Transcript part-1

Atmospheric Properties
Martin Visbeck
DEES, Lamont-Doherty Earth Observatory
[email protected]
Outline
REVIEW
Convection - a form of heat transfer.
Thermodynamic properties of dry air - adiabatic
temperature change.
Atmosphere under gravity - the hydrostatic balance.
The stability of dry air - dry convection.
Water in the climate system - thermodynamic
properties of moist air.
Black Body Emission
T(sun) = 5780 K
T(earth) = 288 K
Black Body Emission
•
Wien's law states that:
lmax= a / T
•
where lmaxis given in mm, T is in units of K,
and a is a constant equal 2897 mm K.
•
The Stefan-Boltzman law states that:
I = s T4
Area ~ Energy
(integrate over log of
wavelength)
•
where I is in units of W/m2, T is in units of
K, and s (the Greek letter sigma) is a
constant equal to 5.67 x 10-8 with units of W
m-2 K-4.
Solar Constant
I = I0 (at the source) r(source)2 / r2
I1
I2
I0
r0
I2 =
r1
r2
I1 ( r22 / r12 )
Greenhouse Effect
absorption by trace gases
Greenhouse Effect
Take away ideas and
understandings
Convection is a from of heat transfer achieved in the
atmosphere through the vertical motion of air parcels.
Convection moves air parcels with their content (water
vapor and droplets, small particles, other gases) and
thus affects visibility, cloudiness, rainfall, and levels of
pollution in the air.
The process of convection is governed by basic physical
laws: gravity and the conservation of energy, and by
a fundamental relationship between three measures of
the state of every gas: temperature, density, and
pressure.
Take away ideas and
understandings
Water, in all three phases, participates in and
strongly affects the convection process, leading to
the formation of clouds and rainfall.
Water is a very important part of the climate system.
In addition to its greenhouse properties, it also acts
as a reservoir of heat. Water cycling through the
climate system supports life and maintains a stable
climate on Earth.
Atmospheric Processes
Atmospheric Processes
Atmospheric
Processes
Fluid Dynamics
Atmospheric
Processes
What is this ?
Atmospheric Processes
Why?
Atmospheric
Processes
Pressure?
Atmospheric
Processes
Pressure
Density
How are they
related?
Atmospheric
Processes
Lets start with
convection.....
Convection - a form of heat transfer
Consider the following:
How does water in a kettle heat up to a boil?
Why is air in a room warmer near the ceiling than
close to the floor?
Why does smoke emerge from the factory stacks
and rise up in the air?
Why does lava ooze out of cracks in the ocean
floor?
How do clouds form?
The answer to all of these is convection.
Convection - a form of heat transfer
Convection is a form of heat transfer
Convection takes place in liquids and gases and
distinguishes them from solids
It works because in a fluid "chunks" o`f matter
(which we will refer to as parcels) can move up or
down with respect to the rest of the fluid as they are
being heated or cooled, respectively (density
change!).
Convection - what governs it?
Air rises because it is lighter than its
environment ...
The processes of convection seem quite intuitive to us. They
are, however, governed by the laws of thermodynamics.
Understanding these laws helps us quantify these
processes, make predictions on the formation of
clouds and fog, and explain how the vertical profile
of temperature in the atmosphere is determined.
Properties of dry air
Dry air is air that contains no
water.
The state of a parcel of
dry air is described by
three properties:
temperature (T,
expressed in °K,
where 273°K = 0°C),
pressure (p, force per
unit area, expressed
in Newtons/m2) and
density (r, the mass of a
unit volume, in
Kg/m3).
Thermodynamic properties of
dry air - adiabatic temperature change
The equation of state - ideal gas law:
In a gas these properties (T,P, r ) are related by a relatively simple
physical law called the ideal gas law (ideal because it is not
exact, albeit quite accurate for most applications in
meteorology). This law states that:
p=rRT
or
r = p / (R T)
R is a coefficient, called the gas constant. It does not depend on either p, r, or
T. The gas constant depends only on the composition of gases that make
up the air (every gas has its own gas constant). Since this composition (for
dry air) is roughly constant throughout most of the atmosphere R of air is
constant and equal to 287 Joules/(kg °K).
Ideal Gas Law
p=rRT
or
r = p / (R T)
Ideal Gas Law
p=rRT
or
r = p / (R T)
Thermodynamic properties of
dry air - adiabatic temperature change
The first law of thermodynamics and adiabatic
expansion:
Let us remove the flame that heated our flexible walled
container, and put it in a chamber where the pressure can
be controlled from the outside, lowered or raised at will.
What will happen to the density of our air parcel when we
lower the pressure surrounding our container? What will
happen to its temperature?
Thermodynamic properties of
dry air - adiabatic temperature change
The first law of thermodynamics and adiabatic
expansion:
Here too the pressure on both sides of the flexible container walls
will equalize - as the outside pressure drops, the container will
expand and the pressure inside will drop by the same amount.
The density of the air parcel in the container will decrease as
well, in agreement with the ideal gas law. But what the ideal gas
law can not tell us is what will happen to the temperature. To
find that out we need to consider the first law of
thermodynamics - a physical law that extends the principle of
conservation of energy to include the concepts of heat and
work.
Thermodynamic properties of
dry air - adiabatic temperature change
The first law of thermodynamics and adiabatic expansion:
In thermodynamics the simplest form of energy conservation is the
balance between
internal energy [E] (the kinetic energy of the body's internal
molecular motion - directly proportional to its temperature),
and the amount of heat [Q] added to the body
minus the work [W] done by the body on its surroundings.
DE = DQ - W
Thermodynamic properties of
dry air - adiabatic temperature change
The first law of thermodynamics and adiabatic expansion:
If there is no exchange (input) of energy [ DQ = 0] the
system is called adiabatic.
internal energy [E] (the kinetic energy of the body's internal
molecular motion - directly proportional to its temperature),
minus the work [W] done by the body on its surroundings.
DE = - W
for an adiabatic system
Thermodynamic properties of
dry air - adiabatic temperature change
J
DE = - W
for an adiabatic system
a container with insulating flexible walls
Adiabatic temperature
change
DE = - W
for an adiabatic system
a container with insulating flexible walls
As our air parcel expands in response to the lowering of the outside
pressure, the force of its internal pressure is moving the walls of the
container outwards. When a force is moving an object over a given
distance it does work. Thus the expanding air parcel does work on its
surroundings. This work must come at the expense of internal energy
(remember, heat is neither added nor taken away from the parcel in
this experiment). Thus the molecular motion within the parcel will
slow down, and the parcel's temperature will drop.
Atmosphere under gravity
- hydrostatic balance.
Hydrostatic balance.
In the vertical direction, gravity is by far the most important
external force acting on the atmosphere. It is the reason
for the existence of this crucial envelop of gases around
the Earth.
The atmosphere does not collapse under the downward pull of
gravity because of the energy embedded in the movement of
the air molecules. This movement creates the force of
pressure which counters the gravitational pull on the
atmosphere. The balance between the force of pressure and
gravity is the hydrostatic balance.
Atmosphere under gravity
- hydrostatic balance.
Hydrostatic balance.
To find the expression for the hydrostatic balance, we first note that
atmospheric surface pressure is due to the weight of the entire
atmospheric column above. As we ascend, there is less of an atmosphere
above us, and hence the pressure drops.
Consider a column of gas Dz meters tall suspended somewhere in the
atmosphere (here D symbolizes an interval or difference). The pressure
acting on its bottom surface is higher than the pressure acting on its top
surface. The pressure difference Dp exactly balances the weight (per unit
area) of the column. Stated in mathematical terms this balance is written
as:
Dp = - r g Dz
where g is the acceleration of gravity = 9.8 m/s2.
Atmosphere under gravity
- hydrostatic balance.
The drop of pressure with height and adiabatic cooling of
rising air.
Pressure drops as we ascend in the atmosphere, but it does
not do so linearly (that is the drop in pressure is not
proportional to the height increase)
Why is that?
The hydrostatic balance provides the clue: density does
not remain constant with height!
Atmosphere under gravity
- hydrostatic balance.
The drop of pressure with height and adiabatic cooling of rising air.
In water (oceans), density stays close to constant as depth increases
because water is not very compressible. Therefore water pressure in
the ocean tends to increase linearly with depth.
As a gas, air is highly compressible. As pressure decreases with height, the
molecules of air are free to move further apart from one another and
the density decreases. Close to the ground, where gravity causes the
air to be rather compressed under the weight of the entire atmosphere
above, a small change of altitude results in a large drop in pressure
(roughly 100 Pa for every 8 meters of ascent).
Atmosphere under gravity
- hydrostatic balance.
J The drop of pressure with height
Atmosphere under gravity
- hydrostatic balance.
The drop of pressure
with height
Exponential Function !
Adiabatic cooling of rising air
We can now combine the thermodynamic laws with the effect of gravity
on pressure. Using the equation of state, the first law of
thermodynamics, and the hydrostatic equation we can find that the
rate of adiabatic temperature change in an ascending air parcel (also
termed the adiabatic lapse rate and denoted Gd ) is constant:
Gd = - DT /DZ = 9.8 °C/km
Note that Gd is defined as the negative of the actual temperature
change, so that Gd is the amount of cooling that the rising parcel
experiences. Sinking air will warm at the same rate as it is being
compressed by the increasing pressure.
Adiabatic cooling of rising air
Gd = - DT /DZ
= 9.8 °C/km
Adiabatic cooling of rising air
Atmospheric Processes
Why?
The stability of dry air - dry convection.
The stability of air under vertical displacement is determined by the
outcome of a small change in an air parcels elevation:
If the environment (the surrounding
atmosphere) is such that
vertically displaced parcels
continue to rise on their own,
even when the lifting exerted on
them stops, the environment is
referred to as unstable.
If vertically displaced parcels sink
back to their initial elevation after
the lifting ceases, the
environment is stable.
If vertically displaced parcels remain
where they are after being lifted,
the environment is neutral.
The stability of dry air - dry convection.
The stability of dry air - dry convection.
GIVE ME A BREAK !