# WX BRIEF

## Defining standard atmosphere

### An ideal understanding of an environment that is anything but ideal.

#### By Karsten Shein

Comm-Inst, Climate Scientist

** Robert Boyle (1627–91), a father of modern chemistry, first made the connection that at a constant temperature, the pressure and volume of a gas (such as air) are inversely proportional. This discovery is the basis of the Ideal Gas Law, which in turn governs the Intl Standard Atmosphere. ISA is a theoretical atmosphere of average surface conditions and fixed lapse rates. Flying in regions where the atmosphere is far different from the global averages results in nonstandard altimeter settings and a need to be vigilant about performance characteristics.**

There are certain facts we know about the atmosphere and the things in it. For example, a strong low usually means low ceilings and storms. When it gets hot and humid the air density decreases until it becomes difficult to get our birds into the air. Windspeed is a function of the difference in pressure between where the wind is blowing from and where it is blowing to.

We use these atmospheric facts to help us figure out what we might be up against when we take to the skies. But, beyond these basics, pilots actually rely quite heavily on approximations as well. In particular, many aircraft performance specifications reference an estimate of an idealized atmosphere, devoid of convection, cold winters or hot summers.

When we turn to the operating handbook to determine a pressure altitude or a climb rate, we are using a set of commonly agreed on values of temperature, pressure and density for any given altitude. These numbers constitute the Intl Standard Atmosphere (ISA). The US has a slight variation on the ISA known as the US Standard Atmosphere, but the product is essentially the same and the values are identical up to at least 32 km (105,000 ft).

Since the 1920s, meteorologists have sent rockets, balloons and even aircraft aloft, rigged with barometers, thermometers and other instruments. Millions of measurements from around the planet have allowed them to discover that, for at least the lowest layer of the atmosphere—the troposphere—average conditions can be approximated by a set of equations.

For example, air density decreases exponentially with increasing altitude. Since the pressure exerted by the air molecules at any given altitude is dependent on the density, pressure also decreases exponentially. Air temperature also declines with increasing altitude, but the decrease is more linear the further one goes from the heating source—Earth's surface.

Using these equations, meteorologists were able to produce tables of what the average ambient conditions should be at any given altitude in the lower atmosphere. Because an aircraft's performance is fundamentally a function of air density, aircraft designers used these equations to provide guidance on how well an aircraft could be expected to perform at different altitudes.

Service ceilings, engine power, rates of climb, pressure and density altitudes, takeoff and landing distances are all referenced against these average conditions, and corrective factors are built into the tables for when the actual ambient conditions differ from standard.

**Ideal gases**

**Thermodynamic diagram—also known as a Skew-T/Log-P chart—shows how temperature and pressure vary with altitude. Actual temperatures from weather balloons are plotted on such charts to evaluate things like the stability of the atmosphere and the potential for severe weather.**

The basis of the standard atmosphere is the known relationship between temperature, pressure and density. Known as the Ideal Gas Law, the relationship is in the form of the equation pressure x volume = amount of the gas x a gas constant x temperature.

Since the gas constant is, well, constant, we can ignore it—and if we divide the amount of gas by the volume, we get density, so we can rewrite the relationship in a more general sense as pressure = density x temperature. In a nutshell this means that, as temperature decreases, so does pressure—and, as density (amount of the gas in the volume) increases, so does pressure.

And so on. When this equation is applied to the average temperature lapse rate of the lower atmosphere, the pressure, temperature and density for any altitude can be estimated.

ISA is based on a set of fixed assumptions, including a constant surface temperature and a constant temperature lapse rate. Until the rapid warming of the atmosphere experienced since the 1980s, Earth's long-term average global temperature was 59°F (15°C).

The average decrease in temperature with altitude through the lowest 11 km (approx 36,000 ft) is roughly 6.5°C per 1000 m (3.6°F or 2°C/1000 ft). Above 11 km, different lapse rates are used, and ICAO has published ISA values all the way up to 262,500 ft.

What these fixed standards mean is that, using the ISA, you could estimate that, at 18,000 ft, the ISA temperature would be –21°C (–5°F), and the pressure would be 506 mb (506 hPa or 14.94 inches Hg)—roughly half that at the surface. At 30,000 ft, you would expect a temperature of –44°C (–48°F) and a pressure of 300 mb (300 hPa or 9 inches Hg). Such known quantities are great to know when you need to estimate the performance of your aircraft, but there are some caveats.

**When things are not standard**

When was the last time you experienced a flight through a beautiful standard atmosphere? One of the great pieces of statistical wisdom is that averages rarely occur. They are simply a mathematical expression of a middle point of the whole of all the observations.

This rarity is especially true in the atmosphere. These standard values are nothing more than estimates from equations that are designed to come close to the average conditions.

Unfortunately, in working to approximate the averages, the equations can and often are oversimplified. An example provided by a Pro Pilot reader serves as a great example of this.

The reader asked why altimeter settings at BOG (El Dorado, Bogotá, Colombia) were normally so high—almost never below 31.00. Indeed, that does seem strange, especially since Bogotá is very close to the Equator. Because of the general circulation of Earth's atmosphere, surface air from both the Northern and Southern Hemispheres converges at the Equator and is heated along the way.

The result is a band of the atmosphere where the converging surface air meets and is forced to rise. We see this on satellite images as a ring of clouds that encircles the Earth at the tropics—also known as the Intertropical Convergence Zone (ITCZ).

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