U.S. Standard Atmosphere My textbook states that "Ideally, we would like to have measurements of pressure versus altitude over the specific range for the specific conditions (temperature, reference pressure) for which the pressure is to be determined. However, this type of information is usually not available. Thus, a "standard atmosphere" has been determined that can be used in the design of aircraft..."
"The standard atmosphere is an idealized representation of mean conditions in the earth's atmosphere"
My question is, why can't we determine how pressure varies with altitude. Say we want to know the pressure at 1000 m. Why can't we measure the pressure at 1000 m for different temperatures?
 A: 
Why can't we measure the pressure at 1000 m for different temperatures?

Meteorologists certainly can do that, and in fact do do that, all the time. They use weather balloons, sounding rockets, and all other kinds of instrumentation to measure conditions in the atmosphere. The resulting picture is rather complex. Conditions vary with place, the seasons, and with the weather. Just because you know the temperature at one kilometer altitude does not mean you know the pressure at that altitude, or vice versa.
You are missing the point of developing the concept of a standard atmosphere model. The intent is to give a rough idea of how temperature, pressure, and composition vary with altitude that is independent of place, the seasons, and the weather.
Key assumptions toward the tropospheric portion of the standard atmosphere model:


*

*The atmosphere has balanced buoyant and gravitational forces.

*Except for water vapor, the troposphere has a nearly uniform composition.

*The gases that comprise the troposphere behave close to ideal.

*Temperature and pressure variations with respect to altitude are close to adiabatic.

*As a starting condition, ignore that one of the components of the atmosphere is water vapor.


For an atmosphere in balance with itself, the buoyant force that results from the pressure gradient with respect to height must equal the force due to gravitational acceleration $g$. This yields the hydrostatic equilibrium condition
$$\frac{dP(h)}{dh} = -\,\rho(P,h)\,g(h)$$
As an aside, the above condition also describes the interior of a star, which shouldn't be that surprising. Perhaps more surprising, it also describes conditions inside the Earth. The mantle is not a liquid. It is solid. However, it is a viscoelastoplastic solid.
This doesn't say much, at least not yet. The right hand side involves density, which varies with pressure and with altitude $h$. This can be replaced by pressure and temperaure by assuming the ideal gas approximation. With this, the hydrostatic equilibrium becomes
$$\frac{dP(h)}{dh} = -\,\frac {\mu}{R} \frac {P(h)\,g(h)}{T(h)}$$
where $mu$ is the mean atomic mass of the molecules that comprise the atmosphere and $R$ is the gas constant. Perhaps temperature is a better quantity to model than is pressure. Adding the assumption of adiabatic conditions and ignoring condensation yields
$$\frac {dT(h)}{dh} = - \frac {\mu g}{R} \frac{\gamma-1}{\gamma}$$
This is constant. Looking at temperature rather than pressure most definitely is a better approach if all of those assumptions are valid (they aren't, of course). The above rate at which temperature decreases linearly with respect to increasing altitude is the dry adiabatic lapse rate.
The biggest problem is the fifth assumption. At some altitude, temperature will decrease to the dew point and water will start condensing out of the atmosphere. This condensation releases heat, and that in turn reduces the lapse rate. It turns out that the temperature drop is linear even with condensation. The rate at which this occurs is wet adiabatic lapse rate. The altitude at which this transition from dry to wet adiabatic lapse rate occurs varies considerably, and this in turn means the wet adiabatic lapse rate itself also varies considerably.
It would be nice to have an average lapse rate that smooths out all of these variations. That is precisely what the US standard atmosphere model does.
A: For aviation purposes, standard atmosphere is considered to be dry air at mean sea level, at 15 degrees C (59F). It is true that pressure decreases with increasing altitude, and temperature usually does, but not always. It is not a simple relationship, because it depends on humidity, heat transfer from above and below, vertical circulation, horizontal circulation, etc.
Check out Lapse Rate.
To a first approximation, we can determine how pressure varies with altitude.
Every aircraft contains a barometric altimeter, and when it is calibrated for the current sea level air pressure, it measures altitude above sea level.
Whether it is accurate or not does not really matter.
What matters is that it is reliable - the same altitude is shown in different aircraft, so they can be safely assigned to different levels.
