knows where to place a point or a line or a polygon or a raster image. It requires the location of these features. Locations are expressed in terms of coordinates. Now is the time to upgrade yourself and learn a few things about coordinate reference system. We might be able to display maps without the knowledge of coordinates, but for analysis and understanding of GIS data we need to know how the locations are conceived in GIS.

## Map projections

A traditional method of representing the earth’s shape is the use of globes. There is, however, a problem with this approach. Although globes preserve the majority of the earth’s shape and illustrate the spatial configuration of continent-sized features, they are very difficult to carry in one’s pocket. They are also only convenient to use at extremely small scales (e.g. 1:100 million) .

### Overview

## How to detect coordinate reference system (CRS)? - I cannot display two vector layers in QGIS at the same time! - Geographic Information Systems

**Projections and Coordinate Systems**

Projections and coordinate systems are a complicated topic in GIS, but they form the basis for how a GIS can store, analyze, and display spatial data. Understanding projections and coordinate systems important knowledge to have, especially if you deal with many different sets of data that come from different sources.

The best model of the earth would be a 3-dimensional solid in the same shape as the earth. Spherical globes are often used for this purpose. However, globes have several drawbacks.

- Globes are large and cumbersome.
- They are generally of a scale unsuitable to the purposes for which most maps are used. Usually we want to see more detail than is possible to be shown on a globe.
- Standard measurement equipment (rulers, protractors, planimeters, dot grids, etc.) cannot be used to measure distance, angle, area, or shape on a sphere, as these tools have been constructed for use in planar models.
- The latitude-longitude spherical coordinate system can only be used to measure angles, not distances or areas.

Here is an image of a globe, displaying lines of reference. These lines can only be used for measurement of angles on a sphere. They cannot be used for making linear or areal measurements.

Positions on a globe are measured by angles rather than X, Y (Cartesian planar) coordinates. In the image below, the specific point on the surface of the earth is specified by the coordinate (60 °. E longitude, 55 den. N latitude). The longitude is measured as the number of degrees from the prime meridian, and the latitude is measured as the number of degrees from the equator.

For this reason, projection systems have been developed. Map projections are sets of mathematical models which transform spherical coordinates (such as latitude and longitude) to planar coordinates (x and y). In the process, data which actually lie on a sphere are projected onto a flat plane or a surface. That surface can be converted to a planar section without stretching.

Here is a simple schematic designed to show how a projection works. Imagine a glass sphere marked with grid lines or geographic features. A light positioned in the center of the sphere shines ("projects") outward, casting shadows from the lines. A plane, cone, or cylinder (known as a *developable surface*) is placed outside the sphere. Shadows are cast upon the surface. The surface is opened flat, and the geographic features are displayed on a flat plane. As soon as a projection is applied, a Cartesian coordinate system (regular measurement in X and Y dimensions) is implied. The user gets to choose the details of the coordinate system (e.g., units, origin, and offsets).

The projection surfaces (i.e., cylinders, cones, and planes) form the basic types of projections:

Standard parallels are where the cone touches or slices through the globe.

The central meridian is opposite the edge where the cone is sliced open.

Different cylindrical projection orientations:

The most common cylindrical projection is the Mercator projection, which is the basis of the UTM (Universal Transverse Mercator) system.

Different orthographic projection parameters:

[Images placed with permission of Peter Dana]

Notice in these images how distortion in distance is minimized at the place on the surface that is closest to the sphere. Distortion increases as you travel along the surface farther from the light source. This distortion is an unavoidable property of map projection. Although many different map projections exist, they all introduce distortion in one or more of the following measurement properties:

Distortion will vary in at least one of each of the above properties depending on the projection used, as well as the scale of the map, or the spatial extent that is mapped. Whenever one type of distortion is minimized, there will be corresponding increases in the distortion of one or more of the other properties.

There are names for the different classes of projections that minimize distortion.

- Those that minimize distortion in shape are called
**conformal**. - Those that minimize distortion in distance are known as
**equidistant**. - Those that minimize distortion in area are known as
**equal-area**. - Those minimizing distortion in direction are called
**true-direction**projections.

It is appropriate to choose a projection based on which measurement properties are most important to your work. For example, if it is very important to obtain accurate area measurements (e.g., for determining the home range of an animal species), you will select an equal-area projection.

*Coordinate Systems*

Once map data are projected onto a planar surface, features must be referenced by a planar coordinate system. The geographic system (latitude-longitude), which is based on angles measured on a sphere, is not valid for measurements on a plane. Therefore, a Cartesian coordinate system is used, where the origin (0, 0) is toward the lower left of the planar section. The true origin point (0, 0) may or may not be in the proximity of the map data you are using.

Coordinates in the GIS are measured from the origin point. However, **false eastings** and **false northings** are frequently used, which effectively offset the origin to a different place on the coordinate plane. This is done in order to achieve several purposes:

- Minimize the possibility of using negative coordinate values (to make calculations of distance and area easier).
- Lower the absolute value of the coordinates (to make the values easier to read, transcribe, calculate, etc.).

In this image, Washington state is projected to State Plane North (NAD83). All of the locations on the map are now referenced in Cartesian coordinates, where the origin lies several hundred miles off the Pacific coast.

Some measurement framework systems define both projections and coordinate systems. For example, the Universal Transverse Mercator (UTM) system, commonly used by scientists and Federal organizations, is based on a series of 60 transverse Mercator projections, in which different areas of the earth fall into different 6-degree zones. Within each zone, a local coordinate system is defined, in which the X-origin is located 500,000 m west of the central meridian, and the Y-origin is the south pole or the equator, depending on the hemisphere. The State Plane system also defines both projection and coordinate system.

The two most common coordinate/projection systems you will encounter in the USA are:

The state plane system includes different projections for each state, and frequently different projections for different areas *within* each state. The State Plane system was developed in the 1930s to simplify and codify the different coordinate and projection systems for different states within the USA.

Three conformal projections were chosen: the Lambert Conformal Conic for states that are longer in the east-west direction, such as Washington, Tennessee, and Kentucky, the Transverse Mercator projection for states that are longer in the north-south direction, such as Illinois and Vermont, and the Oblique Mercator projection for the panhandle of Alaska, because it is neither predominantly north nor south, but at an oblique angle.

To maintain an accuracy of 1 part in 10,000, it was necessary to divide many states into multiple zones. Each zone has its own central meridian and standard parallels to maintain the desired level of accuracy. The origin is located south of the zone boundary, and false eastings are applied so that all coordinates within the zone will have positive X and Y values. The boundaries of these zones follow county boundaries. Smaller states such as Connecticut require only one zone, whereas Alaska is composed of ten zones and uses all three projections.

## How to Geocode Sentinel-1 with QGIS 3.X

Sentinel-1 Ground-Range Detected (GRD) products are available for download from ASF’s Vertex data portal. These Level-1 GRD products are georeferenced to geographic coordinates using the Earth ellipsoid WGS84, but are still in SAR geometry.

By following this data recipe, users will learn how to geocode Sentinel-1 GRD products in QGIS 3.X using the Warp (Reproject) tool. QGIS version 3.4.10 is the current long term release, and while the basic approach is still the same in QGIS 3.X, the interface is slightly different. For instructions specific to QGIS 2.18, refer to ASF’s Geocoding Sentinel-1 GRD Products using QGIS 2.18 Data Recipe.

### Why Geocode?

Once extracted from their zip file, **GRD products downloaded from Vertex can be viewed directly in QGIS without any additional steps**. The georeferenced TIFF files include the information necessary to allow most GIS software platforms to project the data layers on the fly to match the other layers in your GIS, so you can easily visualize the data without additional effort. If you are visualizing the images outside of a GIS platform, however, the images may appear reversed or rotated. To display the images as you would expect to see them, the image must be transformed from its SAR geometry into a map projection. When working with SAR data, this process is called “Geocoding”.

Geocoding the imagery will ensure not only that the image displays at the correct location on the Earth’s surface in any given application, but that the image will also display as expected when it is viewed outside of a spatially-enabled framework (i.e. north is up, features are not stretched or reversed in unexpected ways).

Even when working within a GIS, if you want to go beyond simply visualizing the data and perform analysis or geoprocessing functions using the GRD granule, it should be geocoded to a map projection first. In QGIS, this can be accomplished by using the Warp (Reproject) tool. If you would prefer to use GDAL or ArcGIS to geocode, refer to ASF’s Data Recipes for geocoding products within each of these platforms.

Note that using different geocoding techniques/options may result in slight differences in the output products. While one output is not necessarily “better” than another, it is a good idea to be consistent when generating geocoded products for use in the same project, especially if you are looking at imagery from one location through time. The best approach to use will vary depending on the goals and preferences of the user.

### Geocoding is NOT Terrain Correction

It is important to understand that this geocoding process does not involve terrain correction. To match the imagery to actual features on the earth and correct for distortions caused by the side-looking geometry of SAR data, you must perform Radiometric Terrain Correction (RTC) instead. This will be particularly important in areas of high topographic variation. Refer to ASF’s Data Recipes on Radiometric Terrain Correction, or contact ASF to learn about other resources for RTC processing.

## R as GIS for Economists

This section explains how to create maps from vector data stored as an sf object via geom_sf() .

### 8.1.1 Datasets

The following datasets will be used for illustrations.

### 8.1.2 Basic usage of geom_sf()

geom_sf() allows for visualizing sf objects. Conveniently, geom_sf() automatically detects the geometry type of spatial objects stored in sf and draw maps accordingly. For example, the following codes create maps of Kansas wells (points), Kansas counties (polygons), and railroads in Kansas (lines):

As you can see, the different geometry types are handled by a single geom type, geom_sf() . Notice also that neither of the x-axis (longitude) and y-axis (latitude) is provided to geom_sf() . When you create a map, longitude and latitude are always used for x- and y-axis. geom_sf() is smart enough to know the geometry types and draw spatial objects accordingly.

### 8.1.3 Specifying the aesthetics

There are various aesthetics options you can use. Available aesthetics vary by the type of geometry. This section shows the basics of how to specify the aesthetics of maps. Finer control of aesthetics will be discussed later.

#### 8.1.3.1 Points

**color**: color of the points**fill**: available for some shapes (but likely useless)**shape**: shape of the points**size**: size of the points (rarely useful)

For illustration here, let’s focus on the wells in one county so it is easy to detect the differences across various aesthetics configurations.

**color**: dependent on af_used (the amount of groundwater extraction)**size**: constant across the points (bigger than default)

**color**: constant across the points (blue)**size**: dependent on af_used**shape**: constant across the points (square)

**color**: dependent on whether located east of west of -101.3 in longitude**shape**: dependent on whether located east of west of -101.3 in longitude

#### 8.1.3.2 Polygons

**color**: color of the**borders**of the polygons- fill: color of the
**inside**of the polygons **shape**: not available**size**: not available

**color**: default (black)- fill: dependent on the total amount of pumping in 2010

### 8.1.4 Plotting multiple spatial objects in one figure

You can combine all the layers created by geom_sf() additively so they appear in a single map:

Oops, you cannot see wells (points) in the figure. The order of geom_sf() matters. The layer added later will come on top of the preceding layers. That’s why wells are hidden beneath Kansas counties. So, let’s do this:

Note that since you are using different datasets for each layer, you need to specify the dataset to use in each layer except for the first geom_sf() which inherits data = KS_wells from ggplot(data = KS_wells) . Of course, this will create exactly the same map:

There is no rule that you need to supply data to ggplot() . 94

Alternatively, you could add fill = NA to geom_sf(data = KS_county) instead of switching the order.

This is fine as long as you do not intend to color-code counties.

### 8.1.5 CRS

ggplot() uses the CRS of the sf to draw a map. For example, right now the CRS of KS_county is this:

Let’s convert the CRS to WGS 84/ UTM zone 14N (EPSF code: 32614), make a map, and compare the ones with different CRS side by side.

Alternatively, you could use coord_sf() to alter the CRS on the map, but not the CRS of the sf object itself.

When multiple layers are used for map creation, the CRS of the first layer is applied for all the layers.

coord_sf() applies to all the layers.

Finally, you could limit the geographic scope of the map to be created by adding xlim() and ylim() .

### 8.1.6 Faceting

Faceting splits the data into groups and generates a figure for each group, where the aesthetics of the figures are consistent across the groups. Faceting can be done using facet_wrap() or facet_grid() . Let’s try to create a map of groundwater use at wells by year where the points are color differentiated by the amount of groundwater use ( af_used ).

Note that the above code creates a single legend that applies to both panels, which allows you to compare values across panels (years here). Further, also note that the values of the faceting variable ( year ) are displayed in the gray strips above the maps. You can have panels stacked vertically by using the ncol option (or nrow also works) in facet_wrap(.

Two-way faceting is possible by supplying a variable name (or expression) in place of . in facet_wrap(.

year) . The code below uses an expression (af_used > 200) in place of . . This divides the dataset by whether water use is greater than 200 or not and by year.

The values of the expression ( TRUE or FALSE ) appear in the gray strips, which is not informative. We will discuss in detail how to control texts in the strips section 8.5.

If you feel like the panels are too close to each other, you could provide more space between them using panel.spacing (both vertically and horizontally), panel.spacing.x (horizontally), and panel.spacing.y (vertically) options in theme() . Suppose you would like to place more space between the upper and lower panels, then you use panel.spacing.y like this:

### 8.1.7 Adding texts (labels) on a map

You can add labels to a map using geom_sf_text() or geom_sf_label() and providing aes(label = x) inside it where **x** is the variable that contains labels to print on a map.

If you would like to have overlapping labels not printed, you can add check_overlap = TRUE .

The nudge_x and nudge_y options let you shift the labels.

If you would like a fine control on a few objects, you can always work on them separately.

You could also use annotate() to place texts on a map, which can be useful if you would like to place arbitrary texts that are not part of sf object.

As you can see, you need to tell where the texts should be placed with x and y , provide the texts you want on the map to label .

Supplying data in ggplot() can be convenient if you are creating multiple geom from the data because you do not need to tell what data to use in each of the geom s.↩︎

## Projects and Layers

In QGIS, we work in Projects. To create a new project, first open QGIS. One option would be to click the icon of a piece of white paper in the upper left-hand corner of the page. It is circled in red in the image below.

Alternatively, you could hit the “Project” button in the ribbon at the top of the page and then select “New Project” from the resulting dropdown menu. It is circled in red in the image below.

Another option, evident with the image of the menu above, is to use the shortcut Command-N (for Mac OS X users) or Control-N (for Windows or Linux users).

Once you have created a new project, your QGIS screen should be blank, like the following image.

QGIS, like all GIS, “analyzes spatial location and organizations layers of information into visualizations using maps and 3D scenes. With this unique capability, [it] reveals deeper insights into data, such as patterns, relationships, and situations” (ESRI). It utilizes layers to allow users to dive deep into a location and glean more information from it than traditional maps may have allowed. Layers are added to a project to create a map.

Next, you’ll add your first layer to the QGIS project, the base layer: the OpenStreetMaps XYZ Tiles. An XYZ Tile Layer is “a set of web-accessible tiles that reside on a server. The tiles are accessed by a direct URL request from the web browser” (Tile layers—Portal for ArcGIS (10.3 and 10.3.1) | ArcGIS Enterprise). As such, you’ll need an Internet connection to first add this layer to your project however, it’s essentially a base map of the world that OpenStreetMaps, another open-source project, provides for free from their server.

To add the OpenStreetMap XYZ Tile Layer to your project, go to the Browser menu on the left-hand side of the page and select “XYZ Tiles.” The option “OpenStreetMap” should appear below “XYZ Tiles,” as pictured below.

Double click on “OpenStreetMap” to add the layer to your project. Your QGIS page should now look like the image below, with a map of the world where the blank white space used to be.

You should notice that now “OpenStreetMap” is present in the “Layers” menu, which is beneath the “Browser” menu. One other thing to notice is that there is a checkmark next to the layer name, which means that that layer should be visible on the map. To deactivate that layer, click on the checkbox to remove the checkmark you should then see the map of the world disappear from view.

## Spatial Reference System

A map is a graphic representation of geographical features or other spatial phenomena. Both location and attribute information of a particular object can be read from a map. The location information describes the position of the object on the earth's surface, while the attribute information describes characteristics of the features represented.

In addition to feature locations and their attributes, maps have other technical characteristics that define them and their use. These include scale, resolution, accuracy and projection.

The map scale is the extent of reduction necessary to display a representation of the earth's surface on a map. It is often expressed as a representative fraction of distance, such as

1:1 000 000. This means that 1 unit of distance on the map represents 1 million of the same units of distance on the earth.

Map resolution is the accuracy with which the location and shape of map features can be depicted for a given map scale. In addition to this, maps also contain accuracy constraints in the placement of lines and points on the map page.

A map projection is a mathematical transformation to calculate the position of a geographical feature from its position on the 3-dimensional earth's surface to its position on a 2-dimensional map surface.

The earth is almost a perfect sphere. The ellipticity is approximately 0.003353. To simplify mathematical calculations, the earth is often considered to be a sphere, with a certain radius. This assumption can be used for maps with a scale up to 1:5 000 000. At this scale, one cannot detect the difference between a sphere and a spheroid on a map. For larger scale maps, however, it is necessary to treat the earth as a spheroid (i.e. an ellipsoid which approximates to a sphere).

Because of gravitational variations and variations in surface features, the earth is not a perfect spheroid. Many surveys of the irregularities of the earth's surface have led to the definition of many spheroids. The semi-major and semi-minor axes defining the spheroid that best fit one geographic region are not necessarily the same for another geographic region.

Spherical coordinates are measured in latitude and longitude. If the earth is considered to be a sphere, latitude and longitude are angles measured from the earth's centre to a point on the earth' surface. Latitude and longitude are measured in degrees, minutes and seconds. The equator has latitude 0°, the North Pole 90°, and the South Pole -90°. The Prime Meridian, indicating a longitude of 0°, starts at the North Pole, passes through Greenwich, England, and ends at the South Pole.

Although measurements of latitude and longitude can be used to locate the exact position of a feature on the earth's surface, these measurement units are not associated with a standard length. It is only along the Equator that the distance represented by one degree of longitude approximates the distance represented by one degree of latitude.

To obtain comparable measurement units on a map, a mathematical conversion is needed. This transformation is commonly referred to as a "map projection".

There are four basic properties to map projections: shape - area - distance - direction.

Any representation of the ellipsoid surface in a 2-dimensional map causes distortion of one or more of these map properties. As different projections produce different distortions, they are suitable for some applications but not useful for others.

The GISCO locational reference system is the geographical coordinate system measured in latitude and longitude on a spheroid with a specific datum known as ETRS89 . This system can be used to identify the locations of points anywhere on the earth's surface and is commonly refered to as the Geographical Reference System .

Longitude lines are also called meridians and stretch between the North and South poles, whereas latitude lines are also called parallels and encircle the globe with parallel rings.

The geodetic latitude (there are many other defined latitudes) of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid.

The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane.

Latitude and longitude are commonly either measured in degrees, minutes and seconds or decimal degrees, the latter being the GISCO measurement unit. Latitude values range from 0° at the equator to +90° at the North Pole and -90° at the South Pole. Longitude ranges from 0° at the Prime Meridian (the meridian that passes through Greenwich, England) to 180° when traveling East from 0° and -180° when traveling West fom 0°.

Since longitude lines converge at the poles and converge towards the equator, one degree longitude varies between zero and 111 km at the equator. Therefore, degrees can not be associated with a standard length and furthermore, can not be used as an accurate measure of distance or area.

In order to provide measure of area and length, *.le for length and *.ar for area, info tables have been added to all layers with arc, polygon or region features. The measure is calculated on the basis of the Lambert Azimuthal Equal Area projection.

To demonstrate these tables, the example of the structural funds (SF) version 5 in the community support (cs) theme, will be used:

The SFEC1MV5 cover consists of the following features:

Feature Type | Table Name | Associated Area or Length Table |

arc | sfec1mv5.aat | sfec1mv5.le |

polygon | sfec1mv5.pat | sfec1mv5.ar |

region | sfec1mv5.patsfelcl | sfec1mv5.arsfelcl etc. |

The *.ar and *.le tables can be linked to their corresponding feature tables via the <TABLE-NAME>-ID item. The corresponding relationships can be defined as follows:

Notably, an Arc coverage does not have a one-to-one relationship with its *.le table. Since the convertion from Lambert Azimuthal Equal Area to Geographic Coordinates split some arcs, the relationship from the Arc coverage to the *.le table is one-or-many to one.

The table below gives an overview of all data sets that are not projected in Geographic Coordinates and Spheroid ETRS89. Added are the reference systems they are projected in. In principle, grids are not projected as Geographic Coordinates, but as indicated in the table below. These projection systems are described in the chapters that follow.

Data Set | Projection | Spheroid |

alwdgg | None (geographical coordinates) | Clarke 1866 |

deeu20m | Lambert Azimuth Equal Area | Semi major axis of International 1909 |

deeu3m | Lambert Azimuth Equal Area | Semi major axis of International 1909 |

fawd25mgg | None (geographical coordinates) | Clarke 1866 |

lceugr | Lambert Azimuth Equal Area | Semi major axis of International 1909 |

wawdgg | None (geographical coordinates) | Clarke 1866 |

The Lambert Azimuthal Equal Area projection is a planar projection, which means that map data are projected onto a flat surface. The aritmethic centre of the projection, or the point of tangency, is a single point specified by longitude and latitude that can be located anywhere. This projection preserves the area of individual polygons while simultaneously maintaining a true sense of direction from the centre and is best suited for individual land masses that are symmetrically proportioned.

This projection system used to be the standard reference system for the GISCO Database until the release of november 2002. In order to convert coverages, in former projection systems (before 11/2002) of the GISCO Database, to ETRS89 a usertool has been developed. This tool can be found as $GCAI/atool/arc/la2gc.aml.

Usage : la2gc (a path name can be specified)

The GISCO Lambert Azimuthal Equal area projection is characterised by the following parameters:

Units | meters |

Spheroid | sphere |

Parameters | |

Radius of sphere of reference | 6378388 |

Longitude of centre of projection | 09° 00' 00" |

Latitude of centre of projection | 48° 00' 00" |

False easting | 0.0 |

False northing | 0.0 |

The French overseas areas (DOM: Départements Outre Mer) that are grids, are projected according to different parameters:

For the DOM areas, a Lambert Conformal projection is used, with parameters matched to every region:

Réunion | Units | meters |

Spheroid | International 1909 | |

Parameters | ||

1st standard parallel | -20° 0' 0.000" | |

2nd standard parallel | -22° 0' 0.000" | |

central meridian | 55° 30' 0.000" | |

latitude of projection's origin | -21° 0' 0.000" | |

Guyane | Units | meters |

Spheroid | International 1909 | |

Parameters | ||

1st standard parallel | 2° 0' 0.000" | |

2nd standard parallel | 6° 0' 0.000" | |

central meridian | -53° 0' 0.000" | |

latitude of projection's origin | 4° 0' 0.000" | |

Martinique | Units | meters |

Spheroid | International 1909 | |

Parameters | ||

1st standard parallel | 14° 0' 0.000" | |

2nd standard parallel | 15° 0' 0.000" | |

central meridian | -61° 0' 0.000" | |

latitude of projection's origin | 14° 30' 0.000" | |

Guadeloupe | Units | meters |

Spheroid | International 1909 | |

Parameters | ||

1st standard parallel | 16° 0' 0.000" | |

2nd standard parallel | 16° 30' 0.000" | |

central meridian | -61° 30' 0.000" | |

latitude of projection's origin | 16° 15' 0.000" |

In December 1999 in a workshop, organised by JRC and MEGRIN, the need of a common Spatial Reference System for Europe was discussed as first step to ensure that geographic data are compatible across Europe. The workshop recommended to adopt the European Spatial Reference System ETRS89 at European level. But, a European Spatial Reference System is not enough, there is a need for a set of projection systems for the cartographic representation and grid storage of Pan-European geographic data at different levels of precision. To discuss this subject the JRC and EuroGeographics organised a second workshop (Dec. 14th - 15th 2000, Marne-la-Vallée) with a panel of relevant experts, with the main objective being to analyse the European Commission primary needs for map projection(s) and obtains expert advice to determine the appropriate projections.

Projected data are used in different contexts and for different uses:

- Sampling (for example: data collection of statistical purposes),
- Storing (pictures like satellite images, aerial orthophotos, . but also raster representations of vector data such as digital terrain models, slopes, land cover, . )
- Cartographic Display (both on paper maps or on screen)
- Measurements (measure of linear features, measure of areas, . ). Overlays and measurements of areas and lengths should provide true areas and distances on this scale.
- Spatial Analysis (integrated assessment using different spatial layers).
- Localisation (projected data are used to localise object on the ground).
- Conversion (data projected using National datum must be re-projected to ETRS89 to create Pan-European data sets).

The Workshop noted the need for a Pan-European coordinate reference system in which area remains true (for many statistical purposes) and which also maintains angles and shapes (for purposes such as topographic mapping). These needs cannot be met through usage of the ETRS89 ellipsoidal coordinate reference system alone, and a map projection is required to supplement the ellipsoidal system. The Workshop recognised that mapping of the ellipsoid cannot be achieved without distortion, and that it is impossible to satisfy the maintenance of area, direction and shape through a single projection.

For the purposes of evaluating projection distortion, the area of interest was taken to be a primary area equating to the EU15 except for outlying islands in the Atlantic (Madeira, Canaries, etc) ("EU15"), and a secondary area covering the current EU15 including Atlantic islands plus the EFTA countries and the 13 current EU candidate countries ("EU15+EFTA+CEC13"). In addition, the secondary area was extended eastwards to the Ural Mountains "Geographic Europe".

The primary area is bounded by parallels of 71°N and 34°N and meridians of 11°W and 32°E whilst the secondary area is bounded by parallels of 82°N and 27°N and meridians of 32°W and 45°E. The eastern boundary of the secondary area extension is 70°E. The centre of the area of interest was taken to be 52°N, 10°E.

Figure 1: The Area of Interest

- The workshop reaffirmed the recommendations of the previous workshop to express and store positions in ellipsoidal coordinates related to ETRS89 , with the underlying GRS80 ellipsoid, and to further adopt EVRF2000 for expressing physical heights. For coordinate accuracies of > 1m, the ETRS89 can be regarded as equal to the WGS84 .
- The European Commission should, as far as possible, use ellipsoidal (geodetic latitude, geodetic longitude, and if appropriate ellipsoidal height) coordinates related to ETRS89 for expressing and storing positions. In general, ellipsoidal coordinates should be used for storing vector data. Raster data should be stored in one of the recommended coordinate reference system. The choice of the appropriate system should be based on the objectives of the data. Full consideration should be given to resampling when moving raster data between coordinate reference systems, with expert advice taken on matters such as pixel size.
- For conducting statistical analysis and display the Pan-European Equal Area coordinate reference system of 2001 (ETRS-LAEA), an equal area projection of the ETRS89 coordinate reference system is recommended.
- The European Commission should adopt the Pan-European Conformal coordinate reference system of 2001 (ETRS-LCC) for conformal Pan-European mapping at scales of smaller or equal to 1:500,000 (1:1,000,000. ).
- The workshop recommends to adopt the Pan-European Transverse Mercator grid system (ETRS-TMzn) for its applications requiring a conformal projection, including large-scale topographic mapping, when the collection scale of the mapping data is between 1:10,000 - At the COGI meeting in May 2001, all participants agreed that the coordinate reference system ETRS89 should be adopted by all Commission services using GIS or collecting geo-referenced data. This agreement was affirmed by a formal decision of the European Commission to use ETRS89 for expressing geographical locations.

The European Terrestrial Reference System 1989 (ETRS89) is the geodetic datum for Pan-European spatial data collection, storage and analysis. This is based on the GRS80 ellipsoid and is the basis for a coordinate reference system using ellipsoidal coordinates. The ETRS89 Ellipsoidal Coordinate Reference System (ETRS89) is recommended to express and to store positions, as far as possible.

#### Definition

Table 1: ETRS89 Ellipsoidal Coordinate Reference System Description

Entity | Value |

CRS ID | ETRS89 |

CRS alias | ETRS89 Ellipsoidal CRS |

CRS valid area | Europe |

CRS scope | Geodesy, Cartography, Geoinformation systems, Mapping |

Datum ID | ETRS89 |

Datum alias | European Terrestrial Reference System 1989 |

Datum type | geodetic |

Datum realization epoch | 1989 |

Datum valid area | Europe / EUREF |

Datum scope | European datum consistent with ITRS at the epoch 1989.0 and fixed to the stable part of the Eurasian continental plate for georeferencing of GIS and geokinematic tasks |

Datum remarks | see Boucher, C., Altamimi, Z. (1992): The EUREF Terrestrial Reference System and its First Realizations. Veröffentlichungen der Bayerischen Kommission für die Internationale Erdmessung, Heft 52, München 1992, pages 205-213- or ftp://lareg.ensg.ign.fr/pub/euref/info/guidelines/ |

Prime meridian ID | Greenwich |

Prime meridian Greenwich longitude | 0° |

Ellipsoid ID | GRS 80 |

Ellipsoid alias | New International |

Ellipsoid semi-major axis | 6 378 137 m |

Ellipsoid shape | TRUE |

Ellipsoid inverse flattening | 298.2572221 |

Ellipsoid remarks | see Moritz, H. (1988): Geodetic Reference System 1980. Bulletin Geodesique, The Geodesists Handbook, 1988, Internat. Union of Geodesy and Geophysics |

Coordinate system ID | Ellipsoidal Coordinate System |

Coordinate system type | geodetic |

Coordinate system dimension | 3 |

Coordinate system axis name | geodetic latitude |

Coordinate system axis direction | North |

Coordinate system axis unit identifier | degree |

Coordinate system axis name | geodetic longitude |

Coordinate system axis direction | East |

Coordinate system axis unit identifier | degree |

Coordinate system axis name | ellipsoidal height |

Coordinate system axis direction | up |

Coordinate system axis unit identifier | metre |

#### Relationship between Ellipsoidal and Cartesian Coordinates

The coordinate lines of the Ellipsoidal Coordinate System are curvilinear lines on the surface of the ellipsoid. They are called parallels for constant latitude (phi) and meridians for constant longitude (lamda). When the ellipsoid is related to the shape of the Earth, the ellipsoidal coordinates are named geodetic coordinates. In some cases the term geographic coordinate system usually implies a geodetic coordinate system.

Figure 2: Cartesian Coordinates and Ellipsoidal Coordinates

If the origin of a right-handed Cartesian coordinate system coincides with the centre of the ellipsoid, the Cartesian Z-axis coincides with the axis of rotation of the ellipsoid and the positive X-axis passes through the point "phi" = 0, "lamda" = 0.

The European Terrestrial Reference System 1989 (ETRS89) is the geodetic datum for Pan-European spatial data collection, storage and analysis. This is based on the GRS80 ellipsoid and is the basis for a coordinate reference system using ellipsoidal coordinates. For many Pan-European purposes a plane coordinate system is preferred. But the mapping of ellipsoidal coordinates to plane coordinates cannot be made without distortion in the plane coordinate system. Distortion can be controlled, but not avoided.

For many purposes the plane coordinate system should have minimum distortion of scale and direction. This can be achieved through a conformal map projection. The ETRS89 Transverse Mercator Coordinate Reference System (ETRS-TMzn) is recommended for conformal Pan-European mapping at scales larger than 1:500 000. For Pan-European conformal mapping at scales smaller or equal 1:500 000 the ETRS89 Lambert Conformal Conic Coordinate Reference System (ETRS-LCC) is recommended.

With conformal projection methods attributes such as area will not be free of distortion. For Pan-European statistical mapping at all scales or for other purposes where true area representation is required, the ETRS89 Lambert Azimuthal Equal Area Coordinate Reference System (ETRS-LAEA) is recommended.

#### Definition

The ETRS89 Lambert Azimuthal Equal Area Coordinate Reference System (ETRS-LAEA) is a single projected coordinate reference system for all of the Pan-European area. It is based on the ETRS89 geodetic datum and the GRS80 ellipsoid. Its defining parameters are given in Table 2 following ISO 19111 Spatial referencing by coordinates.

Table 2: ETRS-LAEA Description

With these defining parameters, locations North of 25° have positive grid northing and locations eastwards of 30° West longitude have positive grid easting. Note that the axes abbreviations for ETRS-LAEA are Y and X whilst for the ETRS-LCC and ETRS-TMnz they are N and E.

All EU projections are based on ETRS89 datum and therefore use ellipsoidal formulas. In some GIS applications the Lambert Azimuthal Equal Area method is implemented only in spherical form. Geodetic latitude and longitude must not be used in these spherical implementations. To do so may cause significant error (up to 15 km !). Use the example conversions above to test whether software uses appropriate formulas.

The European Terrestrial Reference System 1989 (ETRS89) is the geodetic datum for Pan-European spatial data collection, storage and analysis. This is based on the GRS80 ellipsoid and is the basis for a coordinate reference system using ellipsoidal coordinates. For many Pan-European purposes a plane coordinate system is preferred. But the mapping of ellipsoidal coordinates to plane coordinates cannot be made without distortion in the plane coordinate system. Distortion can be controlled, but not avoided. For many purposes the plane coordinate system should have minimum distortion of scale and direction. This can be achieved through a conformal map projection.

The ETRS89 Lambert Conformal Conic Coordinate Reference System (ETRS-LCC) is recommended for conformal Pan-European mapping at scales smaller or equal 1:500 000. For Pan-European conformal mapping at scales larger than 1:500 000 the ETRS89 Transverse Mercator Coordinate Reference System (ETRS-TMzn) is recommended.

With conformal projection methods attributes such as area will not be distortion-free. For Pan-European statistical mapping at all scales or other purposes where true area representation is required, the ETRS89 Lambert Azimuthal Equal Area Coordinate Reference System is recommended.

#### Definition

The ETRS89 Lambert Conformal Conic Coordinate Reference System (ETRS-LCC) is a single projected coordinate reference system for all of the Pan-European area applied to the ETRS89 geodetic datum and the GRS80 ellipsoid. Because of the greater extent in longitude than in latitude, a Lambert Conic Conformal projection with two standard parallels is utilised.

The scale factor is only a function of the latitudes of the standard parallels and the latitude of the point where it is computed. Figure 3 shows the variation of the scale factor k against latitude. The maximum and minimum values are shown in Table 3, also in parts per million (ppm).

Figure 3: Variation of the Scale Factor

Table 3: Maximum and Minimum Values of the Distortion

Entity | Value |

CRS ID | ETRS-LAEA |

CRS alias | ETRS89 Lambert Azimuthal Equal Area CRS |

CRS valid area | Europe |

CRS scope | CRS for Pan-European statistical mapping at all scales or other purposes where true area representation is required |

Datum ID | ETRS89 |

Datum alias | European Terrestrial Reference System 1989 |

Datum type | geodetic |

Datum realization epoch | 1989 |

Datum valid area | Europe / EUREF |

Datum scope | European datum consistent with ITRS at the epoch 1989.0 and fixed to the stable part of the Eurasian continental plate for georeferencing of GIS and geokinematic tasks |

Datum remarks | see Boucher, C., Altamimi, Z. (1992): The EUREF Terrestrial Reference System and its First Realizations. Veröffentlichungen der Bayerischen Kommission für die Internationale Erdmessung, Heft 52, München 1992, pages 205-213 - or ftp://lareg.ensg.ign.fr/pub/euref/info/guidelines |

Prime meridian ID | Greenwich |

Prime meridian Greenwich longitude | 0° |

Ellipsoid ID | GRS 80 |

Ellipsoid alias | New International |

Ellipsoid semi-major axis | 6 378 137 m |

Ellipsoid shape | TRUE |

Ellipsoid inverse flattening | 298.2572221 |

Ellipsoid remarks | see Moritz, H. (1988): Geodetic Reference System 1980. Bulletin Geodesique, The Geodesists Handbook, 1988, Internat. Union of Geodesy and Geophysics |

Coordinate system ID | LAEA |

Coordinate system type | projected |

Coordinate system dimension | 2 |

Coordinate system axis name | Y |

Coordinate system axis direction | North |

Coordinate system axis unit identifier | metre |

Coordinate system axis name | X |

Coordinate system axis direction | East |

Coordinate system axis unit identifier | metre |

Operation ID | LAEA |

Operation valid area | Europe |

Operation scope | for Pan-European statistical mapping at all scales or other purposes where true area representation is required |

Operation method name | Lambert Azimuthal Equal Area Projection |

Operation method formula | US Geological Survey Professional Publication 1395, "Map Projection - A Working Manual" by John P. Snyder. |

Operation method parameters number | 4 |

Operation parameter name | latitude of origin |

Operation parameter value | 52° N |

Operation parameter name | longitude of origin |

Operation parameter value | 10° E |

Operation parameter remarks | |

Operation parameter name | false northing |

Operation parameter value | 3 210 000.0 m |

Operation parameter remarks | |

Operation parameter name | false easting |

Operation parameter value | 4 321 000.0 m |

Operation parameter remarks |

Defining parameters are given in Table 4 following ISO 19111 Spatial referencing by coordinates.

Table 4: ETRS-LCC Description

Extreme | Latitude | Scale factor k | Scale (ppm) |

minimum | 51°N (circa) | 0.965 622 | -34 378 |

maximum | 71° N | 1.043 704 | 43 704 |

Entitiy | Value |

CRS ID | ETRS-LCC |

CRS alias | ETRS89 Lambert Conformal Conic CRS |

CRS valid area | Europe |

CRS scope | CRS for conformal Pan-European mapping at scales smaller or equal 1:500 000 |

Datum ID | ETRS89 |

Datum alias | European Terrestrial Reference System 1989 |

Datum type | geodetic |

Datum realization epoch | 1989 |

Datum valid area | Europe / EUREF |

Datum scope | European datum consistent with ITRS at the epoch 1989.0 and fixed to the stable part of the Eurasian continental plate for georeferencing of GIS and geokinematic tasks |

Datum remarks | see Boucher, C., Altamimi, Z. (1992): The EUREF Terrestrial Reference System and its First Realizations. Veröffentlichungen der Bayerischen Kommission für die Internationale Erdmessung, Heft 52, München 1992, pages 205-213- or ftp://lareg.ensg.ign.fr/pub/euref/info/guidelines/ |

Prime meridian ID | Greenwich |

Prime meridian Greenwich longitude | 0° |

Ellipsoid ID | GRS 80 |

Ellipsoid alias | New International |

Ellipsoid semi-major axis | 6 378 137 m |

Ellipsoid shape | TRUE |

Ellipsoid inverse flattening | 298.2572221 |

Ellipsoid remarks | see Moritz, H. (1988): Geodetic Reference System 1980. Bulletin Geodesique, The Geodesists Handbook, 1988, Internat. Union of Geodesy and Geophysics |

Coordinate system ID | LCC |

Coordinate system type | projected |

Coordinate system dimension | 2 |

Coordinate system axis name | N |

Coordinate system axis direction | North |

Coordinate system axis unit identifier | metre |

Coordinate system axis name | E |

Coordinate system axis direction | East |

Coordinate system axis unit identifier | metre |

Operation ID | LCC |

Operation valid area | Europe |

Operation scope | for conformal Pan-European mapping at scales smaller or equal 1 : 500 000 |

Operation method name | Lambert Conformal Conic Projection with 2 standard parallels |

Operation method formula | Lambert Conformal Conic Projection, in Hooijberg, Practical Geodesy, 1997, pages 133-139 |

Operation method parameters number | 6 |

Operation parameter name | lower parallel |

Operation parameter value | 35° N |

Operation parameter remarks | |

Operation parameter name | upper parallel |

Operation parameter value | 65° N |

Operation parameter remarks | |

Operation parameter name | latitude grid origin |

Operation parameter value | 52° N |

Operation parameter remarks | |

Operation parameter name | longitude grid origin |

Operation parameter value | 10° E |

Operation parameter remarks | |

Operation parameter name | false northing |

Operation parameter value | 2 800 000 m |

Operation parameter remarks | |

Operation parameter name | false easting |

Operation parameter value | 4 000 000 m |

Operation parameter remarks |

Note that the axes abbreviations for ETRS-LCC and ETRS-TMzn are N and E whilst for the ETRS-LAEA they are Y and X.

The European Terrestrial Reference System 1989 (ETRS89) is the geodetic datum for Pan-European spatial data collection, storage and analysis. This is based on the GRS80 ellipsoid and is the basis for a coordinate reference system using ellipsoidal coordinates. For many Pan-European purposes a plane coordinate system is preferred. But the mapping of ellipsoidal coordinates to plane coordinates cannot be made without distortion in the plane coordinate system. Distortion can be controlled, but not avoided. For many purposes the plane coordinate system should have minimum distortion of scale and direction. This can be achieved through a conformal map projection.

The ETRS89 Transverse Mercator Coordinate Reference System (ETRS-TMzn) is recommended for conformal Pan-European mapping at scales larger than 1:500 000. For Pan-European conformal mapping at scales smaller or equal 1:500 000 the ETRS89 Lambert Conformal Conic Coordinate Reference System (ETRS-LCC) is recommended.

With conformal projection methods attributes such as area will not be distortion-free. For Pan-European statistical mapping at all scales or other purposes where true area representation is required, the ETRS89 Lambert Azimuthal Equal Area Coordinate Reference System is recommended.

#### Definition

The ETRS89 Transverse Mercator Coordinate Reference System (ETRS-TMzn) is identical to the Universal Transverse Mercator grid system for the northern Hemisphere applied to the ETRS89 geodetic datum and the GRS80 ellipsoid. The UTM system was developed for worldwide application between 80°S and 84°N with the following basic features:

- 60 zones of 6° longitudinal extension numbered consecutively from 1 to 60, beginning with number 1 for the zone between 180°W and 174°W and continuing eastward
- central meridian scale factor of 0.9996 producing two lines of secancy approximately 180 000 m East and West of the central meridian
- negative coordinates are avoided by assigning a false easting value of 500 000 m East at the central meridian and false northing values at the equator of 0 m for the northern hemisphere and 10 000 000 m for the southern hemisphere
- uniform conversion formulas from one zone to another
- unique referencing for all zones in a plane rectangular coordinate system
- meridional convergence (between the true and grid North) to be less than 5
- map distortion within the zones to be less than 1 : 2500

ETRS-TMzn is a series of zones, where "zn" in the identifier is the zone number. Each zone runs from the equator northwards to latitude 84° North and is 6-degrees wide in longitude reckoned from the Greenwich prime meridian. Zone 31 is centred on 3° East and is used between 0° and 6° East, zone 32 is centred on 9° East and is used between 6° and 12° East, etc. Table 5 shows the zones of the ETRS-TMzn.

Table 5: Zones of ETRS89 Transverse Mercator Coordinate Reference System

Zone number | Longitude of Origin | West Limit | East Limit | South Limit | North Limit |

(zn) | (degrees) | (degrees) | (degrees) | (degrees) | (degrees) |

26 | 27° West | 30° West | 24° West | 0° North | 84° North |

27 | 21° West | 24° West | 18° West | 0° North | 84° North |

28 | 15° West | 18° West | 12° West | 0° North | 84° North |

29 | 9° West | 12° West | 6° West | 0° North | 84° North |

30 | 3° West | 6° West | 0° East | 0° North | 84° North |

31 | 3° East | 0° East | 6° East | 0° North | 84° North |

32 | 9° East | 6° East | 12° East | 0° North | 84° North |

33 | 15° East | 12° East | 18° East | 0° North | 84° North |

34 | 21° East | 18° East | 24° East | 0° North | 84° North |

35 | 27° East | 24° East | 30° East | 0° North | 84° North |

36 | 33° East | 30° East | 36° East | 0° North | 84° North |

37 | 39° East | 36° East | 42° East | 0° North | 84° North |

38 | 45° East | 42° East | 48° East | 0° North | 84° North |

39 | 51° East | 48° East | 54° East | 0° North | 84° North |

Figure 4: The ETRS-TMzn Zones

Table 6 contains the fully described ETRS89 Transverse Mercator Coordinate Reference System (ETRS-TMzn) following ISO 19111 Spatial referencing by coordinates.

Table 6: ETRS-TMzn Description

Entity | Value |

CRS ID | ETRS-TMzn |

CRS remarks | zn is the zone number, starting with 1 on the zone from 180° West to 174° West, increasing eastwards to 60 on the zone from 174° East to 180° East |

CRS alias | ETRS89 Transverse Mercator CRS |

CRS valid area | Europe |

CRS scope | CRS for conformal pan-European mapping at scales larger than 1:500 000 |

Datum ID | ETRS89 |

Datum alias | European Terrestrial Reference System 1989 |

Datum type | geodetic |

Datum realization epoch | 1989 |

Datum valid area | Europe / EUREF |

Datum scope | European datum consistent with ITRS at the epoch 1989.0 and fixed to the stable part of the Eurasian continental plate for georeferencing of GIS and geokinematic tasks |

Datum remarks | see Boucher, C., Altamimi, Z. (1992): The EUREF Terrestrial Reference System and its First Realizations. Veröffentlichungen der Bayerischen Kommission für die Internationale Erdmessung, Heft 52, München 1992, pages 205-213 - or ftp://lareg.ensg.ign.fr/pub/euref/info/guidelines/ |

Prime meridian ID | Greenwich |

Prime meridian Greenwich longitude | 0° |

Ellipsoid ID | GRS 80 |

Ellipsoid alias | New International |

Ellipsoid semi-major axis | 6 378 137 m |

Ellipsoid shape | TRUE |

Ellipsoid inverse flattening | 298.2572221 |

Ellipsoid remarks | see Moritz, H. (1988): Geodetic Reference System 1980. Bulletin Geodesique, The Geodesists Handbook, 1988, Internat. Union of Geodesy and Geophysics |

Coordinate system ID | TMzn |

Coordinate system type | projected |

Coordinate system dimension | 2 |

Coordinate system remarks | Projection: Transverse Mercator in zones, 6° width |

Coordinate system axis name | N |

Coordinate system axis direction | North |

Coordinate system axis unit identifier | metre |

Coordinate system axis name | E |

Coordinate system axis direction | East |

Coordinate system axis unit identifier | metre |

Operation ID | TMzn |

Operation valid area | Europe |

Operation scope | for conformal pan-European mapping at scales larger than 1:500 000 |

Operation method name | Transverse Mercator Projection |

Operation method name alias | TMzn |

Operation method formula | Transverse Mercator Mapping Equations, in Hooijberg, Practical Geodesy, 1997, pages 81-84, 111-114 |

Operation method parameters number | 7 |

Operation parameter name | latitude of origin |

Operation parameter value | 0° |

Operation parameter remarks | 0°, the Equator |

Operation parameter name | longitude of origin |

Operation parameter value | central meridian (CM) of each zone |

Operation parameter remarks | central meridians . 3° W, 3° E, 9° E, 15° E, 21° E. |

Operation parameter name | false northing |

Operation parameter value | 0 m |

Operation parameter remarks | |

Operation parameter name | false easting |

Operation parameter value | 500 000 m |

Operation parameter remarks | |

Operation parameter name | scale factor at central meridian |

Operation parameter value | 0.9996 |

Operation parameter remarks | |

Operation parameter name | width of zones |

Operation parameter value | 6° |

Operation parameter remarks | |

Operation parameter name | latitude limits of system |

Operation parameter value | 0° N and 84° N |

Operation parameter remarks |

Note that the axes abbreviations for ETRS-TMzn and ETRS-LCC are N and E whilst for the ETRS-LAEA they are Y and X.

## 6.8 Creating a Presentable Map

Now that you have a points object with the crossings stored, make a map that you can present to policy makers.

First, you should get a nicer basemap than R’s blank slate. Use the

Now, put the rest of the layers in the same projection as the basemap:

Now, plot the crossings in blue on top of the basemap with the railroad in red. You can add a scale bar and north arrow using the

Where are the bears crossing the railroad? It looks like there are two areas of the railroad that get the most bear activity. One in the hairpin turn, and one that’s more spread out between Logatec and Unec. Perhaps there should be wildlife crossings in those areas to protect the more “adventurous” bears.

## 3 Cartography and Visualisation I

Well done on making it through Week 2 - and welcome to what is a more practical introduction to GIScience where we will be focusing on: **how to make a good map**.

It’s not quite as “light” as promised, but this and the previous week will hold you in good stead as you come to learn about more technical analytical techniques after Reading Week.

As always, we have broken the content into smaller chunks to help you take breaks and come back to it as and when you can over the next week.

*If you do not get through everything this week, do not worry. Week 4* **will** *be shorter in content, therefore you will have time to catch up after the seminars at the start of Week 4. The seminar will go through aspects of this week’s work, so it will still be incredibly useful if you do not manage to complete everything we outline in this workshop.*

### Week 3 in Geocomp

This week’s content introduces you to foundational concepts associated with **Cartography and Visualisation**, where we have three areas of work to focus on:

This week’s content is split into **4** parts:

**Videos** can be found in **Parts 1-3**, alongisde **Key** and **Suggested Reading**.

This week, your **1 assignment** is creating the final output from our practical.

**Part 4** is our Practical for this week, where you will be introduced to using the Map Composer with **Q-GIS** and apply the knowledge gained in the previous parts from Parts 1-3 in a practical setting.

If you have been unable to download Q-GIS or cannot access it via [email protected] Anywhere, we have provided an alternative browser-based practical but we recommend reading through the Q-GIS practical as unfortunately we are unable to repeat everything within the AGOL practical.

**Learning Objectives**

By the end of this week, you should be able to:

- Explain what a Geographic Coordinate System and a Projected Coordinate System is and their differences.
- Understand the limitations of different PCSs and recognise when to use each for specific anlaysis.
- Know what to include - and what not to include - on a map.
- Know how to represent different types of spatial data on a map.
- Explain what the Modifiable Areal Unit Problem is and why poses issues for spatial analysis.
- Map event data using a ‘best-practice’ approach.
- Produce a map of publishable quality.

We will build on the data analysis we completed last week and create accurate maps that show changes in crime across our London wards.

### Coordinate Systems and Map Projections

Maps, as we saw last week, are representations of reality. But not only are they are designed to represent features, processes and pheonomena in their ‘form’, they also need to represent, with fidelity, their location, shape and spatial arrangement.

To be able to locate, integrate and visualise spatial data accurately within a GIS system or digtal map, spatial data needs to have two things:

**1. A coordinate reference system** *(often written as CRS)*

**2. An associated map projection**

A CRS is a **reference system** that is used to represent the **locations of the relevant spatial data within a common geographic framework**. It enables spatial datasets to use common locations for co-location, integration and visualisation.

Each coordinate system is defined by:

- Its measurement framework
- Unit of measurement (typically either decimal degrees or feet/metres, depending on the framework)
- Other measurement system properties such as a spheroid of reference, a datum, and projection parameters

Its measurement framework will be one of two types:

**Geographic**: in which spherical coordinates are measured from the earth’s center**Planimetric**: in which the earth’s coordinates are projected onto a two-dimensional planar surface.

For planimetric CRS, a **map projection** is required. This projection details the mathematical transformation to project the globe’s three-dimensional surface onto a flat map.

As a result, there are **two common types** of coordinate systems that you will come across when using spatial data:

**1. Geographic Coordinate Systems (GCS)**: a global or spherical coordinate system such as latitude-longitude.

**2. Projected Coordinate System (PCS)**: a CRS which has the mechanisms to project maps of the earth’s spherical surface onto a two-dimensional Cartesian coordinate plane. These PCS are sometimes reference to as **map projections**, although combine both location **and** the projection in their use.

##### Understanding Coordinate Systems

In summary, a GCS defines where the data is located on the earth’s surface, whereas a a PCS tells the data how to draw on a flat surface, like on a paper map or a computer screen.

As a result, a GCS is spherical, and so records locations in angular units (usually degrees). Conversely, a PCS is flat, so it records locations in linear units (usually meters):

*Visualising the differences between a GCS and a PCS. Image: Esri*

For a GCS, graticules are used as the referencing system, which are tied directly to the Earth’s ellipsoidal shape.

In comparison, within a PCS, a grid is a network of perpendicular lines are used, much like graph paper, which are then superimposed on a flat paper map to provide relative referencing from some fixed point as origin.

Your data must have a GCS before it knows where it is on earth. But, whilst theoretically projecting your data is optional, projecting your map is not. Maps are flat, so **your map will have a PCS in order accurately draw the data**.

In most GIS systems, **a default projection will be used to draw the map** and therefore the system will project your data to match this projection.

For example, if you do not specify the projection of the map or data, both ArcGIS and Q-GIS will draw your map and corresponding data using a pseudo Plate Carrée or ‘geographic’ projection.

**The Plate Carrée Projection**

This projection is actually just latitude and longitude represented as a simple grid of squares and called pseudo because it is measured in angular units (degrees) rather than linear units (meters). It is easy to understand and easy to compute, but it also distorts all areas, angles, and distances, so it is senseless to use it for analysis and measurement and as a result, before you start your work, you should choose a different PCS!

**Which CS you will choose will depend on where you are mapping:** most often, you will not need to choose a GCS as the data you are using was already collected and/or stored in a pre-selected system.

*For example, all GPS receivers collect data using only one datum or coordinate system, which is WGS84. Therefore any GPS data you use will be provided in the WGS84 GCS.*

**However, you will often need to choose your PCS**: which PCS you use depends on where you are mapping, but also the nature of your map — for example, should you distort area to preserve angles, or vice versa?

*For example, if you are using GPS data from the U.K, it is likely that you will transform this data into British National Grid (a PCS).*

#### Understanding Map Projections

Either CS provides a framework for defining real-world locations - however, **when it comes to much of GIScience and spatial analysis work, we will use a PCS to help locate, project, analyse and visualise our data in 2D.**

To locate, project, analyse and visualise our data in 2D, the PCS has, through mathematical transformations known as **map projections**, transformed the surface of our three-dimensional earth into a two-dimensional map canvas (whether paper or digital).

**This ability to create a flat surface from a 3D sphere is however not so simple!**

From a classic geographical metaphor, the easiest way to think about this is to think about peeling an orange - how could you peel an orange to ultimately result in a flat (preferably square/rectangular - computers really like squares!) shape?

Well, luckily, you don’t need to think too hard about it - as Esri’s resident cartographer **John Nelson** (another Twitter recommendation) has done it for us:

*Trying to flatten an orange - our earth - into a flat map. Images: John Nelson, Esri*

As he shows, to create just a *flat* version of our earth from the spheriod itself, it takes some very interesting shapes and direction maniuplation - let alone achieving a rectangle!

(You can see the original blog post these images are taken from here.)

To create a classic square or rectangular map that we are so used to seeing, we have to use other geometric shapes that can be flattened without stretching their surface to help determine our projection.

These shapes are called **developable** surfaces and consist of three types:

*The three types of projection families: cyclindrical, conical and plane. Image: QGIS*

However when any of using these shapes to representing the earth’s surface in two dimensions, there is always some sort of distortion in the shape, area, distance, or direction of the data.

This distortion is explained through Vox’s excellent video:

**Why all world maps are wrong**

We can actually test out this distortion ourselves.

You can head to **The True Size** (https://thetruesize.com) and see how our use of the **Web Mercator** has skewed our understanding of the **size** of countries in respect to one another.

In addition, I highly recommend looking through this short (2 minutes!) blog post where a keen mapper got creative with his own orange peel:

**Blog post:** Visualising the distortion of web mercator maps with an orange peel, Chris M. Whong, Online here

Different projections can therefore cause different types of distortions. Some projections are designed to minimize the distortion of one or two of the data’s characteristics. A projection could, for example, maintain the area of a feature but alter its shape.

Our second short lecture explains how to think through choosing a map projection:

#### Choosing a Map Projection

As explained in our lecture, each map projection therefore has advantages and disadvantages.

Ultimately, the best projection for a map depends on the scale of the map, and on the purposes for which it will be used.

As the excellent Q-GIS Projection documentation explains:

For example, a projection may have unacceptable distortions if used to map the entire African continent, but may be an excellent choice for a large-scale (detailed) map of your country. The properties of a map projection may also influence some of the design features of the map. Some projections are good for small areas, some are good for mapping areas with a large East-West extent, and some are better for mapping areas with a large North-South extent.

When it comes to choosing your map projection, think about:

- Is there a default projection for your area of study (e.g. London and British National Grid)?
- What analysis are you completing? What properties are important to this analysis?
- At what scale and direction are you visualising your data?

What is critical to remember though, is that map projections are never absolutely accurate representations of our spherical earth.

As a result of the map projection process, **every map shows distortions of angular conformity, distance and area**.

#### Why should we care about projection systems?

In summary, **the projection system you use can have impact on both analytical aspects of your work**, e.g. using measurement tools effectively, such as buffers, alongside visualisation.

It is usually **impossible to preserve all characteristics at the same time** in a map projection.

This means that when you want to carry out accurate analytical operations, you will need to use a map projection that provides the best characteristics for your analyses.

For example, if you need to measure distances on your map, you should try to use a map projection for your data that provides high accuracy for distances.

Furthermore, you need to be aware of the CS that your data is in, particularly when you are using multiple datasets.

In order to analyse and visualise data accurately together, they must **all be in the same CS**.

**Transforming/Reprojecting Data**

If you are using datasets that are based on different geographic or projected coordinate systems, you will need transform all your data to one singular system: these are known as **transformations**.

Between any two coordinate systems, there may be zero, one, or many transformations.

Some geographic coordinate systems do not have any publicly known transformations because that information is considered to have strategic importance to a government or company.

For many GCS, multiple transformations exist. They may differ by areas of use or by accuracies. Accuracies will usually reflect the transformation method.

A geographic transformation is always defined in a particular direction, like from **NAD 1927 to WGS 1984**. Transformation names will reflect this: **NAD_1927_To_WGS_1984_1**.

The name may also include a trailing number, as the above example has _1. This number represents the order in which the transformations were defined.

A larger number does not necessarily mean a more accurate transformation.

Even though a geographic transformation has a built-in directionality, all transformation methods are inversible. That is, a transformation can be used in either direction.

#### Moving for with CRS in Geocomputation

Keep in mind that map projection is a very complex topic. There are hundreds of different projections available that aim to portray a certain portion of the earth’s surface as accurately as possible on a digital screen/flat paper.

In reality, the choice of which projection to use will often be made for you.

When it comes to geocomputation and spatial analysis, you need to choose your CRS carefully - thinking through what is appropriate for your dataset, incuding what analysis you are completing and at what scale.

You will find there are specific recommendations by country and, fortunately for us, most countries have commonly used projections. This is particularly useful when data is shared and exchanged as people will follow the national trend.

Often, most countries will utilise the relevant zone within the **Universal Transverse Mercator**.

In addition, a great resource is Esri’s documentation on Choosing a Map Projection.

**The Tyranny of Web Mercator**

One thing to watch out for though is the general (over)reliance on what is known as the Pseudo-Mercator projection (EPSG:3857) by web applications such as Google Maps.

The projected Pseudo-Mercator coordinate system takes the WGS84 coordinate system and projects it onto a square. (This projection is also called Spherical Mercator or Web Mercator.)

This method results in a square-shaped map but there is no way to programmatically represent a coordinate system that relies on two different ellipsoids, which means software programs have to improvise. And when software programs improvise, there is no way to know if the coordinates are consistent across programs.

This makes EPSG:3857 great for visualizing on computers but not reliable for data storage or analysis.

Luckily for us in Geocomputation, for the majority of our work, we will be using the **British National Grid** for our mapping and analysis as we are focusing on analysis on London.

In this week’s practical, we will look at how we can **reproject** our spatial data from one a GCS to a PRS (in this case WGS84 to OSGB1936).

**Key Reading(s)**

**Book (30 mins):** Longley et al, 2015, Geographic Information Science & Systems, *Chapter 4: Geo-referencing.*

**Optional: The Power of the Map**

Maps and map projections have had a long and complicated history with our politics and geopolitics. For example, whilst maps have existed in many forms prior to the periods, we cannot ignore their signficant use for land acquisition and resource exploitation during the “Age of Discovery” and resulting colonialism eras.

There is significant **power** embedded within a map and, even to this day, as we see with the use of the Mercator projection in web technology, a map can be a substantial propaganda tool when it comes to political issues.

Google Maps, for example, has found itself at the centre of various border disputes across the world - resulting, in several occasions, with troop mobilisation and threats of war:

By misplacing a portion of the border between Costa Rica and Nicaragua, Google effectively moved control of an island from one country to the other and was cited as the justification for troop movements in the region in 2010.

The Washington Post, 2020

To further avoid this, Google has created a new techno-political approach within its Google Maps platform in that the world’s borders will look different depending on where you’re viewing them from.

You can read more about this a recent article by The Washington Post: *Google redraws the borders on maps depending on who’s looking* (10 minutes).

Maps therefore are never true representations of reality, but will always include some **bias** - after all, maps are still very much made by humans.

Whilst we won’t cover this in any more detail in our lecture or practical content this week, we do hope you enjoy discussing these issues in your Study Group sessions.

In addition, there are many excellent books on this **power of maps**, including Denis Wood’s *The Power of Maps* and follow-up, *Rethinking the Power of Maps* and Mark Monmonier’s *How to Lie with Maps*. These books all outline how both paper and modern digital maps offer opportunities for cartographic mischief, deception, and propaganda.

If you’d like to avoid reading for a little longer, I would also highly recommend this excerpt from the “before your time” show, the West Wing, which summarises quite a few of the debates well:

### Effective Data Visualisation

In addition to choosing the correct map projection for your spatial data and map, to visualise your data correctly as a map - for visual analysis and publishing - you need to consider:

**How you represent your spatial data effectively.**

**How you present this data on a map that communicates your data and analysis accurately.**

We will first focus on the latter aspect and look at how you can achieve **effective** data visualisation, including how to make a good map as well as detailing the common **cartographic conventions** we’d expect you to include in your map.

Then we look at common types of spatial data and focus on how we can accurately represent **event** and **survey** data that are commonly aggregated to areal units (such as the Administrative Geographies we came across last week) for use within **choropleth** maps.

#### Cartographic Conventions

Making a **good** map is a highly subjective process - what you think looks good versus what someone else thinks looks good maybe entirely different.

That’s why there is a whole discipline out there on **cartography** - it’s also why good data visualisation skills are becoming essential within data scientist roles. As a result, I can highly recommend taking the **Cartography and Visualisation** module by Prof James Cheshire next year!

At its most fundamental, a map can be composed of many different map elements.

- The main map
- Map graticules
- A legend (including symbols)
- A title
- A scale bar or indicator
- An orientation indicator, i.e. a North Arrow
- An inset map (to locate your map within a wider area)
- Data Source information
- Any ancillary information

These elements are all part of the **expected cartographic conventions**, i.e. what should be included on/within your map in order to accurately convey all the information contained within your visualisation.

*Map elements. Image: Manuel Gimond*

However, not all elements need to be present in a map at all times. In fact, in some cases they may not be appropriate at all. A scale bar, for instance, may not be appropriate if the coordinate system used does not preserve distance across the map’s extent.

Knowing why and for whom a map is being made will dictate its layout:

- If it’s to be included in a paper as a figure, then simplicity and restraint should be the guiding principles.
- If it’s intended to be a standalone map, then additional map elements may be required, such as customised borders, graphics etc.

Knowing the intended audience should also dictate what you will convey and how:

- If it’s a general audience with little technical expertise then a simpler presentation may be in order.
- If the audience is well versed in the topic, then the map may be more complex.

Ultimately, to make a **good** map there are several *rules* you can follow:

**Visual hierarchy:** Making sure the most important elements are the most *visible* on the map (e.g. size, placement on map, colour scheme).

**Colour schemes:** Keeping colour schemes simple (less than 12 colour at max) and representative of the data you are showing (more on this later) as well as suitable to all audiences (e.g. being aware of mixing colours indetectable to those colourblind/visually impaired)

**Scale bars and north arrows:** Should be used judiciously! They are not needed in every map, nor do they need to be extremely large - just readable. I advise trying to locate the two together and keeping their design as simple as possible.

- Never use “A map of…” in your title - we know it’s a map!
- Keep font choices simple and reflective of the topic you are mapping.
- Titles are not needed on maps with figure captions.
- Make legends readable - including simplifying their values. Utilise font size effectively to ensure communication of the most important aspects.

The following short lecture explains in more detail how to make a good map:

##### Cartographic Conventions and Effective Data Visualisation

#### Representing Spatial Data

The second aspect of creating effective maps is to ensure that you are representing the type of data you are using effectively and accurately.

As we saw last week, spatial data itself is only a representation of reality.

Some of the types of data we use can be very close representations of reality, such as ‘raw’ geographic data (including satellite imagery or elevation models), whilst other datasets, when used in maps, may be far abstract representations of reality.

The different common types of spatial data you might come across in spatial analysis are outlined in the table below:

**Common Types of Spatial Data**

Data Type | Examples | Digital Representation |
---|---|---|

‘Raw’ Geographic Data | Satellite Imagery LIDAR/RADAR imagery Environmental Measurements (e.g. elevation, air quality, water levels) | Raster/Grids Coordinates / Point Data, with attributes |

Processed or Derived Spatial Data | Geographic Reference Data (e.g. buildings, roads, rivers, greenspace) Gridded Population (Density) Data Digital Elevation Models Air Quality Maps | Points, Lines and Polygons Raster/Grids |

(Spatial) Event (Count) Data | Human Activities ( e.g. crime, phone calls, house sales) Scientific Recordings (e.g. animal and plant sightings) | Coordinates / Point Data, with attributes |

Statistical Survey or Indicator Data | Human Characteristics (e.g. demographic, socio-economic & health information) Scientific Recordings (e.g. total animal counts, leaf size measurements) Voting | Tabular Data, representative at a specific spatial aggregate scale, i.e. areal unit |

Whilst we will come across a variety of these types of spatial data on this course, our main focus for the first few weeks are looking at **Event** and **Statistical** data - because these are the two types of data that are primarily used within the most common data visualisation map tool: a **choropleth** map.

**Choropleth Maps**

At its most basic, **a choropleth map is a type of thematic map in which a set of pre-defined areas is colored or patterned in proportion to a statistical variable that represents an aggregate summary of a geographic characteristic within each area**, such as population density or crime rate.

When using either Event Data or Statistical Data, we tend to aggregate these types of data into areal units, such as the Administrative Geographies we came across last week, in order to create these **choropleth** maps.

Because we see choropleth maps in our everyday lives, choropleth maps, I would say, out of any type of map-based data visualisation are the maps most vulnerable to poor use and data representation. We often think it’s a simple case of linking some table data with our areal units and then choosing some pretty colour scheme…

*An Example Choropleth: London’s Wasted Heat Energy at the MSOA scale. The question is: do you think it looks good? What would you change? Image: Mapping London*

…However, within a choropleth map, many decisions need to be made in terms of thinking through their classification (categorical or continuous/graduated), the ‘class breaks’ used, as well as the type of colour schemes used.

Furthermore, a key challenge to using choropleth maps is that often the **areal units** we use are not of **equal area** - as a result, we have to be careful in how we represent our chosen dataset.

Showing population as a ‘raw’ geographic fact across London Wards as we did last week, for example, would actually be a big no-no in terms of mapping population. Instead, we would want to show the population density - by normalising our population by the area of each ward.

*What’s still missing from this map? London Ward Population Density 2019. Data: ONS*

Without taking these normalisation approaches, we can create incredibly misleading maps. At the most basic, our brain sees the larger areal units within our map as having **more** of whatever quantity we are representing, irrespective of thinking through the underlying area (and/or population) it is actually representing.

This was common amongst the US election maps, for example, where many of the Republican states have a large landmass - but ultimately a low population. Therefore, when representing the results of the election as a categorical choropleth, it presents an overwhelming Republican landslide. However, as we all know, whilst the Party won the Electoral College vote, the Democrats actually won the Popular Vote by 3 million votes.

Hence, when mapping by number of votes rather than state outcome, a different message is conveyed, as we see below. Alas, despite this difference in total votes, the US runs an Electoral College System and in the end, the winner is the winner of the Electoral College vote and no map coud or can change that!

*Different approaches to mapping the 2016 election result in different information communicated (L->R: Business Insider, Time, xkcd)*

Despite their various challenges, choropleth maps can be increidbly useful tools. We provide a more detailed introduction to how to create choropleth maps in the following lecture: