1. SO254 Introduction to Meteorology
Important variables in meteorology Equation of state for dry and moist air
SO254 Introduction to Meteorology

2. Variables
Meteorology is, at its core, calculus and physics applied to air
That means that underlying every aspect of meteorology is math
That math has variables and units that accompany them
To set yourself up for success, it’s important to know the key variables
Table (next slide) summarizes some of the most-used variables in meteorology

3. Variable
Letter or abbreviation
Typical units
Notes
Temperature
T (usually capitalized)
Celsius, Kelvin, or Fahrenheit
SO345 (Atmospheric Thermodynamics) is an entire course devoted to temperatures!
Pressure
p (usually lower-case)
Pascal (Pa)
hectopascal (hPa) millibar (mb)
kilopascal (kPa)
One mb is equal to 1 hPa, and both are equal to 100 Pa
Density
ρ (Greek letter rho, lower-case)
kg m-3
Mass divided by volume
Mass
m (typically lower-case) kg
Distance
x, y, z
meters (m)
Time
t (usually lower-case)
seconds (s)
hours (h, sometimes hr)
Water vapor
w (mixing ratio)
q (specific humidity)
RH (relative humidity)
Td (dew point temperature)
w and q have units of kg kg-1.
RH is unitless.
Td has units of °C or °F
There are other measures of water vapor besides these. We will see more of them later in the course
Velocity
u (east-west velocity component)
v (north-south velocity component)
w (vertical velocity component)
u, v, and w all have units of m s-1

4. Derivation: from an ideal gas to the equation of state for dry air
One of the most important relationships in all of meteorology, and one of the primitive equations that form the basis of all weather prediction models, is the equation of state
It is a very simple equation, p=ρRT, where R is the dry gas constant (R= J kg-1 K-1), and J represents Joules
The equation of state for moist air is very similar, and takes into account water vapor in the atmosphere: p=ρRTv, where Tv is the virtual temperature:
Tv = T + w/6, where Tv is the virtual air temperature in C, T is the air temperature in °C, and w is the mixing ratio of air, in g kg-1
The equation of state for dry air comes from one of the basic equations in physics: the ideal gas equation

5. Derive an equation of state for dry air
Classical physics has derived a simple equation governing behavior of ideal gases (what is an “ideal gas”?)
where p, V, T, R*, and n denote the pressure, volume, temperature, universal gas constant, and number of moles of a fixed collection of matter (i.e., an air parcel).

6. Derive an equation of state for dry air
It is not an easy manner to measure mass in the atmosphere (nor is it easy to measure volume). So we can use the assumptions of atmospheric composition (78% N2, 21% O2, etc) to transform n and R* into useful meteorological forms
We express n as n=m/Md, where m and Md are the mass and molar weight of the dry air parcel
Md = (0.78*N * O *other)
= (0.78*14*2 g/mol *16*2 g/mol +
0.01*40 g/mol)
= g/mol

7. Derive an equation of state for dry air
Start with the ideal gas law, and put it in a form useful for atmospheric science
n=m/Md
R=R*/Md
Move V/m to other side
Density, ρ, = mass ÷ volume

8. Now, some basic properties of the atmosphere

9. How “tall” is the atmosphere?
Depends on what you want
Weather occurs in about the lowest 15 km of the atmosphere
Air extends up about 100 km *

10. How does air pressure change with height?
Exponential decrease
How does density change with height?
Typically decreases exponentially, too
At the surface:
1013 mb
1013 hPa
101,300 Pa

11. Atmospheric pressure decreases exponentially with height
50% of earth’s air lies in the lowest 6 kilometers (3.7 miles)
Atmosphere officially extends up over 100 miles

12. Pressure is basically the “weight” of the air above a location
If your location is at sea level, you will (generally) have a higher atmospheric pressure than other inland locations.
WHY??
Pressure decreases exponentially with height (more air molecules are found in air at the surface than in the same volume of air aloft)

13. How does air temperature change with height?
Not as straight-forward as pressure

14. Important definition:
Inversion: a layer of air where the temperature change with height is opposite normal
In troposphere, inversion is an INCREASE in temp with height