A topographical map of Hawaii. Credit: David Babb
In the last few sections we explored the process for creating contour maps. These maps are so important because they quickly display patterns in the data that are not readily visible in a sea of numbers. However, there is another use for contour maps. In the spirit of a picture is worth a thousand words, contour maps contain site-specific information for any point on the map. The key is to be able to extract this point data from a contour map already which is already drawn.
To begin, let's look again at our topographical map of Hawaii (right). How would we go about figuring out the elevation of the point marked "P"? First, we must identify the two contours that lie on either side of "P". In some cases the contours that we need are clearly labeled; however, in other instances you will need to "count" up or down from a labeled contour. In this case we can see that point "P" lies between 3000 ft and 4000 ft contours. Now, here's the key point: The elevation at point "P" can be anything greater than (but not equal to) 3000 ft but less than (but again, not equal to) 4000 ft. We know that point "P" is not equal to either of these values because it does not lie on one of the contour lines.
Technically, this is all that we can say about the elevation at point "P" -- it can be anywhere between 3000 to 4000 feet. However, often instead of giving a range of elevation we would prefer a single number. In such cases, we can interpolate (make an estimate by assuming the elevation changes linearly) between the two known contours. In this case, we can see that point "P" is about half-way between the two contours and thus can be estimated to have an elevation of approximately 3500 ft. Using interpolation usually provides us with a sufficient approximation, but we must always realize that such single values derived from contour plots are only estimates.
What about closed contours? Look again at the contour map and focus your attention on the southern-most peak, Mauna Loa. How might we estimate the height of this peak? Clearly we do not have two contours to use... or do we? The last drawn contour is 13,000 ft. This means that the peak is higher than 13,000 feet. However, we know that the summit of Mauna Loa is not higher than 14,000 feet. Why? Well, if if were, then the 14,000 ft contour would have been drawn around the summit. So, for closed contours, the range is always between the last drawn contour and the next undrawn contour. You should also note that interpolation cannot be performed in such cases because we have no way of knowing how far away the undrawn contour is. In this case, the summit of Mauna Loa is 13,452 ft (within our deduced range of 13,000-14,000 ft).
Using colors to show differences in elevation is another method of contouring a map. Credit: R. Sterner, Johns Hopkins University
Another way to display the topographical map of the Big Island of Hawaii is to colorize specific bands of elevation. The accompanying elevation key is color-coded for a quick visual tool to determine elevation. By the way, you can access colorful topographical maps of the other 49 states from the web site at Johns Hopkins University.
In similar fashion, we can colorize the interactive isotherm map of the Middle West on which you practiced contouring temperature. Just click the Colorize button on the interactive isotherm map. Consistent with human perceptions, most colorized maps of temperatures use blues and purples to indicate cold air and oranges and reds to highlight warm air.
For a wider perspective of temperature, color-coded national maps give forecasters a bigger picture for pinpointing regions of warmth and chill. Click to access the current national temperature map.
Lest you get the impression that there are no station models over Canada and Mexico, I emphasize that weather reports are indeed routinely taken by observers in our neighboring countries. Indeed, temperature maps provided by the University of Illinois extend their analyses of isotherms to include Canada and Mexico (click on thumbnail labeled "Temperature Contours").
Sometimes, reading values from a contour map can be made easier by adding color. However, one must use care when interpreting which color is which (personally I am looking at the contour values, even if the map is colorized). For example, look at the contour map below. What would you say is an appropriate range in temperature for central Pennsylvania? Given the color is the first shade of green-yellow (or is that yellow-green?), the temperature range is greater than 60 F but less than 65 F. For more practice, check out the group of several closed isotherms over the southwestern U.S. What's a representative temperature inside the smallest closed contour straddling the border between Arizona and Mexico (filled with a relatively deep red)? Answer below...
Temperature maps that contain colored contours allow users to quickly assess patterns of warmth and chill. However, some meteorologists prefer having the actual contours drawn along with their values.
Looking only at the colors, you should note that the small closed contour is three shades of red above pure orange. This means that the temperature is greater than 85 F but less than 90 F. However, you might think that one shade of red looks just like another, so you can approach the problem by simply counting contours. First look at the label for the 60-degree isotherm that begins along the southern California Coast. Note that the contour interval on this map is five degrees, so if you count off from the 60-degree isotherm, you arrive at the indisputable conclusion that the closed contour in question represents the 85-degree isotherm. Thus, temperatures at towns located within the confines of this closed isotherm would range from greater than 85 to less than 90 degrees Fahrenheit.