So, in the preceding two modules,
we talked about the specifics of both the raster and the vector data model.
Now, I want to turn to talking about projections and how we're going to take
data that are on the surface of a sphere, on the surface of the Earth.
And flatten them out in a way that we can systematically analyze them
within the GIS system.
So the way we do this is by using coordinate systems.
And we're all used to thinking about coordinate systems because this is
essentially latitude and longitude and a few other coordinate systems as well.
And it's really any system that represents points in two and three dimensional space.
So we need this to be able to measure distance in area on maps.
And these are things that have been around for a really long time.
And then we can sort of divide them up into two big categories.
We have global coordinate systems which work well for the entire world but
may introduce errors in particular locations.
And we have local coordinate systems that work really, really well for
a particular spot on the world, but we can't do everything with them.
We couldn't plot both data from Borneo and from South Bend,
Indiana on the same map using a local coordinate system.
So we have two main types as well.
In addition to this, we have what we call geographic coordinate systems
that are essentially working off of location on a sphere.
Then we have projected coordinate systems.
Which have taken some sort of systematic way of taking the spherical data and
flattening them out so we can work with them on a paper map.
Now if you've ever dealt with a deflated basketball or
peeled an orange and tried to lay these things out.
Well they don't lay out very well so there's something that has to happen to
convert spherical data, angular data, into something flat.
And we'll talk quite a bit about these projections in a little while here.
But first let's look a little bit at the geographic coordinate system.
This is a global system, this is latitude and longitude,
this is the coordinate system that we're all used to thinking about.
And it's essentially defined by the prime meridian and
the equator are reference planes, and then latitude is the angles north and
south from there and longitude are at the angles east and west.
So it allows us to pinpoint our location on a sphere
based on angles off of these reference points.
These angles are then measured in degrees, either in degrees minutes seconds, so
something like 42 degrees, 32 minutes 16 seconds north.
Or as decimal degrees, something like 45.3178 degrees north.
Either one is the same data, converting back and
forth between them is no problem whatsoever.
It's just the decimal degrees tend to be a little bit easier for computers to deal
with because it's not three numbers, it's just one number with a decimal afterward.
So one thing that's important to remember with
these geographic coordinate systems is that a degree is an angular measurement.
It's not a linear measurement.
So while a degree might be one length at the equator,
as particularly with longitude.
It might be quite a bit different when we get up to the pole.
It's gonna be a lot smaller.
That's just because the circle itself gets smaller
as you move away from those reference planes.
So, it can be quite variable and
it's always important to remember that these are not linear measurements.
These are angular measurements.
So this is what it tends to look like if we take a geographic coordinate system and
sort of flatten it out.
The system we use to flatten it out is important.
And it's something that really does become one of
two major complicating factors in doing digital mapping and
doing even regular, standard cartography and creating paper maps.
And these two things are that it's very hard to map
the surface of a sphere to a flat surface.
And then the impacts of local variation.
So just to address a little bit about the surface of a sphere and
mapping this out onto a flat location.
This is what we see.
I showed that map before and I didn't show that there's distortion in there, but
there is.
There always is when you take something spherical and try to flatten it out.
It's impossible to maintain both shape and scale.
So both size and shape.
Something is going to be distorted.
And we end up needing to choose the best method depending on the size and
the nature of the map we're trying to create.
And you can see an indication of this here in these things that
are called Tissot's Indicatrix.
Which are essentially circles of a standard size put on a globe.
And then when we flatten the map out in some way
you can see that they either get distorted or the size gets different.
So either the scale of them or
the shape of them distorts as we flatten the map out.
And this is because we're using something called a projection so
we're trying to project some part of this sphere onto a flat plane.
And we can really only maximize either conformity, so
the shape of things, or equivalence, so the size of things.
We have to have a trade off between these.
This should be familiar to everyone if you've ever looked at a globe.
Looked at Greenland on a globe versus looked at Greenland on a map.
Generally, Greenland is either going to be a different size or shape because it's
very far from the equator if you look at it on a paper map versus on a globe.
Now the way that we do this, the mathematical method that we use for
projecting this spherical thing onto a flat plane can be
kind of thought about as if we had a light in the middle of the globe.
And then we're doing something we're wrapping a piece of paper
around the globe.
And then sketching, tracing the outlines of continents or
the outlines of any other geographic features onto that piece of paper.
There are three main types of these.
There's what we call cylindrical projections, we're imaging as if there's
a cylinder of paper that's been sort of put around the equator, and
then we're sort of sketching everything onto it from there.
A cone, which might work really well for the northern hemisphere or
the southern hemisphere.
Or a plane, where we're simply setting a piece of paper and
then sketching what we see on there.
So let's look at each one of these in just a little bit more detail.
The cylindrical projection is one of the earliest and
most common that we still see.
Oftentimes these are called Mercator projections,
after one of the really famous ones that gets used quite a bit.
And you can see that here where we have,
essentially what happens is everything's very, very accurate at the equator.
And then it gets bigger or smaller as you're getting farther away
because as you imagine the globe is sort of pushing this way.
We can see more of that thing as we're trying to sketch it.
And it ends up being a much, much large geography than it really is.
And this is why you see Greenland is enormous,
Antarctica looks like it's larger than every other continent put together.
So this is one of the more famous Mercator Cylindrical projections.
This is actually the projection that's used in Google Earth and Google Maps.
So it's really, really, common in most web mapping uses as well.
We also have conic projections which is essentially like wrapping a cone of paper
around the earth.
So it's gonna work really well for either the northern hemisphere or
the southern hemisphere or particular spots.
What ends up happening, because the cone is sort of curved, when we sketch on it,
things that would normally be a straight line,
something like latitude, is gonna actually end up being curved.
So the size is going to be closer to correct but
the scale of things is gonna be a little bit different.
The shape of things is gonna be a little bit different.
So these tend to work quite well for parts of the world
that are sort of on one hemisphere and kind of wide.
So things like the continent of North America,
the continent of Asia These tend to be used quite regularly here.
We can use different methods for
kind of maximizing what we're gonna show in these different projections as well.
So in this case we have what we call a Lambert projection of Europe.
This one is working to maintain conformity, so shape.
We have ones that are working to maintain area, so somewhere in between.
We have ones that are working to maintain distance, as well.
So there's different ways that we can do these same projections,
even on the same, even using the same technique.
The last one that we might encounter are planar projections, and this is
essentially where you're just putting a piece of paper down on the globe and
then sketching what you see.
They tend to work really well for small areas.
Most commonly, they're used either in state planes, so
each state might have a way that it's gonna map its particular area.
Or, they're used for the poles because the poles are almost never well represented in
the planar in a flat map using any of the other projections.
So it's really common that we'll see these for the South Pole or for the North Pole.
Now there's one last type of projection that is really important.
And it's kind of a modified version of one of,
this is what we call the Universal Transverse Mercator System or UTM.
And this is a type of cylindrical projection it's
a mercator projection cylindrical projection, but
the other one that we saw was the paper was essentially touching at the equator.
A UTM is actually transverse, so it's been turned and
the paper is running between the poles.
So what this means is it's extremely accurate, it's very accurate for
one little swath from the North Pole to the South Pole and
then all the way back around.
So it's actually, this is a standard system that's used internationally.
This is the most common sort of GIS-based coordinate system that you'll run in to.
And it's really important because it's only accurate for one little spot.
To think about this not so much as a universal system where it's
one projection, but is a series of 60 different coordinate systems,
each of which is really good for about a sixth degree swath of the world.
They all fit together well, but
it is important to remember what the zone you're in.
For example, here in Indiana we're in zone 16 north, New York would be zone 18 north.
Its really easy to find math and I'm going to show in a second that
demonstrates what cell your emanating part of the world.
Now the units in a UTM system is meters and
they are meters away from the equator north of..
The equator and sort of east of the western edge of that zone.
So having a meter based system is actually quite useful for some reasons.
We'll talk about it in a little more detail in a second here, but it overcomes
some of that problems with degrees where it's not a linear measurement.
Meters are a linear measurement.
They're very, very useful for finding out distances.
So these are the UTM zones of the world.
Each one is six degrees of longitude
numbered from zero to 60.
And this is what it would look like if I were to take one zone and
try to project the entire world from that zone.
So knowing your zone number is really, really important so
you can make sure that it's accurate.
In this case this is the zone that Indiana is in 16 north.
And you can see that you can you can see the things nearby on either side.
15 and 17 fairly well, but
it begins to degrade in term of accuracy as you get further and further away
Now again, having a meter based system is very, very useful for
finding our distances, as opposed to working with angular measurements.
Now there's one thing that's even a little bit more important about having
a meter based system.
That comes in when we're dealing with raster data,
because if you remember from the second module when we talked about raster data,
we talked about the spatial resolution of the image, so
the amount of length in real world coordinates along one side of a pixel.
Well because a degree of longitude varies as far as how many meters it is,
how many kilometers it is with latitude what we end up having
is if we have a raster data set, where the default measurement is angular,
those aren't gonna be squares as you get further and further away from the equator.
So it's really important to have these things in a meter based system.
As far as just displaying them, modern computers can overcome a lot of this and
display them fairly accurately.
But just as far as analysis goes, it's always always better to have because
you're limited to having square pixels in there,
to have those square pixels defined as meters as opposed to degrees.
So we talked about the two main factors in converting something
on a sphere into something flat.
And the first of those was just that whole nature of doing that.
But then we also have problems of the impacts of local variation.
And that comes in because the Earth is not a perfect sphere.
It's more like an ellipse, a squished sphere.
Even then there are continents, there are rivers, there are mountains.
There is all sorts of stuff that makes it so it is not a perfect sphere.
So the actual geometric surface of the earth is something we call the geode.
You can see that sort of exaggerated here,
in the fact that its not even in the perfect ellipsoid.
And because of this we need a model for
understanding what the surface of the earth looks like.
If were dealing with surfaces with angles off of the surface,
you can imagine that it's gonna be quite different whether were further out
on the top of a mountain or whether we're down in the bottom of the Grand Canyon.
So we have to have an understanding of what the surface is like.
And the models of the best ones is something mathematical,
so it doesn't have to store the elevation of every point on the Earth,
it has it smoothed out to be about 100 meters or so of accuracy.
We call these datums and I apologize for any latin scholars watching this
the plural that we use here for the datum is actually datums.
Data would sound a little silly in this context so a datum is
reference surface for the earth defining the size, the shape, the origin,
the orientation of the coordinate systems that are being used.
So different datums are better for different areas.
Some are better for North America, some are better for Europe, some are better for
the entire world.
But it's important to remember that these are the basis for our coordinate system,
this is how the coordinate system is defined is based on the datum.
These are three of the most common ones up here that we will run into throughout
the course of these modules and probably further in your GIS career.
There are two up here that are listed for North America, the NAD 27 and the NAD 83.
They're very good for Canada, North America, and Central America.
They're not quite as good for the rest of the world.
So the one we use most commonly that's accurate for
pretty much everywhere is this WGS 84 datum.
And this is overwhelmingly the most commonly used.
So the way that it would work is,
if you were scanning a map it would be written on there, if you're downloading
data it's gonna be part of the file what the datum is that it's using.
Now I wanna stress here that projections and datums are linked.
The datum kind of forms the reference for the projection, so if you're
dealing with a projection, you're not just gonna see Lambert conformal or
UTM Zone 16, you're gonna see WGS 1984 Lamber conformal.
WGS 1985 UTM zone 16 north.
So they're linked together and it's very hard to separate them out.
In fact, if you take a map and
put the wrong projection on it you're gonna end up having quite a lot
of different errors between how it should look and how it actually does look.
So it's really important to know that you're dealing with the right reference,
the right datum, the right projection.
In the right coordinate system.
Now I want to talk a little bit about the process of what
we call georeferencing maps and imagery.
And this is how we would take something that we scanned, a paper map,
an aerial photograph, something that had no coordinates with it, and
defining both the projection, the coordinates system, the datum, and
then flattening it out in a way that we can begin to use it in GIS analysis.
Now there are two different sort of systems here.
Geo-referencing and rectification,
and they're both kind of designed to making an image fit the world.
So, we're changing the geometry.
Changing any distortion that's in there from sort of camera angles.
From the curvature of the Earth.
Really from a bad scan, even.
And there are two systems that we might use, two definitions.
If we're registering an image, it means it's already been projected,
so it's a scanned map, something like that.
We're just assigning coordinates to the pixels.
We're saying this corner is this location, this corner is this location,
making everything else fit in there.
And then the concept of georeferencing is when we're actually doing both this and
we're making it conform to a map projection.
So we're taking something that's a picture or
an image of the spherical surface and both assigning coordinates to pixels and
flattening it out in some way, projecting it in some way.
So these are two different things, technically.
Colloquially and
in the GIS world we refer to almost both of them pretty much as georeferencing.
So if you hear me say georeferencing it may be registration,
it may be formal referencing but it's really just usually called the same thing.
Now how we do this is we have to have known points.
We have to have what we call GCPs or
Ground Control Points and these are physical features within a known location.
This could mean that it's a location that I know the X, Y coordinates for,
I know the latitude and longitude for.
It could mean that it's a coordinate that I can find between two different images.
It could be that the coordinates are printed on the map itself.
I just have to have a known location to be able to tell the computer to
tell the software where that place is.
Now once I've done this a few times, once I have a few points on there,
I can begin to actually start georeferencing the image.
And I do this by using some sort of transformation system.
By using some sort of polynomial transformation to create a mathematical
relationship between the location in space in the real world and
each of the pixels in that image.
So spots in the image and the coordinate system itself.
So there are different methods that'll allow us to overcome different types of
distortions in the original image.
But most often and in the case of the demonstration for
this module, we're gonna work with the Affine System, or first order polynomial.
Which is essentially a linear relationship between the original image,
and The space in the real world.
So essentially what we end up with is we're
creating a mathematical relationship, a line that explains the difference between
the x-coordinate on the image, so the number of pixels in,
along the x-axis on the image and the x-coordinate in space.
And then doing the same thing for the y-coordinate.
So, we need three different points to be able to do this.
Anything after that is either gonna improve our model, or
give us an understanding of the error.
And this will allow us to do things like change the size, change the orientation,
skew it a little bit, and
really kind of begin to work the image to fit the real world coordinates.
There are also higher order transformations we can do, second and
third order polynomial transformations.
They don't assume a linear relationship.
They may assume this kind of a curvier linear relationship.
Where we end up with having a lot,
needing a lot more control points to be able to explain that relationship.
And these will allow us to do things like overcome any really systematic warp.
If we had a fish eye lens,
if there was curvature of the Earth, if the angle of the photograph was taken
at kind of an oblique angle as opposed to being straight down.
These are things that we can overcome with these higher ordered transformations.
Now it's always important when you're doing this to understand how good of
a job you've done.
So we always want to get some measure of the error associated with the linear
relationship, with the model that we've created to transform that image.
And this is usually measured as the deviation from a few
extra ground control points, from the curve that's been generated,
based on the first three or the first nine, or something like that.
The system that RGIS uses to work with in the demonstration is the Rubrian Squares
or RMS Error, and again this is essentially the deviation from
the actual linear relationship that we've just sorta created from our model.
So this is a little bit of an overview of the concept of projections,
how we might be able to take a spherical surface and flatten it out onto a map.
And then how we would actually do the process of scanning something or
taking an aerial photograph and actually making it conform to the real world.
Now in the future, the following modules,
we're gonna focus a little bit more on specific topics.
First off related to satellite imagery.
And then working a little bit with creating vector data.