**
**Map Projections and Coordinates Systems

**The Shape of the Earth**

The shape of the Earth is best described as an** imperfect sphere**
which bulges at the equator and flattens at the poles. It can be mathematically modelled
by an **Ellipse** (in 2 dimensions) and an **Ellipsoid**
(in 3 dimensions).

**Latitude and Longitude Coordinates**

In order to describe positions on a sphere we use the Latitude, Longitude coordinate
system.

**Latitude** is the angular distance of a point away from the
equator measured from the center of the globe 90 degrees North (0 to +90) or South (0 to
-90) .

**Determination of Latitude:**

**Longitude** is the angular distance of
a point from the **Principal Meridian** measured from the center of
the globe 180 degrees East (0 to +180) or West (0 to -180). The Principal Meridian is also
referred to as the **Prime Meridian or Greenwich Meridian**.

**Determination of Longitude:**

**Map Projections**

Map projections are a **representations of a sphere** (the Earth)
in two dimensions. A **mathematical transformation** is required in
order to convert Latitude & Longitude coordinates into **Cartesian
Coordinates** on a two dimensional surface. This transformation results in **distortions**
of the original three dimensional surface in two dimensional maps.

**Map Distortion**

Distortions result in changes to the **shape, size, area,** and **direction**
on a map.

**Conformal** **Projections** are characterized by **shape
retention** (i.e. *Lambert Conformal Conic*). So that a small
circle on globe will remain a circle on the projection, but the scale or size may be
different.

**Equal Area (or Equivalent) Projections** are characterized by **area
retention** (*Albers Equal Area Conic*). So if South America is eight
times larger than Greenland on the globe, it will also be eight times larger in the
projection.

**Projection Examples**

**Orthographic Projection
(Equatorial)**: Preserves the appearance of a globe and shows only half
the Earth at a time. Distorts shape and direction and is useful for**
illustrations**.

**Planar (Azimuthal) Projection
(Lambers Equal Area Azimuthal Projection): **Used to represent the projection
of a region (northern hemisphere) onto a plane tangent to the globe, in this example, the
north pole is used.

**Conic Projection (Lamber Conformal Conic):**
Made by fitting a cone over part of the globe. The projection **depicts
mid-latitudes** shapes and areas well. It is used to depict large regions up
to the size of the USA.

**Cylindrical Projection (Mercator):** is
based on a cylinder tangent to the equator. Good for **equatorial regions**
but greatly distorted at high latitudes. This one of the oldest and most common
projections

**
**

**Transverse Cylindrical Projection (Universal
Transverse Mercator, UTM)**: is based on a cylinder tangent to the globe along
a chosen pair of opposite meridians. The scale of the map is constant only along the **central
meridian**.

**UTM** is
a commonly used projection for **USGS maps** ranging in scale from
1:24,000 to 1:250,000. The UTM projections are based on **60 UTM Zones**
each defined by a central meridian and covering **3 degrees of Longitude**
to the East and West.

**UTM Coordinates**

Maps based on the UTM Projection have a **Cartesian Coordinate grid system**
which is used to define any point on the map. Positions are defined by the** UTM
Zone**, an 'X' coordinate called the **Easting (in meters)**
and a 'Y' coordinate called the **Northing (in meters)**. A typical
example in the Upper Peninsula of Michigan would be:

**UTM Zone: 16**

Easting: 704019

Northing: 5149326

The **Northing** is the distance north (or south) from the **Equator**
measured in metres; The **Easting** is an arbitrary **reference
line** located 500,000 metres west of the Central Meridian. Easting
measurements increase west from the reference line.

**UTM Coordinates** can measure position to the meter, making
this an **easy and accurate** way of identifying locations on a map.

**General Land Office Survey**

The **US Public Land Survey System** provides a descriptive way
of describing an area or parcel of land. For example, in Michigan land is subdivided in
terms of **Counties, Townships, Sections, and Parcels**. **Baselines**
which run East-West and **Principal Meridians** which run
North-South, form the X and Y coordinate axes. The location of townships is determined
based on **Township lines** (north-south) and **Range
lines** (east-west). Townships are subdivided into **36 Sections**
which are then subdivided into fractions.

**Legal Description**: a legal description of a tract of land
requires note of the **Meridian, Township, Range, Section and Fraction**
(generally in reverse order): for example

**NE 1/4 of NE 1/4 of S32, T4N, R3E, Michigan Meridian**

**USGS Topographic Map Series**

The **United States Geological Survey** subdivides topographic
maps into rectangular areas called **Quadrangles** based on **Latitude**
and **Longitude** lines (Meridians and Parallels). These Quadrangles
vary in scale from the large scale 7.5' x 7.5' , **1:24,000 topographic maps**
to the small scale, 1 degree by 2 degrees, **1:250,000 topographic maps**.
Because these 'base' maps are used as the fundamental starting point for other types of
surveys, many types of maps follow the same naming convention i.e. **Geological
maps, Land Use/Cover maps.**