300 million years old
(Israeli archaeologists digging in caves east of Tel Aviv have discovered eight human teeth dating from 400,000 years ago,
which may be the earliest traces of the human species. Read more:)
well-mixed atmosphere
the speed of the motion of atoms and molecules is a function of temperature
$T = \alpha \cdot m_W\cdot v^2$, where $T$ is measured in Kelvins (K), $\alpha = 4.0 \times 10^{-5} \mbox{K} \mbox{sec}^2\mbox{m}^{-2}$, $m_W$=the atomic mass,
and $v$ is the average magnitude of the molecule's velocity in m/sec. The speed of individual molecules form a (continuous) distribution about the mean velocity
the perpetual, energetic, and random motion of individual molecules (spelled out more exactly in a simple theoretical model known as the kinetic molecular theory) in conjunction with significant horizontal and vertical motions of atmospheric parcels (aggregations of atmospheric molecules), result in a well-mixed atmosphere
only constituent that exists in all three phases (solid, liquid, vapor) in our atmosphere
precipitation
residency of atmospheric moisture is about 8-9 days - the total atmospheric moisture at any one time could provide only one-weeks worth of world-wide precipitation.
energy transfer by latent heat
green house gas (GHG)
carbon dioxide (CO2)
change : 315 ppmv (1960) to 407.4 ppmv (2018) ... represents a 29.3% increase
A molecule of carbon dioxide, generated by burning fossil fuels will, in the course of
its lifetime in the atmosphere, trap a hundred thousand times more heat than was released
in producing it (Caldeira - Lawrence Livermore National Laboratory in the $\textit{New}$ $\textit{Yorker}$ $\textit{Magazine}$, Nov 20, 2006)
ozone (O3)
stratosphere - absorbs ultraviolet radiation in the process called photodissociation
O3 + h$\nu$ $\rightarrow$ O2 + O
surface level - causes smog
methane (CH4)
more efficient GHG than carbon dioxide
aerosols - tiny solid or liquid suspended particles
anthropogenic - nitrogen dioxide (NO2) from automobiles, sulfur dioxide (SO2) from sulfur-containing fuels (results in acid rain)
serve as condensation nuclei in the precipitation process
Aitken particles - (radii less than 0.2 micrometers) 1,000 to 10,000 per cm3
larger nuclei - (radii between 0.2 and 1.0 micrometers) 1 to 1,000 per cm3
giant nuclei - (radii greater than a micrometer) 1 to 10 per cm3
Atmospheric Parcels
A conglomeration of atmospheric constituents that maintains its identity (the constituents "stay together") over a period of time. However, there may be relative motion among the parcel constituents. (A group of friends meandering through a crowded shopping mall may serve as a good analogy.)
The mass of a given parcel remains constant, but different parcels can have different masses.
The "size" of a parcel is large enough so that the mean free path length of any constituent is "short" relative to a given dimension of the parcel, yet small enough so that the parcel has uniformity in such quantities as temperature, density, and pressure.
The mean free path $\lambda$ is 68 nm (nano-meter = 10$^{-9}$ meter) at an atmospheric pressure of 1013 mb (standard surface pressure). At 300 mb, $\lambda$ is 0.1 - 1000 $\mu$m (micro-meter = 10$^{-6}$ meter)
The Knudsen number (Kn) is small (much less than 1.0) for an air parcel. The number is defined by $Kn = \frac{\lambda}{L}$, where $\lambda$ = mean free path and $L$ = a representative length scale.
The volume of a given parcel can change over its time of existence. For example, the volume of a parcel will increase (decrease) as the parcel rises (sinks).
The percentage of permanent atmospheric constituents, by volume or weight, is the same for every parcel.
"An imaginary body of air to which may be assigned any or all of the basic dynamic and thermodynamic properties of atmospheric air. A parcel is large enough to contain a very great number of molecules, but small enough so that the properties assigned to it are approximately uniform within it and so that its motions with respect to the surrounding atmosphere do not induce marked compensatory movements. It cannot be given precise numerical definition, but a cubic foot of air might fit well into most contexts where air parcels are discussed, particularly those related to static stability." - Wiktionary definition.
$T = \alpha \cdot m_W \cdot \bar{v}^2$, where
$\alpha$=4.0$\times$10-5 K sec2/m2 is a constant of proportionality,
$m_W$ is the molecular mass of the material (for the earth's atmosphere, $m_W$ = 28.9),
$\bar{v}$ is the average molecular speed (measured in m/sec), and
$T$ is the temperature of the parcel measured in Kelvins (K) - the absolute temperature scale.
$T$ = 0 K means kinetic energy of the molecules is zero, the molecules are not moving
other units of measure are Celsius (C) and Fahrenheit (F)
C = K - 273
F = $\frac{9}{5}$C + 32 and C = $\frac{5}{9}\left(F-32\right)$
the global average surface temperature is 15 degrees C (or 59 degrees F) (Decorah average is 46.2 degrees F)
troposphere (0 - 10km): temperature decreases linearly with height
$T(z) = T_s - \frac{6.5}{1000}z$,
where $z$ is height, or elevation, above ground level (agl) measured in meters, and $T_s$ is the surfacetemperature measured in degrees C.
Also, $\Delta T = -\frac{6.5}{1000} \Delta z$, where $\Delta T$ is the change in temperature (in degrees C or K) and $\Delta z$ is the change in elevation (in meters)
stratosphere (10km - 50km): temperature is constant, then increases with height due to the absorption of the sun's ultraviolet energy by ozone - O3
mesosphere (50km - 85km): temperature is constant, then deceases linearly with height
thermosphere (85km - 120km): temperature is constant, then increases with height due to absorption of solar radiation by diatomic nitrogen (N2) and oxygen (O2)
density - $\rho$
density = mass per volume measured in kg/m3 or g/L
1 kg/m3 = 1 gm/L, because 1 kg = 1000 gm and 1 m3 = 1000 L (liter)
average surface density is 1.22 gm/L (same as 1.22 kg/m3)
density decreases exponentially with height (assuming a constant temperature with height - which is not the case)
$\rho(z) = \rho_se^{-z/8000}$.
where $z$ is height, or elevation, above ground level (agl) measured in meters, $\rho_s$ is the surface density, and $e$ is the natural base ($e \approx 2.71828$)
Expression derived assuming hydrostatic equlibrium and the using the Ideal Gas Law for the Earth's atmosphere.
pressure - $P$
force = mass times acceleration : $F = m \times a$
1 Newton (N) = 1 kg $\times$ 1 $\frac{\mbox{meter}}{\mbox{sec}^2}$
A force of one Newton accelerates a 1 kg mass one meter per second each second.
pressure = force per area : $P = \frac{F}{Area}$
1 Pascal (Pa) = 1 N per m2
one bar = 100,000 Pa
1 millibar (mb) = ($\frac{1}{1000}$)100,000 Pa = 100 Pa = 1 hectopascal (hPa) = 0.1 kilopascal (kPa)
average surface pressure is 1013 mb or 1013 hPa or 101.3 kPa
pressure decreases exponentially with height (assuming a constant temperature with height - which is not the case)
$P(z) = P_se^{-z/8000}$
where $z$ is height, or elevation, above ground level (agl) measured in meters, $p_s$ is the surface pressure, and $e$ is the natural base
mandatory pressure levels - radiosonde data collection
where
$\Theta$ (parcel potential temperature) and $T$ (parcel temperature) are measured in K, and
$R$ = 287 J/(K$\cdot$kg) and $c_p$ = 1004 J/(K$\cdot$kg)
The parcel's temperature $T$ and potential temperature $\Theta$ have the same value at the earth's surface where the pressure is approximately 1000 mb. Suppose a parcel at 850 mb (an elevation of approximately 1500m) and a parcel at the surface ($P$ = 1000mb) have the same temperature. The parcel at 850 mb has a greater potential temperature, and that potential temperature is equal to the temperature the parcel will be if it is brought to the surface. The parcel warms to its potential temperature by the time it reaches the surface, and the warming is due to the work done on the parcel by the increasing atmospheric pressure it experiences in the down-ward movement.
A derivation of the potential temperature formula is given here.