From the Archive: Finding Map Area Using a Dot Grid

From the Archive: Finding Map Area Using a Dot Grid

Today’s post is part of a new effort to bring back some of the most successful context from’s long history. These posts will cover the full range of past TS topics, including Japanese language learning resources, geography, Esperanto, international futbol, NERD stuff, bread baking, fly tying, and data science stuff. The original article was published on in 2005.

The area of a surface with square corners and straight edges on a map or photo can be found by multiplying the length of the surface by its width and then converting to real-world units using the scale of the image.  What do you do if you need to find the area of an organic shape, or of a very complex geometric shape?  One method that is widely used is the dot count using a dot grid.

A dot grid is a transparent sheet printed or drawn with dots arranged in a regular and even pattern such as a grid.  When the dot grid is calibrated to the scale of the map or photo you are studying (finding the number of dots that falls in a known area), the area of an unknown surface can be found by laying the dot grid over the area, counting the number of dots that fall in and on the surface, and dividing that number by the number of calibrated dots per unit area.  This gives you the area of the surface you are estimating in the units of your calibration.

As an example, let us suppose that I have calibrated my dot grid on an aerial photograph using a farmer’s field, bounded by section-line roads, as my known distance.  How do I know the area of the farmer’s field?  Often, fields are laid out along the US Public Land Survey System, with roads following the 1-mile edges of sections.  A field bounded by such roads would be 1 square mile.  These human features are obvious in aerial photos and on maps, and are very useful for establishing scale and for calibrating dot and square grids.  Calibrating against the 1-square-mile field, suppose that I find that my dot grid is a size that there are 225 dots per square mile.

Now suppose that I have to find the surface area of a lake on the same photograph as the 1-square-mile field.  Using the dot grid that I have just calibrated, I cover the lake with the dot grid and count 675 dots on the lake.  The number of dots in my area-for-estimation (675), divided by my number of dots per unit area (225 dots per mile square) gives the lake an area of 3 square miles.

There are a few key points to using the dot grid:

  1. A dot count is a statistical method.  It is important that you don’t line up the grid to get the best fit to count in your object.  The whole point of the dot count is to see how many dots randomly fall within the area when the dot grid is placed in a random relationship to the area.
  2. When you are counting dots, each dot that falls completely within the area is given the weight of 1 full dot.  Any dot that touches the side of the object, whether it is inside, outside, or one the line, gets a weight of 1 half dot.  The number of whole dots plus the number of half dots (or the number of half dots divided by two, actually) is the total number of dots to be used in estimating the area of a surface.
  3. Once you have begun counting dots, don’t move the dot grid.  If you do accidental move the grid, don’t just keep counting.  You have to start over from the beginning.
Dot Grid

I have created a dot grid for you to use in trying this method out.  To use the dot grid, click on the image above to download “dotgrid1.pdf.”  This file needs to be printed on plastic transparency, which is available for inkjet and laser printers, as well as copy machines for between $0.15 and $0.75.

Better Map Design

As I’ve said before, I’m no GIS expert. I am certainly not a beginner, but there are many things I don’t know or don’t care to know how to do. Something I really would like to learn, though, is how to make better, more beautiful maps. I have seen some really good looking maps. I wish that I had made any one of them. Today I have a couple of links that I thought looked like they might help get beyond just putting data together, and discover a little more of the art in cARTography.

The first of the links is to the Color Brewer by Cindy Brewer, Associate Professor at Pennsylvania State University. Color Brewer is an online tool that helps create color schemes for maps with classes of sequential, qualitative, and diverging data. A user just indicates the number of classes and the type of data, and a number of different choices of color schemes are presented.

Making Maps Easy to Read is a literature review and links to studies done on map usability issues by Richard Phillips, Elizabeth Noyes and others at University College London, at the Royal College of Art and at the University of Nottingham.

Quantitative Techniques in Map Interpretation

This will surely be my last post of 2005. I came across a set of pages posted as a manual by Dr. William Locke at Montana State’s Department of Earth Sciences, called Reading Between the Lines – A manual for the analysis and interpretation of topographic maps: Quantitative techniques in map interpretation. Topics on the pages include discussions of techniques to find area, volume and trend on topographic maps. Hope that this is useful for someone.

Peculiar Liquid: Water – Part 3

Water. It’s essential to life on our planet. But did you know how weird water is? In this series we are looking at the peculiarities of H2O. In Part 1, we showed that floating ice makes life possible. In Part 2, we talked about freezing and boiling temperatures. Today we will look at the interaction between water and light.

Water is transparent to visible light. The only way to see anything is for photons to reflect off of something, and then register on the photosensitive cells in the eyes. If water wasn’t transparent, we wouldn’t be able to see anything, at least not in the range of light that we do now.

Water is opaque to U.V. 95% of U.V. radiation is absorbed in the first four inches of water. Because the temperature of an object goes up when it absorbs radiation, this means that the surfaces of Earth’s water bodies are warmed, while subsurface water remains cool. The warm upper layer of water is called the epilimnon.

Peculiar Liquid: Water – Part 2

Water. It’s essential to life on our planet. But did you know how weird water is? In this series we are looking at the peculiarities of H2O. In Part 1, we showed that floating ice makes life possible. Today we will look at freezing and boiling temperatures.

Generally, the lower the molecular weight, the lower the heat of fusion and vaporization (the temperatures at which a chemical freezes and boils). On Earth, most chemicals with low atomic weights exist naturally only as gases because their boiling temperature is much lower than normal temperatures on our planet. Water, however, because its molecular configuration, has a very high heat of vaporization and a high heat of fusion (in relation to other chemicals with low atomic weight). This means that all three states of matter of water can be found on Earth’s surface, enabling the hydrologic cycle (we’re talking rain and snow) to function.

Peculiar Liquid: Water – Part 1

Every school child knows that water is 75% of the Earth’s surface, 75% of our bodies, 75% of a good, balanced meal, and 75% of just about anything that you can make up a bogus and totally random statistic about. Water has many peculiar properties that seperates it from other types of materials. This article is Part 1 of a series looking at the effects of Earth’s peculiar liquid: water.

Everyone knows that ice-cubes float. But did you know that the peculiar property of water that, unlike the solid of any other material, makes it less dense (and therefore “floaty”) when it is frozen, actually makes life on Earth possible?

The molecules of most chemicals bunch up as they get colder, reducing the volume and increasing the density of the mass as it approaches freezing. The crystaline structure of water, on the other hand, becomes more rigid, with the individual molecules moving into alignment and actually expanding 9% as it freezes.

So why do I say that this makes life possible? Imagine an Earth where every winter, water at the surface froze as it lost heat to the cooling atmosphere, and then sunk. The sunken ice at the bottom of all the water bodies would never have enough time to thaw before the end of summer heat, which means that the next winter’s ice would sink down to stack on the ice of the summer before, eventually locking the world’s water in a never-melting block of ice.

Floating ice, on the other, other hand, insulates the water below it, keeping it from freezing through the winter, and allowing aquatic organisms to survive the cold season. So there you have it: ice floats = life on Earth.