Atmospheric Structure and Processes

Spring 2012, Lecture 6

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Tropospheric Properties

• As altitude increases within the troposphere, temperature decreases

• Heating is from the ground up

• Mountain climbers experience cooling at altitude

• At the level of the tropopause, a temperature minimum occurs – about -70º C

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Stratospheric Properties

• Above the tropopause, the temperature begins to climb again

• The ozone layer within the stratosphere absorbs ultraviolet (UV) radiation, and reradiates it in the infrared

• This produces in-situ heating• Since the UV radiation comes from the sun, heating

is strongest at the top of the stratosphere3

Pressure

• Pressure is the force per unit area applied perpendicular to the surface of an object

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Response to Pressure

• Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change

• Objects may be said to be compressible or incompressible, depending on the degree of volume change they experience per unit of pressure

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Compression of Water

• Water is often said to be incompressible

• At a depth of 4 km, with pressures are around 40 megapascals, water has a volume decrease of 1.8%

• At 0º C, the compressibility is less than one part in a billion per Pascal

• (One atmosphere is 101,000 Pascals)

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Linear Pressure Response

• As the figure shows, this means that water shows a linear response to an increase in pressure

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Non-Linear Pressure Response

• The figure is a graph of the actual change in pressure with increasing altitude, and is clearly non-linear

• At an altitude of 8 kilometers, pressure is half as much as at sea-level

• This is because the atmosphere is compressible

Vertical scale is km 8

Compressible vs. Incompressible

• The figure shows a response to pressure by a compressible substance (air), and an incompressible substance, water

• There is more air per meter at low altitude than at higher altitude

• The amount of water per meter does not depend on the depth to a significant extent

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Exponential Function

• The change in pressure with altitude is an example of an exponential function

• Q = ekx, where:oQ = quantity in questiono k is a constant, which may be positive or negativeo x is a variable o e is an irrational number equal to 2.718281828….

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Exponential Change

• Exponential change can be positive, like ex in the diagram o Population growth is an

example

• Exponential change can be negative, often called decay, like e-x in the diagramo Radioactive decay is an

example

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Change of Pressure with Altitude

• Pressure clearly decays (grows smaller) with altitude

• We can calculate the change in pressure as followso P(z) = 1 atm • e-z[km]/8 km

• z is the height above the ground, measured in kms

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Temperature

• Temperature is related to the average kinetic energy of the molecules in the volume under consideration

• The faster molecules move, the higher the temperature

• It does not matter how many molecules there are per unit volume

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Heat Content (Enthalpy)

• The heat content is equal to the energy required to create a system, plus the energy required to displace the surroundings, creating room for the system

• If a gas is compressed, it warms up – we did work on the system to compress it, which added energy

• If a gas expands, it cools down – the gas expanded, doing work on the universe

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Adiabatic Change

• Adiabatic change refers to change with no change in heat content

• Adiabatic expansion – a gas occupies a bigger volume, but the molecules move slower

• Adiabatic compression - a gas occupies a smaller volume, but the molecules move faster

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Lapse Rate

• As gas rises in the atmosphere, it expands, because pressure is less

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• If conditions are adiabatic, the gas will behave as shown in the diagram, depending on how much water it holds

Lapse Rate Definition

• The lapse rate is defined as the change with height of an atmospheric variable

• The variable is usually temperature

• The adiabatic lapse rate is the change with constant heat content

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Phase Changes

• Substances, such as water, can exist in any of three phasesoGas (Water vapor)o Liquido Solid (Water ice)

• A change in phase involves heatoWater vapor → Water + heato Ice + heat → Water

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Latent Heat

• If you stick your hand in an oven at 100º C for a short time, you will not be burned

• If steam from a kettle contacts your hand, you probably will be

• Steam has extra energy, called latent heat

• When the steam hits your hand, some of it condenses, transferring energy to your hand, and burns you

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Vapor Pressure

• Water molecules in the air contribute to the total pressure within a system

• The pressure is known as the vapor pressure

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• Vapor pressure is primarily a function of the temperature

• The higher the temperature, the higher the vapor pressure

Saturation

• At any given temperature, air can hold a certain amount of water vapor at equilibrium

• Equilibrium means if one water molecule evaporates, another will condense

• If the water vapor content is below the equilibrium value, the air is undersaturated – water will tend to evaporate

• If it is above the equilibrium value, it is supersaturated – water will tend to condense

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Humidity

• Relative humidity is the water vapor pressure divided by the saturation pressure

• As relative humidity increases, it is harder to evaporate water – sweating as a means of cooling becomes less and less efficient

• Absolute humidity is the amount of water the air holds, per unit volume oUsually expressed as grams per m3

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Convection

• Convection is a movement of molecules within a fluid, either liquid or gas

• It is sometimes used to mean the heat transfer produced by such motionoAs such, it is a third means of heat transfer, along

with radiation and conduction

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Producing Convection

• Convection may occur when a fluid is heated from below, which causes the bottom fluid to expand, becoming less dense, and thus rising

• Or it may be produced by cooling from above, which causes the top fluid to contract, becoming more dense, and thus falling

• Convection is a common process in thunderstorms and hurricanes

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Convection Diagram - 1

• In A, a fluid has a uniform temperature, and is well-mixedo In this situation, the fluid is stable

• In B, the fluid is heated from below, increasing the temperature and decreasing the density o The fluid is now convectively unstable

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Convection Diagram - 2

• If the fluid consists of two immiscible components, the heated portion will rise to the top, float until it cools, and then sink – the principle of a lava lamp, as shown in C

• If the fluid is a single component, it will mix, and the entire fluid will become warmer, as shown in D

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Lava Lamps

• Slow heating • Rapid heating

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Convection in Compressible Fluids

• Figure a represents a stable situation in the troposphere, with temperature decreasing with altitude

• Figure b shows heating from below – the heated air is less dense, so it rises, but along its own adiabat – it can rise to the top of the gas column if mixing does not occur

• If mixing occurs, the temperature profile of the whole column is increased

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Dry vs. Wet Adiabats

• If air with relative humidity = 100% rises in the atmosphere, it will expand and cool

• Cool air holds less moisture, so the water vapor will start to condense to form droplets

• Condensing water releases latent heat, helping to offset the cooling due to expansion

• This accounts for the dry and wet adiabats in the diagram

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Radiative vs. Convective Equilibrium

• In the layer model we examined, there is no convection, only blackbody radiation

• In reality, convection is important

• The radiative equilibrium lapse rate is about 16K/km

• The convective lapse rate for a dry adiabat is around 10K/km, and for a wet adiabat around 6K/km

• This is called radiative-convective equilibrium30

Radiation Altitude• Some IR radiation goes directly into space, through IR

windows

• Other IR wavelengths are absorbed and reradiated from the coldest part of the atmosphere, the tropopause

• We can imagine an equilibrium altitude that averages the different wavelengths, and this was the skin altitude encountered earlier

• Skin temperature is commonly defined as the temperature of the interface between the earth's surface and its atmosphere

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Increasing Skin Altitude

• As GHG concentration goes up, more radiation is trapped, and more radiation to space comes from the tropopause

• This raises the skin altitude, which we can denote as zskin

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Calculating Ground Temperature

• We can calculate the worldwide average ground temperature if we know the skin temperature altitude and the lapse rate

• If the lapse rate is 6K/km, and the skin altitude is 5 km, the calculation is as follows:o Tground = Tskin + 6K/km • 5 km , or

Tground = Tskin + 30K

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Changing Skin Altitude

• If GHG concentration goes up, so does skin altitude

• This shifts the point at which the moist adiabat intercepts the ground to a higher temperature

• Thus, greenhouse warming

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Changing Skin Altitude

• We can rewrite the equation for changing ground temperature with changing skin altitude, as follows:o ΔT= Δzskin • 6K/km , where

• ΔT is the change in temperature

• Δzskin is the change in skin altitude

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Incompressible Atmosphere

• If the atmosphere were incompressible, convection would keep the temperature equal at all altitudes, thus making the lapse rate zeroo ΔT= Δzskin • 0K/km = 0

• There would be no greenhouse effect

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Ground Temperature Sensitivity

• The lapse rate determines the sensitivity of the ground temperature to increasing GHG concentration

• Thus, this is a critical parameter for model calculations

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