It is important:

1. take your time until you get to be experienced at it;

2. to label your isopleths so you don't get confused over their values;

3. draw lightly so that you can erase and redraw without having to start over or make a total mess out of your analysis;

4. take a few extra minutes at the end to look over your work and make it more presentable by smoothing out the rough spots;

5. use a pencil so you can erase any mistakes or move any lines that need to be adjusted.

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Let's do a step-by-step example drawing isotherms at 10^oF intervals: 30, 40, 50, ....

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Getting started. There are a number of ways to go about the task of isoplething. One way is to find the range of values in the field you have to isopleth, and then first draw isopleths near the maximum and minimum values. This often establishes bounding isopleths between which the other isopleths must be drawn.

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In step 1, we look for the minimum value, which is 23. Then the lowest-valued isopleth we have to draw is 30. Let's go through the data and find pairs of nearby data points whose values straddle 30. Then we'll interpolate between the data points to estimate the position where 30 would occur. In the example, the temperatures are assumed to vary linearly between stations. Let's put red dots at each location.

Find adjacent data points with values straddling 30^oF.

Interpolate the locations of the 30^oF value.

Diagram 1 -- values at one extreme

Four 30^oF points are shown by big red dots and arrows.

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In step 2, we connect our dots with as smooth a line as possible.

Connect the dots to form the 30^oF isopleth.

Diagram 2 -- the 30^oF isopleth

The data points were pretty far apart in northern Minnesota, so we didn't draw a dot between the 23 and 32 points. Maybe at a later stage we should shift our isotherm a little to the south toward that 32 value.

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Now we'll go through the same procedure to find the maximum bounding isotherm. The highest temperature is 75^oF, so the 70 isotherm is the highest one we have to draw. Now we'll go through and find pairs of data points straddling the 70 value, and then put red dots at locations where 70 should have occurred. Seven such red dots are shown. Connecting the dots gives the 70^oF isopleth.

Find adjacent data points with values straddling 70^oF.

Put dots at interpolated location where 70^oF will occur.

Diagram 3 -- the other extreme (left)
Diagram 4 -- the 70^oF isotherm (right)

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Now we have bounding 30 and 70 isopleths, so a good practice is to draw an isopleth about midway between these values. Let's work on the 50 isopleth.

Find adjacent data points with values staddling an intermediate value, 50^oF

Put red dots at interpolated location where 50^oF will occur; connect dots. Diagram 5 -- an intermediate value (left)
Diagram 6 -- the 50^oF isotherm (right)

As before, we find pairs of points with values straddling the 50 value, and interpolate the position of the 50 value. The 50 isopleth lies nicely between our 30 and 70 bounding isopleths, but not exactly halfway between them on the map.

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Now we're ready to do the 40^oF isopleth.

Do another intermediate isotherm, 40^oF Diagram 7 -- interpolating 40^oF positions
Diagram 8 -- the 40^oF isotherm

When we connect the dots, the 40^oF isopleth isn't quite parallel to the 30 and 50^oF isopleths and is more wavy. We also note in the data gap area of southern Minnesota that there's a 37^oF temperature pretty far from the 40^oF isopleth. We may have to adjust our 40^oF isopleth somewhat toward the northeast.

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Next we'll do the 60 isopleth.

Do another intermediate isotherm, 60^oF Diagram 9 -- interpolating 60^oF positions
Diagram 10 -- the 60^oF isotherm

When we plot it, it really has some waves in it. Those southwestward protrusions are sort of into data gap regions, and we might want to reconsider whether or not they are real. The two northeastward bumps are both consistent with nearby data points.

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Now we have all of our trial isopleths drawn, but hopefully we have drawn lightly enough that we can make some adjustments so that the adjacent isotherm patterns are fairly consistent, and smooth. Let's make those adjustments we mentioned earlier, as suggested by arrows.

• Inspect the preliminary analysis
• Work toward smoothness and a consistent pattern

Diagram 11 (left) -- first draft analysis
Diagram 12 (right) -- a "cleaned-up" analysis

We wind up with a fairly smooth, nearly parallel pattern of isotherms.

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If you practice this approach a few times, before long you won't need to actually plot the dots, and you'll be able to perform the interpolations and draw the isotherms "automatically".

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