Download 5 Atmospheric Stability

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5
Atmospheric Stability
Introduction
In Chapter 4, we examined the concept of horizontal and vertical atmospheric motion, and
how pressure differences create the winds that form on a variety of different scales. In this
chapter, we examine the consequence of the vertical lifting of air; atmospheric stability. As
you could predict from the terms, an atmosphere that is stable will usually bring fine weather,
and one that is unstable may produce stormy weather. This chapter answers the questions of
what constitutes a stable atmosphere and what changes cause a stable system to decompose to
an unstable one.
Setting the scene (the stability toolbox)
We now need to apply all of the physical aspects of meteorology that we have learnt from the
previous chapters. We will observe how buoyancy (which creates convection) and the
horizontal pressure gradient force (hPGF), which creates advection) work together with
pressure, temperature and density to create the stable and unstable weather we observe.
EQUATIONS OF STATE AND GAS LAWS
To see how all of these come together, we need to explore some of the governing equations,
the first of which is called the equation of state.
The equation of state
ρ=
P
RTv
Where, at sea level;
ρ
P
R
T
=
=
=
=
atmospheric density in kg/m3
atmospheric pressure in kPa
gas constant
atmospheric temperature in K
Using this equation we can determine the unknown parameter by solving with the three
known parameters. In the equation given, we are obviously solving for density, but we can
easily rearrange to solve for pressure and temperature.
EXERCISE
You would probably have encountered equations similar to this in the laboratory calculations
unit. Use the skills you have learnt to solve the following problems.
¤
¤
Solve the above equation for density given a pressure of 99.4 kPa, and a temperature of
306 Kelvin.
Rearrange the equation of state above to solve for pressure given a density of 1.18
kg/m3 and temperature of 303 Kelvin.
But what does all this mean? The fact that these parameters are related means that if we
change one variable, we will change all the others as well, and we need to have a better
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understanding of what these relationships are. For example, if we change the temperature,
does that change the density of the air?
The gas laws
The gas laws describe the relationships between all of the physical variables that the
atmosphere (or gases in general) exhibit. We cannot explore the behaviour of the atmosphere
without understanding the basics of how gases work. Some of the relationships have been
explored already, but now we need to understand the mechanisms of change by examining
some of the calculations.
EXERCISE 5.2
This is an appropriate time to perform the gas laws task found in the Ch 5 tab of the
MetExplore spreadsheet. There you will find a variety of gas laws and other interactive
material that will shed light on this tricky subject!
THE PRESSURE/HEIGHT RELATIONSHIP
The second significant relationship we need to be reminded of is the pressure/height
relationship. The pressure through a vertical slice of the atmosphere is not the same – it
follows a curved pattern that decreases with altitude as seen in Figure 5.1 below.
Plot of altitude versus pressure
Altitude (km)
40
35
30
25
20
15
10
5
0
0
200
400
600
800
1000
Pressure (hPa)
Figure 5.1 – Graph showing how atmospheric pressure changes with height. Graph was made in
Excel using the Barometric Formula.
This is due to the compressibility of air (which creates a pressure gradient), the gravitational
force, as well as the pressure gradient force. As you could imagine, physicists have created
many formulas for calculating the change in pressure for any given height (MetExplore
spreadsheet Ch5).
THE EFFECT OF WATER
You should know by now that water has some very unique properties; a high specific heat
capacity, found in all three states of matter, highest density is at 4°C, can easily sublimate
under the right conditions, and there are many more. What you may not know is that water
plays an enormous role in determining the stability of weather, which implies that measuring
the relative humidity is important for things other than knowing how comfortable (or
uncomfortable) the weather will be tomorrow!
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Let’s begin by understanding how water changes its physical state, i.e. solid, liquid and gas
(vapor). The change of state is controlled by temperature, obviously, so solid ice melts to
become liquid water at 0°C (the melting point), which boils to become a gas at 100°C (the
boiling point). Figure 5.2 below shows the states of matter (assuming water) where the images
are depicting the common definitions used when defining the states of matter and how the
three states interact with the container that holds them.
What you may not know is that water not only changes state from liquid to gas at 100°C but
also everywhere in-between, furthermore, solid ice can change into gaseous water vapour
without first becoming a liquid! This process is called sublimation (and for our purposes here,
we shall assume this is the reason that no atmosphere can be totally dry or free from water
vapour).
Figure 5.2 – The three states of matter showing how they interact with the container that holds them.
Adapted from http://www.grc.nasa.gov
But you already new this, because this non-boiling change of state is called evaporation! This
vaporisation of water produces a small partial pressure which is added to all of the other
partial pressures exerted by the gases in the atmosphere (all of which are related to the %
compositions of each gas). The pressure exerted by vaporised water in the atmosphere is
called the vapour pressure of water, and is immensely important parameter in meteorology.
Water evaporates at all temperatures, but obviously more so at higher temperatures (another
curved graph!) and again, scientists have formulated many equations to calculate the amount
of vapour that comes off water or ice (MetExplore spreadsheet). The vapour pressure of water
can have many units, a common one being kPa or some other derivative.
Pressure (mm Hg)
Plot of vapor pressures for liquid water
760
660
560
460
360
260
160
60
-40
274
294
314
334
354
374
Temperature (Kelvin)
Figure 5.3 – Graph showing how water vapour pressure changse with temperature. Note that the
vapor pressure of water is equal to that of atmospheric pressure when T = 100°C (i.e.374 K = 760 mm
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Hg). Graph made in MS Excel using the Clausius-Clapeyron equation. Refer to MetExplore
spreadsheet under the Ch 5 tab.
One derived unit of measure that you would be very familiar with is called the relative
humidity (% RH). The % RH value is a measure of the moisture content as vapour in the air.
It can be calculated directly from various equations, but most people are familiar with looking
the % RH value up from a humidity table (Appendix A, or MetExplore spreadsheet under the
‘Humidity Table’ tab). Just like vapour pressure, the % RH increases with increasing
temperature.
So, now that we know that water evaporates with an increase in temperature producing water
vapour, and that the most common measure of this water vapour is relative humidity, we can
start to look at the reverse situation in which we see water vapour condense out of the air into
liquid water. Obviously we need a reduction in temperature for this to occur, and the
temperature at which this occurs is called the dewpoint temperature.
THE DEWPOINT TEMPERATURE (Td)
The dewpoint temperature effectively asks the question “to what temperature will we need to
reduce a parcel of air in order to achieve 100% RH (assuming a given temperature and
relative humidity <100 %)”. We do this by calculating the dewpoint temperature. To
understand exactly how the air temperature, dewpoint temperature and relative humidity are
related, it is best to view a graph of the difference between the two temperatures against the
relative humidity (or vice versa).
Relative Humidity (%)
Plot of T-T d versus % RH
120
100
80
60
40
20
0
0
5
10
15
20
25
Difference between Air & Dewpoint Temp (T - Td)
Figure 5.4 – Graph showing the relationship between the dewpoint temperature and the relative
humidity. The closer the dewpoint temperature is to the ambient air temperature (i.e. a difference of
zero on the x axis in the graph above) the higher the relative humidity.
THE MOISTURE/DENSITY RELATIONSHIP
Finally we need to look at how air containing moisture exhibits a change in density, and how
this density changes the buoyancy of an air parcel, which will eventually lead to the rising or
falling of an air parcel. Figure 5.5 below shows how the density of air decreases as the vapour
pressure of water increases, but why is this so! It is due to the fact that the molar mass of air is
~29, but that of water is only 18, so the more water vapor you add, the less dense the air
becomes, the more buoyant air becomes.
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Plot of density versus vapor pressure
1.4
Density (kg/m 3)
1.2
1
0.8
0.6
0.4
0.2
10
00
00
80
00
0
60
00
0
40
00
0
20
00
0
0
0
Vapor pressure (Pa)
Figure 5.5 – Plot of air density (kg/m3) versus vapour pressure (Pa). An Increase in vapour pressure
(or relative humidity) corresponds to a decrease in density as water has a molecular weight of only 18
compared to airs molecular weight of ~29 – a kind of ‘mass dilution’!
Lifting Mechanisms in the Atmosphere
Applied to the atmosphere, the term ‘stability’ simply means ‘resistant to change’. As
mentioned in the introduction, the mention of stability here refers to vertical stability, as any
form of sustained vertical motion will generate an unstable atmosphere. This upwards motion
causes turbulence in the air, usually rapid turbulence, and combined with the condensation of
water due to adiabatic cooling, usually produces some stormy weather, which may or may not
produce rain at the surface. To achieve this we need to start ‘lifting’ the air, and this can
generally be caused by one (or more) of four mechanisms; orographic lifting, convergence,
diabatic heating and frontal systems.
OROGRAPHIC LIFTING
Orography is a concept in geography (specifically topography) that deals with the height of
land. Mountainous terrain (can) provide a natural barrier to horizontal winds, the consequence
of which is the vertical motion of air as the wind hits the mountain; it is forced to go upwards
(unless is can go around). The process of a parcel or layer of air rising as a result of the
topography is referred to as orographic uplifting.
If the parcel or layer of air contains moisture (in the form of vapour – humidity) then as air
rise up the side of the mountain, the pressure and temperature decrease adiabatically until it
reaches the lifting condensation level (LCL), which is that point in a parcel of air when the
pressure and temperature has dropped to the point were relative humidity approximates 100
%, and clouds start to form (which is why the underneath of these types of clouds are
generally flat.
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Figure 5.6 – Orographic lifting. The learning outcome here is two-fold. From a lifting perspective, the
lift is created by the topography (the air is forced up by the mountain). The cloud forms due to the
resulting instability (vertical movement of air is enhanced – change cannot be resisted!). Image from
http://www.waterencyclopedia.com/Ce-Cr/Climate-Moderator-Water-as-a.html
CONVERGENCE
Convergence is another mechanism that can force air near the surface to rise. If winds
blowing in different directions meet each other, the different moving air masses become an
obstacle to one another. The air converges and has no place to go but upwards. At the surface
air flows inward to the center of low pressure where it converges and then rises.
Air is forced to lift
Advecting air
Advecting air
Figure 5.7 – Convergence of air parcels resulting in a lifting mechanism of air.
Convergence also occurs when air flowing over a smooth surface suddenly hits a rougher
surface and slows due to increased friction. The air piles up at the rough surface where the
friction is greater, and this causes some of the air to move in a vertical direction.
DIABATIC HEATING
The radiation emitted by the earth (which comes from the Sun) heats the air at the surface. Of
course both the degree (amount) and rate of heating depends explicitly on the surface that
radiates the heat (see albedo). Air that is relatively warm compared to its surrounding rises,
and it can (and usually does) cool adiabatically. As a result, the temperature drops in response
to the change in pressure as per the laws of adiabatic expansion and compression.
Heating that occurs via the sun’s radiation as diabatic heating, which is the opposite of
adiabatic. The suns radiation energy is absorbed by matter (air, land, water etc), which results
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in the convection of warm air. which expands the air, creating a parcel that is of lower density
and therefore able to rise vertically through the atmosphere, and is therefore a form of lifting.
You can safely assume that this is the most common form of atmospheric lifting.
Figure 5.8 – An example of diabatic heating, which effectively results from conduction of radiated
energy the sun through matter which results in the convection of heat energy creating buoyant air that
rises
vertically
–
causing
lift.
Image
adapted
from
http://geography.berkeley.edu/programcourses/CoursePagesFA2006/Geog40/L10.pdf
FRONTAL SYSTEMS
The final lifting mechanism which we will discuss is the overriding of air at frontal
boundaries. Moist air, because it is less dense, will override dry air. But how is this different
from convergence? In the case of convergence, the lifting results from air molecules pushing
one another upward, like pushing two small piles of sand together with your hands, forcing a
larger pile to form. When two frontal boundaries meet, the lifting that occurs is due to the
relative buoyancy of the two air masses. The more buoyant air mass will override the lesser
buoyant air mass. The buoyancy is determined by the characteristics of the air masses (i.e.
temperature and moisture content).
Cold Front
Warm Front
Figure 5.9 – Warm and cold fronts. Assume that a cold front ‘cuts’ under warm air, and a warm front
‘rolls’ over cold air. Either way, a parcel of air is lifted. Adapted from www.classzone.com.
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Adiabatic Processes
Think about where we are up to. We now know all of the significant behaviours of the
atmosphere; pressure changes, temperature changes, density changes, and the relationships
between these three variables; the fact that air is convecting and advecting, as well as the laws
of buoyancy and adiabatic expansion and contraction. Of all of these behaviours, the most
important or ‘keystone’ variable behaviour is temperature.
When air rise and cools (assuming adiabatically), it doesn’t just get suddenly colder, the
temperature changes by a certain degree per unit of altitude, which we call a rate. Because we
talk about the temperature getting cooler, we refer to the rate of change as the lapse rate, of
which there are four key rates to consider;
¤
¤
¤
¤
Dry
Saturated
Environmental, and
Dewpoint
The key thing to remember here is that knowing the rate at which rising air cools is vital in
determining the stability of the atmosphere. One important distinction should be made at
this time; if a lapse rate increases, then the temperature gets colder as an air parcel rises
and vice versa. To avoid confusion, we shall suggest in these notes that parcels of air rise and
fall, but lapse rate increase or decrease.
THE DRY ADIABATIC LAPSE RATE (DALR)
When a parcel of air rises, it expands, and the temperature decreases. Likewise, when air
sinks, it compresses, and the temperature increases. When a parcel of air, either dry or
containing water vapour (<100%), rises or sinks without the addition or extraction of heat,
that process is said to be a dry adiabatic process. Scientists have determined that this
‘theoretical’ lapse rate is equal to 9.8°C/km (-9.8 if the parcel rises, + 9.8 if it falls).
Plot of the Dry Adiabatic Lapse Rate
O
9.8 C/km
12
Altitude (km)
10
8
6
4
2
0
-80
-60
-40
-20
0
20
40
O
Temperature ( C)
O
Figure 5.10 – Plot of DALR showing theoretical linear decrease in temperature at a rate of 9.8 C per
kilometer. The term ‘lapse’ applies to rising air, ‘gain’ to falling air.
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SATURATED ADIABATIC LAPSE RATE (SALR)
Note that the saturated adiabatic lapse rate (SALR) is also called the moist (MALR), wet
(WALR) (sometimes even called pseudo) adiabatic lapse rate. everything that we have learnt
so far, it comes as now surprise that colder air contains less water vapour due to the adiabatic
and gas laws, so that when a parcel of air reaches its saturation point (dewpoint), condensation
begins and eventually clouds will form.
As water vapour condensed to liquid water at the dewpoint, latent heat is given off back to the
air parcels environment, thus warming the air. In the reverse process, evaporation, we find
that latent heat is taken up from the air parcel, thereby cooling the parcel of air. Since no heat
is exchanged between the parcel and the environment, we still refer to this heating and
cooling as an adiabatic process.
However, during the processes of condensation and evaporation, the cooling and heating of
the saturated parcel varies somewhat from the purely dry adiabatic process we discussed
above. A rising saturated parcel cools at a slower rate due to the release of
O
O
Plot of the DALR (9.8 C/km) & SALR (6.5 C/km)
note that SALR is atmospheric average
12
Altitude (km)
10
8
DALR
6
SALR
4
2
0
-80
-60
-40
-20
0
20
40
Temperature (OC)
Figure 5.11 – Comparison of DALR and SALR.
latent heat, and a sinking saturated parcel heats more slowly due to the conversion of heat
energy during evaporation. This cooling of a rising (or heating of a sinking) saturated parcel is
called the saturated adiabatic process which has been calculated to be an average of
6.5OC/km. The figure above shows that the SALR is much less than the DALR.
ENVIRONMENTAL LAPSE RATE (ELR)
So, the DALR is a sort of theoretical, calculated ‘moistureless’ lapse rate equalling
9.8OC/km, and the SALR is a warmer lapse rate due to moisture levels approximating
6.5OC/km. So what do we get if we raise a weather balloon in the air and measure the actual
temperature of the atmosphere? The easy answer is environmental lapse rate (ELR).
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The problem is that the atmosphere can really be doing three things when it comes to
temperature. The temperature at any point can be in a state of;
¤
¤
¤
Lapse
Isothermal
Inversion
We already know that a lapse means a decrease with altitude, so the environmental, or real,
atmosphere is getting colder (indicated by a negative slope on a graph). Isothermal means
‘staying the same’, or ‘paused’, and so the temperature remains constant with altitude
(indicated by a vertical line on the graph). Yet sometimes we can see an increase in
temperature with an increase in altitude, and this is called a temperature inversion. These
three states can be seen on the hypothetical plot in Figure 5.12 below.
Example of the Environmental Lapse Rate (ELR)
12
Altitude (km)
10
Lapse
8
Inversion
6
4
2
Isothermal
0
Temperature (OC)
Figure 5.12 – The Environmental Lapse Rate (ELR) showing the three possible states of temperature
change; lapse, isothermal and inversion. Graph from Excel.
THE DEWPOINT ADIABATIC LAPSE RATE (DPLR)
Even though a parcel of air may contain moisture, if the parcel is rising, then it cools
according to the dry adiabatic lapse rate until it reaches the dew point temperature, Td. We
refer to the pressure where the actual temperature equals the dew point temperature as the
Lifting Condensation Level (LCL). At the LCL, the cooling process becomes a moist or
saturated adiabatic process.
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Stable, Neutral, and Unstable Atmospheres
The stability of the atmosphere is basically determined by comparing the lapse rate of a parcel
of air to the lapse rate of the surrounding air, which we also refer to as the environment. If we
know the temperature and dew point of the air parcel before it begins to rise, then we can
pretty accurately determine the temperature change as it rises. Measurement data provides us
with a profile of the environment with which to compare our rising air. But, keep in mind, our
profile is merely a snapshot of the atmosphere. The measurements only give us a view of the
atmosphere at a point in time. Motion in the atmosphere makes these comparisons
complicated because motion causes changes in the lapse rates we wish to compare.
We have found that there are three basic categories in which the atmosphere or a layer in the
atmosphere can be classified in terms of stability. These categories, which we discuss next,
are stable, unstable and conditional.
Figure 5.13 – Stable, conditional and unstable atmospheres as shown by comparing three different
environmental lapse rates (ELR’s ΓE1,2,3) to both the DALR (Γ) and the SALR (Γs).
THE STABLE ATMOSPHERE (& NEUTRAL)
As previously mentioned, a stable atmosphere is strongly resistant to changing its vertical
position (regardless of the height of the atmosphere), so if there was some force trying to push
the air up or down, in a stable atmosphere this ‘push’ would be resisted, and the air parcel, if
pushed, would move back to where it came from.
Reference 2 states that “In a stable atmosphere, if you lift a parcel of air, the temperature of
the rising air will decrease fast enough that its temperature will always be colder than the
temperature of the environment. Colder air sinks. If the force pushing the air up suddenly
disappeared, the parcel would sink back down to its original position where its temperature
and pressure would be in equilibrium with the environment.” This is indicated by figure 5.13
above.
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Absolute stability occurs when ELR is less than SALR (and therefore less than DALR). This
means that ELR must be lower than SALR (which varies between 3.9ºC/1km and 7.2ºC/1km)
which will never be more than 7.1ºC/1km (if SALR is at its maximum).
Neutral stability occurs when ELR and DALR are equal. That is, when ELR is 9.8ºC/1km. It
is called 'neutral' because the thermal keeps its initial momentum and does not accelerate or
slow down. This is not indicated in figure 5.13.
THE UNSTABLE ATMOSPHERE
An unstable atmosphere is one where a parcel or layer of air is encouraged to rise or fall. In an
unstable layer, the lapse rate of a rising parcel is less than the lapse rate of the environment.
Because the parcel is warmer than the environment, the parcel has positive buoyancy and
continues to rise on its own.2
Absolute instability occurs when ELR is greater than DALR. We have learned that DALR is
9.8ºC/1km, therefore we can conclude that absolute instability exists when ELR is 9.9ºC/1km
or greater. Meteorologists call this a "super-adiabatic lapse rate" since heat loss with elevation
is so rapid.4
CONDITIONAL INSTABILITY 2,4
To determine if the atmosphere is conditionally unstable, we compare the lapse rate of a
parcel to the environment as it passes through the LCL. The atmosphere is described as
conditionally unstable if the environmental lapse rate is less than the dry adiabatic lapse rate
beneath the LCL and greater than the saturated adiabatic lapse above the LCL. So, conditional
instability can be easily determined by making a comparison of all three lapse rates.
Conditional Instability occurs when ELR is less than DALR but more than SALR. In other
words, it is when ELR is between SALR (which varies between 3.9ºC/1km to 7.2ºC/1km) and
DALR (which is 9.8ºC/1km). The 'condition' for instability is only when the thermal becomes
saturated, not before.
CONCLUSION
Atmospheric stability is not an easy concept to absorb. Overall, meteorologists use weather
balloons to measure the vertical layers of the atmosphere for many parameters including
temperature and pressure. From this data they produce one of four common thermodynamic
diagrams to examine the atmospheres stability (SkewT-LogP, Tephigrams, Stuve Diagrams
and Emagrams). Appendix B is an example of one of these diagrams from the BoM. Good
luck with that.
Lapse rates of the atmopshere
4
Altitude(km)
3.5
3
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
30
Temperature (OC)
DALR (9.8)
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SALR (~6.5)
DPLR (~1.8)
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What you need…
WHAT YOU NEED TO BE ABLE TO DO
¤
¤
¤
¤
¤
¤
¤
¤
¤
¤
Be able to understand the significance of equations of state
List and describe the relevance of the Gas Laws
Explain the causes of the relationship between pressure and altitude
Explain vapor pressure and humidity
Explain the relationship between humidity and temperature
Define the term Dewpoint Temperature and explain its relevance
Discuss the relationship between humidity and air density
List and describe four major mechanisms which lift air.
List and describe the four major lapse rate
Discuss the three common atmospheric stability scenarios
REFERENCES
1.
Sturman, A.P, Tapper, N.J., (2000). The weather and climate of Australia and New
Zealand. Oxford University Press. Melbourne. Australia.
2.
The Shodor Education Foundation Inc. Air Quality Meteorology. A Developmental
Course of the US Environmental Protection Agency in conjunction with the US
National
Oceanic
and
Atmospheric
Administration.
http://www.shodor.org/metweb/index.html
3.
Bureau of Meteorology. Melbourne. Department of Environment & Heritage
http://www.bom.gov.au (accessed 18/04/08)
4.
Woodruff, S.W. Atmospheric Stability. Pierce College.
http://www.piercecollege.edu/offices/weather/stability.html (accessed 2007-8)
FURTHER READING & ONLINE LEARNING AIDS
MetExplore spreadsheet Ch5 contains interactive information on equations of state, gas laws,
pressure/height relationships, vapor pressure and other related material.
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IMPORTANT TERMS
Atmospheric stability
Equation of state
Evaporation
Partial pressure
Relative humidity
Dewpoint temperature
Density
Orographic lifting
Convergence
Diabatic heating
DALR
SALR
ELR
DPLR
Stable
Unstable
Neutral
Conditional stability
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REVISION QUESTIONS
1.
What information can an equation of state tell us?
2.
What relationship does Boyles Law state?
3.
What relationship does Charles Law state?
4.
What relationship does the Gay-Lussac Law state?
5.
What relationship does Avogadro’s Law state?
6.
What is so impressive about the Ideal Gas Law?
7.
State how and why pressure changes with altitude?
8.
What is vapor pressure?
9.
What is the relationship between water vapor and humidity (trick question?)
10.
What is partial pressure?
11.
How does vapor pressure change with temperature?
12.
What is the dewpoint temperature?
13.
What is the relationship between the dewpoint temperature and humidity?
14.
Describe the relationship between humidity and air density.
15.
List and describe the four main lifting mechanisms that can occur in the atmosphere.
16.
List and describe the three common atmospheric stability scenarios.
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