Geography 140
Introduction to Physical Geography
Lecture: Temperature as an Element of Weather
I. This lecture begins a new major section on weather.
A. Weather refers to our day-to-day experience of conditions in the
troposphere, where climate can be thought of as the average state of
the weather and its typical range of variation over a sustained time
period.
B. There are four basic elements of weather:
1. Temperature
2. Pressure
3. Moisture
4. Storms
II. The first element of weather is temperature.
A. The earth's radiation balance.
1. The ultimate source of virtually all heat in the atmosphere is the
sun (there are trivial contributions from geothermal and, I suppose
for the sake of rhetoric, a vanishingly dinky contribution from
stellar sources).
2. All solar radiation that enters the earth system eventually leaves
it. The pathways of this energy into, around, and out of the earth
system is called the "earth's radiation balance."
3. Even though any incoming energy is balanced by outgoing energy at
any given point in time, the particular energy that enters right
now does not need to leave immediately. It can stay around for
even a really long time, just as long as some stale old energy
leaves when it arrives.
4. Much energy, some two-thirds of it, in fact, does stay in the earth
system for a while. This happens because it changes its form soon
after arrival (it is absorbed and then re-radiated at a different,
longer wavelength). The change of form delays its exit, and the
delay allows the earth's atmosphere to be heated above its
theoretical blackbody temperature.
B. Solar energy as it arrives at the top of the earth's atmosphere (TOA).
1. When radiant energy leaves the sun, it leaves in the form of
"short-wave radiation." Electromagnetic energy, of which solar
energy is an example, travels in wave patterns.
a. "Short-wave" simply means the distances from one wave crest to
the next (or one trough to the next) is "short."
![[ transverse wave features, Center for Astrophysical
Research in Antarctica, 11 September 1999 ]](http://astro.uchicago.edu/cara/outreach/se/ysi/1999/diagram.jpg)
b. How short, you want to know. Well, solar radiation is emitted
in wavelengths ranging from about 0.25 microns (sometimes called
micrometers) to about 2.5 microns. You remember microns? One
millionth of a meter (which is a tad more than a yard).
2. The reason it adopts this short-wave form is the tremendous heat of
its source.
a. The hotter a radiant body is, the shorter the wavelength of its
emissions.
b. The sun, powered by nuclear fusion of hydrogen (H) into helium
(He), generates a surface temperature of about 5,770 K (NASA).
i. Kelvins are degrees centigrade above absolute zero.
ii. Absolute zero is the temperature at which all molecular
motion ceases.
iii. This is 273° below 0° C (which is about 460°
below 0° F).
iv. So, the freezing point of water at sea level is 273 K and
the boiling point of water at sea level is 373 K. Pleasant
room temperature would be, oh, 293 K to 298 K. Just trying
to give you a frame of reference for Kelvins.
c. Wien's Displacement Law predicts the wavelength of peak
radiation intensity as a function of the temperature of the
source.
i. It states that there is an inverse relationship between
temperature of the radiation source and the wavelength of
its radiant output: Peak radiation intensity is displaced
towards the shorter wavelengths by hotter radiant bodies
and towards the longer wavelengths by cooler radiant
bodies.
ii. L = 2,897/T, where:
L = waveLength of peak radiation intensity (in microns)
T = Temperature of radiant body (in Kelvins)
iii. So, applying Wien's Displacement Law, we would expect that
the peak radiation intensity emitted by the sun would be:
L = 2,897/5,770 K = 0.50 microns
iv. This places the peak radiation intensity within the visible
light portion of the electromagnetic spectrum (within the
wavelengths most of us would perceive as light blue or
aqua).
a. As you can see, a significant amount of solar radiation
arrives at the top of the atmosphere in the form of
ultraviolet radiation: This is the portion of solar
radiation filtered out by its being absorbed by ozone.
1. We can't perceive it directly, but it causes our
skins and eyes a lot of damage in the suntan-sunburn-
skin cancer progression and in the form of cataract
acceleration: Slip, slap, slop (and don't forget your
UV-certified sunglasses).
2. Interesting geotrivia: Some insects, such as bees,
and some birds, such as pigeons, can see some of the
UV-A!!! For them, it's another color.
b. Also, a large amount of solar radiation is emitted in
the infrared wavelengths, too, some of the longer
wavelengths of which we perceive as heat.
![[ irradiance distributions of Earth and Sun ]](https://home.csulb.edu/~rodrigue/geog140/sunwavelength.gif)
v. Geobonus: See if you can figure out the peak radiation
intensity of the earth. You know the average temperature
of the earth as a whole is 15° C. You know that 0°
C = 273 K. So, what's the average temperature of the
earth, expressed in Kelvins? Okay, now you have that, you
can plug it into the Wien's Displacement Law formula above,
as the denominator. Soooooo, what's that peak irradiance
wavelength in microns? You should compare your answer with
the graph above to see if you're in the ballpark.
3. That sunlight that arrives at the top of the earth's atmosphere and
descends into the earth system is called "insolation," for INcoming
SOLar radiATION.
a. Insolation is not a very significant portion of the sun's total
output.
i. Earth intercepts only about 0.002 percent of the sun's
total output of radiation.
ii. This is because Earth is a tiny target and it's far away
from the sun.
iii. In a manner of speaking, all the planets, moons, asteroids,
and comets are minor impurities in the near vacuum of space
around the sun! Kind of puts things in perspective,
doesn't it?
iv. Earth is one astronomical unit (1 AU), or 149,597,870.66 km
from the sun, or about 150,000,000 km.
v. The sun's surface irradiance is 62,900,000
Joules/m2/s; its surface lies 696,000 km from
its center (the sun's radius, then, is about 55 times
greater than Earth's radius of about 12,660 km!
vi. So, we can figure out the solar constant with just this
information and the inverse square law. The solar constant
is the average amount of energy received on a surface
oriented perpendicular to the sun's rays at the top of the
earth's atmosphere (basically, the energy received under
the direct ray of the sun).
vii. S = I*(R/D)2
Where: S = Solar constant
I = Irradiance of the sun at its surface
R = Radius of the sun
D = Distance of the earth from the sun
So: S = 62,900,000 * (696,000/150,000,000)2
= 62,900,000 * (0.00464)2
= 62,900,000 * (0.00002153)
= 1354.21 J/m2/s
(or 1354.21 watts/m2
viii. 1354.21 is 0.002 percent of the sun's surface irradiance.
ix. See if you can figure out how much solar energy is
intercepted by the earth at perihelion, when the earth is
"only" 146,400,000 km from the sun in early January, and at
aphelion, when the earth gets as far out as 151,200,000 km
from the sun in early July. Just plug those numbers in as
the denominator of the second term in the solar constant
equation above.
x. So, how much greater is the incident solar energy at
perihelion than at aphelion? Subtract the aphelion figure
from the perihelion figure and then divide that answer by
the perihelion figure. Multiply your answer by 100 to
express it as a percentage.
b. Insolation is not equally intense all over the earth.
i. It varies according to sun angle.
a. If the sun's rays are coming in perpendicularly (we're
talking about being under the direct ray of the sun),
then more sun "beams" can be concentrated in a given
unit of area, such as a square meter. If the sun's
rays are coming in at a more acute angle, that same
amount of energy will be smeared over a wider area.
![[ insolation as a function of sun angle, physicalgeography.net]](http://www.physicalgeography.net/fundamentals/images/incidence.gif)
b. I = S*cos(A)
Where: I = Incident solar radiation at a location
S = Solar constant
cos means cosine
A = Angle that the sun makes with the zenith
(the point in the sky right overhead) that
day at that latitude -- at the poles on that
day, this angle would be 90°; at the
equator, it would be 0° (aligned with
the zenith)
c. So, at 45° N on an equinox, that would be:
I = 1354.21*cos(45°)
= 1354.21*0.7071
= 957.57 Joules per square meter per second
This is 71% of the energy at the direct ray.
d. At 60° N on an equinox, that would be:
I = 1354.21*cos(60°)
= 1354.21*0.5
= 677.11 Joules per square meter per second
This is 50% of the energy at the direct ray.
ii. Plot complication: The location of the direct ray of the
sun shifts over the course of the year from
23½°N to 23½°S, so we have to factor
in declination.
a. You have to subtract the declination from the angle the
sun makes with the zenith when the declination is in the
same hemisphere as you are and add it when it's in the
other hemisphere.
b. I = 1354.21*cos(A+d)
c. So, if you were at 60° N around June 21:
I = 1354.21*cos(60-23.5)
= 1354.21*0.8039
= 1088.59 Joules per square meter per second or 80% of
the solar constant
d. If you were at 20° S on that date:
I = 1354.21*cos(20+23.5)
= 1354.21*0.7254
= 982.31 Joules per square meter per second or 72% of
the solar constant
e. If you're curious, you could work out I for, oh, three
latitudes in each hemisphere in June and in December and
see whether summer or winter produces the biggest
changes in insolation with latitude.
iii. Yet another plot complication: The angle the sun makes with
the zenith changes over the course of the day from 0°
at sunrise and sunset to the maximum value for the latitude
and time of year at local noon. Gets pretty maddening, eh?
C. Adventures in solar energy as it descends through the atmosphere to
the surface.
1. About one third of it is bounced right back into outer space,
unchanged, having done no work in the earth system. This is the
"earthlight" seen by astronauts and by cameras and other imagers in
orbit or on the moon. This reflectance is called "albedo." You
will sometimes see two subtypes of albedo differentiated:
![[ earthrise over lunar horizon, NASA, Apollo 11, 19 July
1969 ]](https://home.csulb.edu/~rodrigue/geog140/earthrise.jpg)
a. Normal albedo is the amount of light reflected directly right
back up into the source of incident radiation. In other words,
it's the light that would hit a surface perpendicularly and then
do a 180. So, if you shone a light straight down on a snow-
covered field and caught the light bouncing right back to where
you were waiting with an imager, you'd find it had a normal
albedo of close to 100%. If you did that on a field covered
with coal, it would be closer to 0%.
b. Bond albedo is more comprehensive, and it's the one geographers
mean when they're talking about earth processes: It's the
percentage (or proportion) of all incident radiation of all
wavelengths that is reflected, unchanged, in ANY direction.
It's named for an American astronomer, George P. Bond, who
compared this sort of albedo for the moon and Jupiter back in
1861.
2. Earth's average Bond albedo is not quite 31 percent (the normal
albedo is about 37 percent).
3. Different elements in the earth system are differentially
responsible for the earth's Bond albedo.
a. Dust and gas molecules scatter or diffusely reflect about 6
percent of insolation.
i. Dust and especially gas molecules are so small compared to
the wavelengths of insolation that they tend to reflect
only the shorter wavelengths, biasing their reflection
toward blue and violet and aqua wavelengths. This is why
the diffused light from the sky is blue. The dust and the
gas molecules scatter longer wavelengths, but less
efficiently (about 10 percent as efficiently), and so we
don't notice them among all the blue light.
ii. At sunset, however, the solar beams are angling through the
atmosphere, which makes their trip through the atmosphere a
lot longer. This gives more opportunity for the longer
wavelengths to be reflected, which means we start to notice
yellow, orange, and red wavelengths. And the closer you
look toward the horizon, the redder (longer) the
wavelengths: That's where the sun beams are coming in at
the lowest angle with the ground and, therefore, have to
make the longest trip through the atmosphere.
b. Clouds reflect about 20 percent: They reflect pretty equally
across the spectrum of visible light, so, when we see all
wavelengths in the VL, we perceive the light as white. You
really notice this when you're flying over the tops of clouds!
c. About 4 percent of insolation manages to make it all the way to
the earth's surface, only to bounce, unchanged, off the surface
itself.
i. Surface albedo varies a lot.
ii. Snow and light surfaces have relatively high albedos.
a. Snow and ice have Bond albedos of around 70-95 percent
b. Deserts reflect about 20-45 percent.
iii. Dark vegetation and soil have relatively low albedos.
a. Forest is usually around 10-20 percent.
b. Dark, moist soils are around 5-15 percent.
iv. Oceans and other water bodies have low normal albedos (2-4
percent), for insolation coming down onto it at high
angles, but they have higher Bond albedos when you factor
it their high reflectivity when the light is coming in at
low angles.
v. You can notice albedo differences in the built environment:
a. A concrete sidewalk isn't generally too hot to walk on
barefoot, even in summer, because of its higher albedo
(usually around 17-27 percent)
b. An asphalt parking lot, on the other hand (especially a
newly paved one), is dangerously hot to bare feet in
summer because of its low albedo (and consequent high
absorption and reradiation). Blacktop has albedo
somewhere around 5-10 percent.
d. You can see a large graphic showing the earth's energy budget by
clicking here. The upward arrows that are light yellow
in color represent albedo.
D. Absorption of insolation in the earth system.
1. A Bond albedo of 31 percent leaves about 69 percent of insolation
to be absorbed somewhere in the earth system. This radiation is
trapped, its form is altered, it does some sort of work in the
earth system, and it is, thus, delayed in its eventual departure
from the planetary system. We will find the same players in
reflecting insolation also engage in absorption, too.
2. Absorbing agents in the earth system:
a. Dust and gas molecules absorb about 16 percent of insolation, so
they are better absorbers than reflectors.
i. Ozone, we saw earlier, absorbs ultraviolet radiation.
ii. Atmospheric water absorbs in a wide range of near and
middle infrared wavelengths.
iii. Carbon dioxide absorbs very well, especially in the middle
infrared.
iv. Dust absorbs in the visible light (which is why it darkens
the sky and makes it look, well, dirty) and infrared
wavelengths.
b. Clouds absorb about 3 percent of insolation.
i. This is especially the case when ice crystals or liquid
water droplets in them evaporate and the cloud diminishes
or disappears.
ii. Clouds are, then, much stronger reflectors than absorbers.
c. The earth's surface itself absorbs around 51 percent of
insolation.
i. Land surfaces are excellent absorbers of insolation: They
rapidly soak up sun energy and heat up quickly with the
energy they've stored. They then rapidly reradiate that
stored energy at longer wavelengths.
a. A good absorber is a good reradiator (Kirchoff's Law).
So, land heats up fast in the daytime (and summer) and
cools down fast at night (and in winter).
b. Land has a relatively low specific heat: This means
that it takes low amounts of energy to produce a given
change in temperature.
ii. Water surfaces are not so good at absorbing insolation,
which means they are also lousy at reradiating that stored
energy at longer wavelengths, according to Kirchoff's Law.
a. It takes about five times as much energy flow to produce
a given temperature change as it would to heat the same
mass of land or rock. So, water has a higher specific
heat than land.
b. Water, then, heats up very slowly over the course of the
day or summer and, conversely, cools down very slowly
over the course of the night or winter.
iii. The different specific heats of water and land are critical
to understanding climates, as we'll see later.
iv. For a sneak preview of coming attractions, though, check
out these weather records for two pairs of cities, one pair
from Northern California (San Francisco on the Pacific and
Chico well inland) and Southern California (Morro Bay and
Twentynine Palms). Average monthly temperatures are given
for all four cities in degrees Fahrenheit (isn't that a
relief?). Average monthly temperatures mean that you
average the daily daytime high and the daily nighttime low.
a. Now, for each pair, figure out the hottest month. Is it
later inland or along the coast?
b. That done, figure out the difference between the hottest
month's average and the coldest month's average for each
of the four towns. Which towns have the least variation
from summer to winter, the coastal or the inland city?
Pretty impressive difference, isn't it?!
-----------------------------------------------------------------
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
SF 50.7 52.8 53.4 54.2 55.3 57.1 58.4 59.5 60.3 59.2 55.2 50.9
CH 44.8 49.4 53.2 58.7 65.8 73.0 78.4 76.4 71.8 62.8 52.5 45.4
MoB 52.3 53.4 53.6 54.4 55.2 57.2 58.7 59.7 60.3 59.9 56.5 52.3
29P 49.2 53.5 58.4 65.7 73.7 82.6 88.4 86.8 80.4 69.3 56.8 49.3
-----------------------------------------------------------------
E. So, how does the absorbed insolation get out of the earth system to
preserve the radiation balance?
1. Absorbed radiation escapes the earth by being reradiated at a
longer wavelength that then can get back into outer space.
2. Just because it's reradiated at a longer wavelength doesn't mean
it's going to escape just like that necessarily: There is always
the chance that reradiated energy will itself be reabsorbed by
carbon dioxide, water, dust, or whatever.
3. The process by which absorbed energy escapes.
a. First, absorption of energy heats the absorbing object (perhaps
dramatically, in the case of substances with low specific heats,
or less dramatically, in the case of substances with high
specific heats).
b. The absorbing object is a radiant object, so it reradiates the
energy it has stored.
c. Time out to apply Wien's Displacement Law:
i. There is no way that any object on our dinky little planet
is going to be heated to 5,770 K, right?
ii. So, these radiant bodies are necessarily cooler than the
surface of the sun.
iii. The cooler the radiant body is, the longer the wavelength
of its emissions, remember?
iv. On average, the entire earth is about 288 K. Remember
plugging that in as the denominator in the Wien's
Displacement Law? And you got an answer of about 10
microns? And you compared your answer to the chart and
classified that peak radiation intensity as infrared?
v. So, Earth objects generally reradiate absorbed energy
somewhere in the infrared.
4. Now, the problem with reradiation in the infrared, for the escape-
"minded" energy packet, is that the infrared is very attractive to
carbon dioxide and water and dust, which are apt to reabsorb the
energy. You can see that in the graph below, which shows the real
distribution of solar energy from about 0.2 microns out past 3.0
microns (which is a lot lumpier and spikier than the idealized
Planck distribution you saw in the earlier graph). This graph
shades in the wavelengths where carbon dioxide and water like to
absorb, labelling each of those absorption areas by the culprit(s)
involved there.
![[ spectral distribution of solar irradiation with shaded
areas showing absorption by various atmospheric gases ]](https://home.csulb.edu/~rodrigue/geog140/irradiation.gif)
5. So, the trick is to be reradiated out an "atmospheric window,"
which is a wavelength not likely to be reabsorbed by gas, dust, or
what-have-you. Atmospheric windows are sort of ugly wavelengths
that none of these absorbers find attractive, so radiation can get
out of the earth system by being reradiated at just those
wavelengths. You can see them on the graph above as the bumps
shaded white in between the absorption spectra.
6. Only about 6 percent of the original insolation manages to get it
right on the first try: It heats the absorbing object to just the
right temperature (apply Wien's Law) to reradiate at an ugly
wavelength, to escape out that atmospheric window.
7. The other 64 percent or so will be reabsorbed somewhere else in the
earth system, by gas, dust, or the land and sea. And reradiated to
try to escape again. If it hits an atmospheric window, yay! If
not, it gets rereabsorbed and rerereradiated.
8. Eventually, this trapped energy will be reradiated out an
atmospheric window and be able to get back into space, The Final
Frontier.
9. Meanwhile, the trapped energy heats our atmosphere and maintains
the planetary thermostat at roughly 288 K. This heating does the
work behind winds, thunderstorms, ocean currents, and, ultimately,
precipitation patterns, rivers, glaciers, and the erosional
sculpting of the land. Amazing what a little delay can do! Gosh,
it's almost like delaying studying for this class and getting a lot
of housework done, eh?
F. The transfer of heat energy: At this point, we'll consider the
specific methods by which trapped energy changes air temperatures.
Two of them are directly understandable from the preceding discussion;
the others are more indirect, requiring the mediation of pressure and
moisture factors to be discussed a bit later.
1. Direct methods of changing temperatures, meaning they can take
place in still, quiet air.
a. Conduction.
i. Conduction is the transfer of heat energy through direct
contact with a warm object.
ii. The rate of transfer depends on how different the
temperatures of the two objects in contact are and the
materials involved (some, such as metals, are excellent
conductors; others, such as wood, are poor conductors)
iii. This is the most efficient heat transfer mechanism.
iv. An example is touching the hot radiator on your car when it
breaks down on the San Diego Freeway! Very efficient! For
those of you too patrician to experiment with impromptu
auto repair, perhaps you've encountered the same experience
by picking up a silver spoon (excellent conductor) you left
in a cup of hot tea (that's one of the reasons why
etiquette forbids leaving spoons in cups!).
b. Radiation.
i. This involves the transmission of energy through space:
Contact is not necessary.
ii. It's not as efficient as conduction, though.
iii. Examples would include popping the hood on your car and
feeling the heat of the engine room and deciding to
reconsider your plan to put water in the radiator; sitting
in front of a campfire, enjoying the radiation of heat to
you on a log two meters away.
c. The interaction of conduction and radiation is what produces the
normal lapse of temperature with altitude in the troposphere
(and, for that matter, in the mesosphere, where temperatures
resume dropping with gains in altitude, after the rude reversal
in temperatures caused by the ozone layer in the stratosphere).
i. Conduction is a minor player here, the warmed ground
transferring heat energy to the air molecules touching it
and then they transferring heat to the next air molecules
they encounter in their Brownian motion (air molecules move
chaotically about as they slam into one another and change
trajectories)
ii. Radiation and the Inverse Square Law produce less and less
effective heating through reradiation the higher you move
from the surface of the earth.
iii. In the troposphere, the normal lapse rate (or
"environmental lapse rate") averages about 6.5° C for
every kilometer (1,000 meter) gain in height. Just thought
I'd remind you of that.
d. Conduction and radiation also interact to produce reversed lapse
rates, too, one of the ways producing a situation called an
"inversion" (of smog fame).
i. At night, the ground is no longer absorbing insolation and,
good reradiator that it is, it quickly cools down, rapidly
becoming colder than the air above it.
a. So, now, the heat flux is in the opposite direction:
Heat goes from the air to the ground through conduction
and radiation.
b. Now, air is going to have a harder time of it warming
the ground than the ground has warming the air during
the day, because of the far greater density and solid
state of the ground, but a cold layer will form right
above the ground, notwithstanding. Sometimes it's only a
few centimeters thick, and you might notice it when you
walk across a lawn in the summer evenings, when your
feet feel cold and the rest of you feels toasty. You
sometimes see this in humid areas by a thin Dracula B-
movie fog that forms right on the ground.
c. Because the lowest layer of the atmosphere is colder
than the air lying just above it, it's an inversion of
the normal situation where temperatures become
progressively cooler as you move up in the atmosphere:
This is what's meant by inversion.
ii. Plot complication: What if the countryside is uneven, with
hillsides and valleys?
a. In uneven terrain, the same process goes on, with a thin
cold air layer forming right above the surface of the
ground.
b. But the air has chilled, so its overall Brownian
molecular motion declines. This allows the molecules to
pack in a little more closely together: The density of
the air increases and, with it, so does its mass. On a
hillside, this denser, heavier layer of air will slide
down the slope, slipping downhill and into any
depression, such as a valley.
c. This can be derived from Charles' Law, which states that
the volume occupied by a gas is directly related to its
temperature. If the temperature drops, the volume
drops, too, which increases the density of the gas,
making it heavier.
d. Meanwhile, back up on the hillside, the removal of one
layer of chilled air only allows another to form and
slip down the slope. In this way, by early morning, you
can have a rather thick layer of cold air underlying the
warm air above: The inversion can get up to dozens, if
not hundreds of meters thick.
e. The reason such inversions are important is because they
trap smog. Auto exhaust, smokestack exhaust, fireplace
and woodstove smoke, and industrial pollutants are quite
warm. Obeying Charles' Law, they expand and become,
therefore, less dense and more buoyant. So, they tend
to rise through the dense, cold air. They rise until
they encounter a layer of air as warm and light as they,
which means they cannot continue to rise. So, they
spread out over the roof of the inversion. The
inversion gradually fills with pollutants.
f. This is the most common situation in which most cities
in the middle and higher latitudes experience smog,
especially if they are surrounded by hills. This is
also the kind of pollution you experience in the
Rockies, in places like Vale and Aspen, and in the
Sierra, when everyone heats their homes with woodstoves
and forgets about cold air drainage. It's mainly a
winter phenomenon in such places. This is the kind of
inversion that creates Southern California's winter smog
problems, too.
g. There is another kind of inversion, related to
convection, which is most associated with California's
famous summer smog problem, but I'll get to that in
another lecture.
2. Indirect methods of heat transfer involve convection and, so,
require the mediation of other weather elements, such as pressure
and moisture, to get the air moving in a vertical direction.
a. Evaporation and transpiration
i. Whenever water evaporates or ice sublimates into vapor,
heat is absorbed and hidden in the work of changing the
physical state of the water. Thus latent in a gas, water
vapor, heat can be advected horizontally or convected
vertically. So it is that a lot of the surplus heat of the
tropics is moved from the tropics to higher latitudes, to
be released upon precipitation later.
ii. Transpiration is the movement of water from soil through
plants' roots to their leaves, from which it is released as
vapor through the leaf stomata and may involve water
released from the plant during its respiration.
iii. Evaporation and transpiration are often treated together,
as evapotranspiration.
b. Heat exchanges involving convection are those moving heat energy
with the substance in motion itself. Heat gets moved, because
the air has moved. If the air's motion involves a vertical
component, there will be additional changes in temperature due
to changes in density. If air moving upward expands and cools
enough for precipitation to take place, there will also be the
release of latent heat as the water changes state.
i. The dry adiabatic process: Temperature changes in dry air
moving up or down.
a. The motion of air up or down changes its density.
1. As air moves up, it finds less and less of the
atmosphere weighing down on it from above. If you
reduce pressure, according to Boyle's Gas Law, you
necessarily increase the volume of the gas, which
reduces its density.
2. The reduction in density means there is less overall
molecular motion, as the air molecules have a little
more "elbow room" to move around before being slammed
into by another molecule (longer mean straight path
between collisions).
A. Heat can be thought of as molecular motion: The
less molecular motion, the less heat.
B. This argument explains another old observation and
law, Amonton's Law: Pressure is proportional to
temperature. The greater the pressure (and
density and molecular collisions and motion), the
greater the heat. The less the pressure, as we
have in air moving upward, the cooler the air.
This was figured out toward the end of the 17th
century by Guillaume Amonton.
3. So, air moving up expands and cools; air moving
downward compresses and heats.
b. This messes up the normal lapse rate of temperature with
altitude, wouldn't you know, because of the additional
compressional heating and expansional cooling.
1. The result is a larger lapse rate because of the
extra cooling on climbing and the extra warming on
descent.
2. The new lapse rate is about 10.0° C per kilometer
increase in altitude: For every 1,000 m the air
climbs, it cools off 10° C; for every 1,000 m the
air sinks, it warms 10° C. No more wimpy and
anæmic -6.5° C/km!
3. The new lapse rate only applies to air moving
vertically, up or down, and not experiencing any
water vapor condensation or freezing (dry air).
4. The new rate is called the "dry adiabatic lapse rate"
(or DALR to its friends).
c. Let's apply the dry adiabatic lapse rate and compare its
results with the normal lapse rate that applies in
still, quiet air.
1. Let's say, on a clear, still, warm day, you decide
you're going to hike to the top of a 3,000 m (3 km)
mountain. That would, admittedly, be pretty
ambitious of you (that would be a nearly 10,000'
mountain).
A. At the bottom of the mountain, let's say it's a
gorgeous 30° C (~86° F).
B. So, since there isn't a breath of breeze stirring,
which lapse rate would apply? ... ... ... yep,
the normal lapse rate (which is ...?).
C. After a 1 km climb (assuming you hike fast), the
air would be 6.5° C cooler, or 23.5° C;
after 2 km (my, you're really fit), it would be
17° C (time for a sweater); at the top of the
mountain, the air would be 10.5° C (pleasantly
chilly, sweater weather, around 50° F).
2. So, you are so invigorated by this experience that
you talk a friend into going with you the next day,
but this day a Santa Ana is blowing. When the air
hits the mountain, it's forced to climb.
A. At the bottom of the mountain the next day, it's
still that suspiciously convenient sunny and clear
30° C
B. Because the air now is moving vertically, though,
the normal rate no longer applies. Because of the
vertical air flow, we need to switch to the dry
adiabatic lapse rate, which is .......?)
C. Now, after a 1 km climb, it's already only 20°
C (and you already have to think about sweaters);
after 2 km, it's down to 10° C; at the top of
the mountain, it is FREEZING (0° C, and your
friend is mad at you, and you hear about it all
the way back down the mountain, and you're mad at
yourself for forgetting this little detail from
that Geog 140 class you took years ago!).
ii. The wet adiabatic process: Temperature changes in air
experiencing condensation and freezing and precipitation.
ONLY air moving UP can experience the wet adiabatic
process.
a. So, the expansion of air moving upward causes it to cool
quite rapidly (you're still smarting about it from that
second hike up the mountain).
b. Plot complication: The colder air gets, the less water
it can hold as a gas, as water vapor. This is an
extremely important point: The capacity of air to hold
moisture is directly related to temperature.
c. This means that, sooner or later (depending on the
absolute amount of water vapor in the air), the air gets
so cold that it cannot hang onto the water vapor it came
in with: It has to drop some of its water vapor load to
bring that load back in line with its reduced capacity.
1. Air holding exactly as much water vapor as it is
capable of holding is described as "saturated," and
its relative humidity (more on that later) is 100
percent.
2. The temperature at which saturation occurs is called
the "dew point" (lots more on that later).
3. The elevation at which saturation occurs is called
the "lifting condensation level" or "dew point
elevation."
3. IF air continues to move upslope after reaching its
dew point temperature (saturation), any further
cooling forces the air to change state and condense
or freeze (depending on how cold the dew point is for
that package of air), which enables precipitation to
start in the form of rain or snow.
4. So, water vapor is compelled to change state from gas
to liquid or solid.
A. The change of state causes the release of latent
heat!
B. This release of latent heat as sensible heat in
the surrounding air slows down the change in
temperature being forced by expansion in rising
air: It doesn't reverse the cooling, but it does
partially offset it.
5. This, of course, messes up the dry adiabatic lapse
rate for us, reducing it by the amount of sensible
heat created by the release of latent heat.
A. This much smaller adiabatic lapse is called (of
course) the "wet adiabatic lapse rate" (or the
WALR or the "saturated adiabatic lapse rate" or
SALR, too, and some folks call it the "moist
adiabatic lapse rate!).
B. It varies a bit, depending on the temperature of
the air (remember, the hotter the air, the more
vapor it can be holding) and the mix of freezing
and condensation going on (remember, melting of
water absorbs substantially less energy than
evaporation). It can be as low as -4° C/km in
warm air holding a lot of vapor and it can
approach -10° C/km in really cold air that
can't and isn't holding much water vapor.
C. Let's go for -5.0° C/km, then, especially as
this actually is a typical WALR for air around
10° C, which is not an uncommon average daily
temperature for rainy days around here.
6. Because you're a madperson, you decide to climb a
tropical mountain when it's raining.
A. Suspiciously, this mountain just happens to be
3,000 meters (3 km) tall and, fortuitously, the
air temperature at the bottom of the mountain is
30° C.
B. This time, though, the air, propelled by the Trade
Winds from over the sea, is saturated: As soon
as you step outside, you notice it's foggy and
rainy: You can scarcely see. The "fog" turns out
to be a cloud that covers the mountain from bottom
to top. But you're a madperson, so you head up
the mountain anyhow, heedless of the danger,
friendless and alone this time!
C. In these conditions, which lapse rate pertains?
Yes, the wet adiabatic lapse rate, which we'll
assume is about -5° C/km.
D. At 1 km into it, the air has cooled only to about
25° C; at 2 km, only to 20° C; and, at the
top of the mountain, it has only managed to cool
to 15° C! Because of the release of latent
heat during condensation and raining, the air is
substantially warmer than it was at the top of
that other mountain when the air was dry and the
Santa Anas were blowing. It's even somewhat
warmer than it was on the day you went up the
California mountain in still, quiet, dry weather!
So, the release of the latent heat on condensation
or freezing doesn't reverse the cooling, but it
partially offsets the cooling, with the result
that air at higher elevations is quite a bit
warmer when the WALR pertains.
7. It is VERY important to remember that the wet
adiabatic lapse rate can ONLY apply to air moving
UPWARDS: never downwards.
A. Sinking air compresses, which concentrates its
heat energy in a smaller volume, which means it
gets warmer.
B. The warmer the air gets, the more water it can
hold as vapor: Its capacity to hold vapor
increases, but the vapor load doesn't. This means
its relative humidity decreases. The air is no
longer saturated. There is no more reason for
condensation or freezing and precipitation.
C. Descending air NEVER precipitates!!! Burn this
into your hard drives, folks!
iii. As a result of the wet adiabatic lapse rate, air can be
much hotter on one side of a mountain range than it was
when it started out at the same elevation on the other side
of the mountain range.
a. If an air mass loaded with vapor approaches a mountain
and is forced to climb high enough to reach the lifting
condensation level (dew point elevation), it will rain
on the windward side of the mountain (and cool at the
smaller rate when it does), but it will NOT rain on the
leeward side of the mountain range and will descend the
whole way at the higher dry adiabatic lapse rate.
b. The leeward side of a mountain range (if it's in an area
with a prevailing or common wind direction) will be both
drier and hotter than the windward side. This is called
the "rainshadow effect."
c. We can see this all over the place in California:
1. Think about Morro Bay in San Luis Obispo County and
its lush pine, sage, and chaparral vegetation and
then contrast that with Buttonwillow off I-5 in the
Great Central Valley of California with its desert
and grassland vegetation.
2. Look at the heavy sequoia and Doug fir forests of the
western Sierra Nevada around Yosemite and Kings
Canyon and contrast that with Death Valley east of
there.
3. The southwestern San Joaquin Valley and Death Valley
are examples of rainshadow deserts (so're the Gobi
Desert in Mongolia and Inner China and the Patagonian
Desert of Argentina).
d. Let's work this out with an example.
1. The mountain range is 4 km high this time. It faces
the sea on the west slope, which is where moisture-
laden breezes come. Let's say there's a valley to
its east, which just happens to be at sea level (this
isn't entirely preposterous: Sierra peaks get to 4
km high (Mt. Whitney is 4,417 m or 4.4 km high) and
Death Valley is at and below sea level (Badwater, the
lowest spot in the Western Hemisphere, is 70 m below
sea level).
2. The air blowing off the sea today is 25° C, and
it has enough water vapor in it (~5 g of water vapor
per kg of air) that its dew point is 5° C.
A. So, how far must it cool before it reaches the dew
point? It starts out at 25° C and has to cool
to 5° C. So, that is 20° of cooling
before it hits dew point.
B. At which rate will it cool to dew point? Since
dew point is the temperature at which saturation
occurs and the air must begin condensation or
freezing, the air is drier than saturation,
meaning it is plain dry. Since the air is not
precipitating, it must be cooling at the dry
adiabatic lapse rate, which is the 10° C rate.
C. So, what's the lifting condensation level or dew
point elevation? 20° C/10° C = 2. Two km
is the LCL, then. If the air continues to rise
above 2 km, it will experience condensation and
precipitation. The release of latent heat changes
the drop in temperatures to the wet adiabatic
lapse rate.
D. The mountain, at 4 km, sticks out 2 km past the
lifting condensation level. The air will climb
those last two kilometers at the wet adiabatic
lapse rate. Two km times 5° C = 10° C of
cooling below the dew point temperature. The dew
point (5° C) minus 10 equals -5° C. So,
it's 5° below 0° C at the top of the
mountain.
E. Once the air crests the mountain and starts down
the leeward side, condensation and freezing and
precipitation stop. The air now warms. Because
the air is now dry, the air warms at the dry
adiabatic lapse rate, 10° C for every
kilometer of descent.
F. The air will descend a total of 4 km at the DALR.
Four kilometers times 10° C equals 40° C
of total adiabatic warming. Forty degrees warmer
than the temperature at the top of the mountain is
35° C (-5° C + 40° C = 35° C).
This is fully 10° C warmer at sea level on the
leeward side of the mountain range than when the
air started out at sea level on the windward side
(18° F warmer).
G. This gain in temperature is produced by the
intervention of the wet adiabatic lapse rate on
just ONE side of the mountain, the windward side,
while all of the descent on the leeward side was
at the larger dry adiabatic lapse rate. So now
you know why it can be 95° F in Death Valley
when it's only 77° F on the Central Coast.
iv. There are many examples of adiabatically heated winds in
the world today. These are winds that experience increases
in temperature due to descent at the dry adiabatic lapse
rate (their actual heat energy content is unchanged but
compression concentrates it in a smaller volume, which
creates a higher temperature and a lower relative
humidity).
a. Our own Santa Ana winds (sometimes called Santana winds;
both forms existed historically) descend to us from Utah
and Nevada some 1,000 to 1,500 meters.
b. The Chinook winds come down the east face of the Rockies
and Cascades. They have been known to produce warming
of 20° C in just one HOUR!!! This has sometimes
melted snowpacks at rates of 1.5 m/day, producing sudden
flashfloods downstream. The winds are sometimes called
"snoweaters."
c. Argentina has a similar wind coming down off the Andes,
which is called the Zonda.
d. The eastern Alps produce the Foehn or Föhn.
e. The Mistral blows down off the western Alps down the
Rhône Valley into the French Riviera.
Some ideas to take away from this lecture include the earth's radiation
balance, insolation, where the sun's radiance falls on the electromagnetic
spectrum compared to Earth's, Wien's Displacement Law, how to predict incident
solar radiation flux from latitude and declination, albedo, which agents
reflect insolation and which absorb it, atmospheric windows, how absorbed
energy escapes the earth system, conduction, radiation, convection, dry
adiabatic process and rate and when it applies, wet adiabatic process and rate
and when it applies, inversions and smog, how the wet adiabatic lapse rate
applied to the windward side of a mountain range can create a much hotter
leeward side, rainshadow effects, and adiabatically heated winds.
The next lecture will examine pressure in more detail as an element of weather
in the troposphere.
Document and © maintained by Dr.
Rodrigue
First placed on web: 10/14/00
Last revised: 06/14/07