METR 104: Our Dynamic Weather (Lecture w/Lab) Drawing and Interpreting Contour Maps Dr. Dave Dempsey Dept. of Geosciences SFSU, Spring 2011

### Contour Maps and Contour Lines

Introduction. To understand how the atmosphere behaves and to make weather forecasts, meteorologists have to measure, analyze and display patterns of temperature, pressure, humidity, wind speed, wind direction, etc. Typically, networks of surface weather-stations and stations for launching radiosondes (balloon-borne instrument packages), supplemented by ships, buoys, aircraft, satellites, weather-radars, and other specialized instruments, record these data simultaneously, mostly on a regular schedule. The data are then sent to the National Centers for Environmental Prediction (NCEP) near Washington, D.C., for analysis.

One way to display the data—say, temperatures recorded by weather stations at the earth's surface—might be simply to plot the temperatures on a map. The accompanying Figure 1 shows an example.

However, it's not easy to look at such a map and see the spatial patterns of temperature—it just looks like a bunch of headache-producing numbers scattered around. We'd prefer to display the temperature pattern in some way that's easier to interpret. One common method of doing that is called contouring. A map produced using the method of contouring is called a contour map. For example, Figure 2 is a contour map for the temperature observations shown in Figure 1. (A common, nonmeteorological example of a contour map is a topographic map, which shows patterns of the elevation of the Earth's surface above sea level.)

Contour Maps. A contour map typically shows a bunch of lines, often wavy or forming concentric, irregular closed loops or other patterns. Each of these lines, called a contour or contour line, is simply a line along which some quantity (temperature, for example) is everywhere the same. Contour lines bear more specific names depending on what quantity the contour map shows:

 Meteorological Quantity: pressure temperature wind speed dew-point temperature etc. Name of Contour Line: isobar isotherm isotach isodrosotherm

(The prefix "iso" is Greek, meaning "equal" or "same". In the case of the term "isobar", "bar" means "pressure"—hence, isobar means "same pressure".

Restated, a contour line connects places that all have the same value of temperature, pressure, or whatever quantity is being contoured. An isotherm connects places that all have the same temperature; an isobar connects places that all have the same pressure; etc.

Each contour line has a value associated with it and is usually labeled with that value. For example, an isotherm connecting all places where the temperature is 0°C would have an appropriate label (typically just "0") somewhere on it.

Contour maps show contour lines with values at regular intervals, including some standard reference value. The contour interval is arbitrary but should be chosen so that the contour map shows enough contours to reveal the pattern clearly without being crowded with too many contour lines. Usually the contour values are nice, round numbers, including a standard reference value such as 0, 100, or 1000. For example, on a temperature map, isotherms might be drawn at 5 degree intervals, based on a standard reference value such as 0°F. That is, the map might show the 0°F isotherm and other isotherms at intervals of 5°F above and below 0°F (that is, ...., -15, -10, -5, 0, 5, 10, 15, 20, ....). Sea-level pressure maps almost always show the 1000 millibar isobar (if present) and others (if present) at intervals of 4 mb above and below 1000 mb.

To draw attention to places where values are higher or lower than most or all places in the immediate vicinity, an "H" or "L" is often drawn at such local maxima or minima.

A contour map should always include a title or caption that identifies the quantity shown and the contour interval used.

A common enhancement of contour maps is to fill in the zone between each adjacent pair of contour lines with a different color, so that a particular color corresponds to the range of values lying between the two contour values. This enhancement is called "color filling". Figure 3 is an example of a color-filled contour map, for the same data as in Figures 1 and 2.

### Drawing Contours

When drawing a contour line, you can't expect it to pass directly through many radiosonde or surface-weather stations, because it's rare for an actual observation to match your contour value exactly. However, every place has a temperature, pressure, or whatever, whether or not a station happens to be there to measure it. Most likely, the places with values matching your contour value mostly lie somewhere between stations. Hence, when drawing contours, you usually have to interpolate values between observations. In practice, this means that you have to look for pairs of stations adjacent to each other and near your contour, with one station reporting a value higher and the other station a value lower than your contour value. Your contour line must then pass somewhere between two such stations.

Refer to "Contour Analysis" for some online practice and instruction to complement this document.

Here's a general procedure for drawing contours:

1. Decide what contour values you will draw. That is, choose a standard reference value and a contour interval, which together define the set of possible contours that you might draw. For reference, write down a sequence of them. (For example, contours of temperature at 3 km above sea level in degrees Celsius, drawn at 5° intervals with a standard reference value of 0°: -20, -15, -10, -5, 0, 5, 10, 15, etc.)

2. On the map, find the highest and lowest values overall from among those values plotted. These define the range of values that your contours will cover. The contour with the highest value that you can draw will not exceed the highest value plotted on the map, and the contour with the lowest value will not be less than the minimum plotted value.

3. To start, draw either the contour with the highest value possible (that is, drawn from your list of possibilities in step 1 above but not exceeding the highest value plotted on the map) or the lowest possible value. (For example, if the highest temperature plotted on a map of temperature at 3 km above sea level is 8.7°C, the highest possible contour value that you could draw would be 5°, so you might start with that one. If the lowest plotted value were -14.3°C, the lowest possible contour value that you could draw would be -10°.)

Following the tactic described in the first paragraph under "Drawing Contours" above, find a spot on the map where you think there's a value corresponding to your contour value, and precede from one pair of observations to another (and occasionally passing directly through a observation, if you're lucky) until (a) you reach the edge of the plotted values on the map (in which case you simply end the contour), or (b) you reconnect to the other end of the same contour, forming a closed loop. (Don't worry—you'll almost never have much choice in the matter! The data always tell you where your contour has to go.) Your contours should be drawn as smoothly as possible. Label your contour on each end and (if it's relatively long) somewhere in the middle.

[Note that different contours should never cross each other. Since, by definition, a contour line is a line along which the value of a quantity is everywhere the same, it follows that, at any point where two different contours crossed, the quantity would have to have two different values (such as temperature or pressure) at once. That is impossible. Similarly, no single contour line should ever split or fork.]

4. Repeat step 3. above for the next contour value down (or up) on your list in step 1. this time, you might be able to interpolate between observations and previously drawn contours (which, after all, represent places where you believe you know the values, even if they aren't actual observations!) Continue until you've drawn all possible contours. (Note that in some situations, you might have to draw more than one contour of a particular value.)

5. Put an "H" or "L" at places where values are higher or lower than anywhere else or almost anywhere else nearby—that is, at local maxima and minima. These locations are typically surrounded by a contour line that forms a closed loop.

### Interpreting Contour Maps

Here are some tips for interpreting contour maps:
1. Immediately to one side of a contour line, values are always higher than they are on on the contour itself; immediately to the other side, values are always lower. Hence, contour lines divide the map into a region where values are higher than they are on the contour line itself and a region where they are lower.

2. Along a contour line, values don't vary at all (by definition of a contour line). However, across a contour line values do vary, and values vary most rapidly in a direction perpendicular to a contour line. The amount by which values vary across each unit of distance in a direction perpendicular to contour lines is called the gradient.

On a temperature map, the temperature gradient would be the amount by which the temperature varies across each unit of horizontal distance. It could be expressed in terms of the temperature difference in °C or °F across a unit of distance such as 100 kilometers or 100 miles, for example. The pressure gradient is the amount by which pressure varies across each unit of horizontal distance, and might be expressed in terms of millibars per 100 kilometers, for example.

The gradient is a measure of how rapidly a quantity varies with spatial position (that is, from place to place).

3. The gradient is larger where contour lines are packed closer together. This is because across each unit of distance, there would be more contour lines crossed and therefore a greater difference in values across that distance.

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