The altimeter installed in the aircraft you fly is designed to sense the atmospheric pressure outside of the aircraft. As a barometer it is very accurate. Ironically, as a gauge to assess our altitude, it has some serious shortcomings. Not all is lost, however. Fortunately, all aircraft use the same basic altimeter and therefore all have the same errors. However, these errors don't typically cause a problem until the temperature is very cold. Let's explore this error a bit further. One of the more common altimeter errors is due to non-standard pressure. When the weight of atmosphere above our position changes, the atmospheric pressure also changes. Less weight means lower pressure; more weight means higher pressure. Such a change in pressure is not a problem since we can adjust our altimeter for non-standard pressure. This correction is done through the altimeter setting and is adjusted in the Kollsman window (which could be an analog or digital gauge depending on the installed equipment). We update the altimeter setting periodically as required by FAA regulations. The density of the air below our flight level also plays an important role. The density of air is a function of both temperature and moisture. An increase in moisture and/or temperature decreases the air density. Conversely, a decrease in moisture and/or temperature increases the air density. Since moisture has a much less significant role, we will focus on the role of non-standard temperature in this post. Adjustments to account for non-standard pressure, however, do not compensate for non-standard temperature. In fact, pilots don't specifically account for non-standard temperature. Air is a mixture of many gasses. When the temperature of air is increased, for example, the molecules in this mixture will achieve a higher kinetic energy and space themselves farther apart resulting in a decrease in air density. As air temperature is decreased, the molecules in the mixture will achieve a lower kinetic energy and the molecules in the mixture are spaced closer together resulting in an increased air density. Let's assume that you are flying at a constant pressure level of 850 mb resulting in an indicated altitude of 5,000 feet. Now, imagine that the temperature the air below you suddenly increases. How will this change your indicated altitude?
Since the atmosphere is not a closed container, increasing the air temperature will cause it to expand in all directions. To keep the explanation simple let's limit the discussion to expansion (or contraction) of air in the vertical. The only variable that has changed is the temperature. There has been no change in the mass (weight) of the air. In other words, we have not added or removed any molecules of air so the pressure at the surface remains the same. Instead, the same molecules in this air have simply moved farther apart, and therefore, decreased the overall air density.
In response to the sudden decrease in density, all of the the pressure surfaces below you have expanded upward. The 850 mb pressure surface you were flying is now above your current altitude and now your altimeter is sensing a higher pressure (note the altimeter setting hasn't changed). This is because the pressure surfaces below you expanded upward. In order to get back to the 850 mb pressure surface you will need to climb since it is above you. Consequently, the sudden decrease in air density due to the increase in temperature caused your altimeter to now read a lower altitude. Essentially, you have to increase your true altitude to stay at a constant indicated altitude of 5,000 feet. Excluding differences in the height of terrain, this places you farther from the surface of the Earth after the climb.
The opposite is true in response to a sudden decrease in temperature (increase in density). In this case, all of the pressure surfaces settle and move downward toward the earth. This places the 850 mb level below you requiring that you descend or lose true altitude to stay at a constant indicated altitude of 5,000 feet. This places you closer to the surface of the earth after the descent. As you might imagine when the temperatures are much colder than standard, this error can reduce your separation with obstacles when flying close to the earth. This is summarized in the graphic above.
This error increases in magnitude the higher you are above the airport's elevation and only depends on the temperature of the air below you. If you are on the surface, there’s no air below you, so there’s no error. As you increase your altitude above the airport, you may begin to experience the effect of non-standard temperature. This error is not exactly linear, but fairly close to being linear at the altitudes general aviation pilots normally fly piston aircraft. The error is about 4-percent for every 10°C departure from standard.
The cold temperature table above uses absolute temperatures (not departure from standard). Standard temperature at the surface is 15°C. 10°C below standard would be 5°C which is between the first two rows of the table. So let's say you are at 3,000 feet above the airport on a day where the air is 10°C below standard. What is the error? As mentioned above, every 10°C above (or below) standard temperature there's approximately a 4-percent error in your indicated altitude. Four percent of 3,000 feet is equal to 120 feet of error in the indicated altitude. Using the table above, interpolate between 170 feet and 60 feet (numbers from the first two rows in the table under the 3,000 feet column circled in red), the error depicted by this table is 115 feet at 5°C (or 10°C below standard assuming a standard lapse rate up to 3,000 feet). The magnitude in error increases with increasing true altitude, but isn't quite enough to cause an issue while en route. Where it can become an problem is on an instrument approach to an airport. In very cold temperatures you can be 50 to 100 feet below your decision height which is charted as a true altitude based on standard temperature conditions.
Most pilots are weatherwise, but some are otherwise™
Weather Systems Engineer
CFI & former NWS meteorologist