Atmospheric Properties Martin Visbeck DEES, Lamont-Doherty Earth Observatory

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.

T(sun) = 5780 K T(earth) = 288 K Black Body Emission

Wien's law states that:   max = a / T where max is given in  m, T is in units of K, and a is a constant equal 2897  m K. The Stefan-Boltzman law states that: I =  T 4 where I is in units of W/m 2, T is in units of K, and  (the Greek letter sigma) is a constant equal to  5.67 x with units of W m -2 K -4. Area ~ Energy (integrate over log of wavelength)

Solar Constant I 2 = I 1 ( r 2 2 / r 1 2 ) I0I0 I1I1 I2I2 r0r0 r2r2 r1r1 I = I 0 (at the source) r (source) 2 / r 2

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

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/m 2 ) and density ( , the mass of a unit volume, in Kg/m 3 ).

Thermodynamic properties of dry air - adiabatic temperature change The equation of state - ideal gas law: In a gas these properties (T,P,  ) 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 =  R T or  p / (R T) R is a coefficient, called the gas constant. It does not depend on either p, , 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 =  R T or  p / (R T)

Ideal Gas Law p =  R T or  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.  E =  Q - 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 [  Q = 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.  E = - W for an adiabatic system

Thermodynamic properties of dry air - adiabatic temperature change  E = - W for an adiabatic system a container with insulating flexible walls

Adiabatic temperature change  E = - 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  z meters tall suspended somewhere in the atmosphere (here  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  p exactly balances the weight (per unit area) of the column. Stated in mathematical terms this balance is written as:  p = -  g  z where g is the acceleration of gravity = 9.8 m/s 2.

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  d ) is constant:  d = -  T /  Z = 9.8 °C/km Note that  d is defined as the negative of the actual temperature change, so that  d 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  d = -  T /  Z = 9.8 °C/km

Adiabatic cooling of rising air

Atmospheric Processes Why?

The stability of dry air - dry convection. 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 air under vertical displacement is determined by the outcome of a small change in an air parcels elevation:

The stability of dry air - dry convection.

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