Pat Arnott Chapter 3: Atmospheric Thermodynamics Objectives: 1.Demonstrate quantities used by Atmospheric Scientists to relate properties of air parcels aloft with those at the surface. 2.Develop increasingly more accurate models for the temperature, pressure, and density of air in the atmosphere. 3.Stability of air parcels. Should be very familiar with these topics as we cover this chapter: a. Ideal gas equation applied to dry and moist air. SEE THIS AWESOME SIMULATION!SEE THIS AWESOME SIMULATION! b. Virtual temperature. c. Potential temperature. d. Hydrostatic equation. e. Increasingly detailed description of the temperature and pressure distribution in the atmosphere. f. SkewT logP diagrams. z. Relative humidity, absolute humidity. g. Dew point temperature. h. Wet bulb temperature. i. Equivalent potential temperature. j. Latent heat release and absorption in condensation and evaporation of water. k. Stability of air parcels. l. Indices on soundings.m. Lapse rate, adiabatic lapse rate, deviations from adiabatic lapse rate, pseudoadiabats.

Pat Arnott Equation of State for an Ideal Gas: Air V = volume 1.molecule size is ignorable. 2.molecules don’t interact (attract or repel each other). 3.molecular collisions are like hard point like spheres. Most primitive, intuitive form of the I.G.L. (ideal gas law): PV = NkT Now we manipulate to find a satisfying form of the I.G.L for analysis: P = pressure N = # molecules T = absolute temperature (Kelvin) k = Boltzmann’s constant = 1.38 x Joules / (molecule K)

Pat Arnott Various Equivalent Forms of the I.G.L. Note the useful bottom line form P  =RT: We will use this most often.

Pat Arnott Partial Pressure and Ideal Gas Mixtures EACH GAS SEPARATELY OBEYS THE IDEAL GAS LAW.

Pat Arnott Applications of Dalton’s Law of Partial Pressures… What is the total pressure in the room? What is the partial pressure due to nitrogen molecules N 2 ? What is the partial pressure due to oxygen molecules, O 2 ? What is the partial pressure due to carbon dioxide molecules, CO 2 ? Wait a minute… how can it be that these molecules apply pressure according to their number concentration? They don’t all have the same mass… What is going on? Dalton's law is not exactly followed by real gases. Those deviations are considerably large at high pressures. In such conditions, the volume occupied by the molecules can become significant compared to the free space between them. Moreover, the short average distances between molecules raises the intensity of intermolecular forces between gas molecules enough to substantially change the pressure exerted by them. Neither of those effects are considered by the ideal gas model. The fine print from Wikipedia…

Pat Arnott Applications of Dalton’s Law of Partial Pressures… What is the total pressure in the room? 860 mb on 9/9/2010. What is the partial pressure due to nitrogen molecules N 2 ? 860 mb * 0.78 = 670 mb. Air is composed of 78% N 2 molecules. What is the partial pressure due to oxygen molecules, O 2 ? 860 mb * 0.21 = 180 mb. What is the partial pressure due to carbon dioxide molecules, CO 2 ? 860 mb * = 0.34 mb. For 10 mb water vapor partial pressure, air is about 1% water vapor.

Pat Arnott Kinetic Theory of Pressure (Wikipedia…) Box of sides L mvxvx Nature is fair … On average, molecules share the burden of random kinetic energy, also known as heat. K.E.=mv 2 /2. On average, molecules with smaller m move faster than large m molecules. Pressure in the kinetic theory of gases …

Pat Arnott Special Case: Partial Pressure of Water Vapor, e

Pat Arnott Virtual Temperature T v. dry air moist air same for both T = temperature P = pressure V = volume N = # molecules P = P D P = P D +e Total pressure= partial pressure due to dry air. Total pressure= partial pressure due to dry air + water vapor.  dry air >  moist air TWEAK … Raise the temperature of the dry air on the left to lower its density so that it is the same as the density of the moist air on the right. We have to let some of the molecules out of the box. This raised temperature is the virtual temperature by definition. It is a useful construct because the I.G.L. for dry or moist air is written P  = R D T v. P  RT

Pat Arnott Virtual Temperature T v Calculation. dry air moist air same for both T = temperature P = pressure V = volume P = P D P = P D +e Total pressure= partial pressure due to dry air. Total pressure= partial pressure due to dry air + water vapor. Crank up the temperature of box 1, keeping pressure and volume constant (let some dry air molecules leak out), until the mass (density) of box 1 is the same as that of box 2. P  RT box 1 box 2 From the I.G.L. TvTv T General Note: T v >T.

Pat Arnott Virtual Temperature Example Let e=10 mb P=1000 mb T=280 K Remember  =0.622 Then T v ≈ T [1+e(1-  )/P] = T( ) ≈ 281 K This gives us a rough idea of the temperature increase needed to make dry air have the same density as the moist air described above. (binomial expansion was used to show an equivalent form)

Pat Arnott

Potential Temperature Adiabatic compressional warming (and cooling by expansion) lends itself to predicting large-scale weather patterns, because air motions in large weather systems are, for all practical purposes, generally adiabatic in nature.

Pat Arnott

sustainable only with diabatic heating!

Pat Arnott

LCL: Lifting condensation level. LFC: Level of free convection. EL: Equilibrium level. CAPE: Convective available potential energy. CIN: Convective inhibition. Solar heating, surface convergence promote parcels to the LFC: Must pass above the inversion in the CIN area. CAPE (J/kg): (small) (moderate) (large) > 4000 (extreme). CIN (J/kg): 0 to -25 (weak) -25 to -50 (moderate) - 50 to -100 (strong convective inhibition)

Pat Arnott

Winds on Skew T Log P Charts wind is 15 knots coming from the northeast.

Pat Arnott

Moist Adiabats: Trajectories of Saturated Parcels. Pseudoadiabats because products of condensation may fall out of the parcel as precipitation. Trace a few of them below.

Pat Arnott The Saturated Adiabatic Lapse Rate Temperature Changes and Stability Inside Clouds from

Pat Arnott Temperature Changes Inside Clouds Two processes occur simultaneously inside clouds that affect the temperature. (1)Rising air expands, does work and cools; (2)Condensation releases latent energy which is then stored as internal energy and warms the air inside the cloud.

Pat Arnott Temperature Changes Inside Clouds (Cont.) Normally, the cooling due to the work of expansion is greater than the warming associated with the release of latent energy and its conversion to internal energy.

Pat Arnott Temperature Changes Inside Clouds (Cont.) Thus, as air rises inside a cloud it still gets colder, but it does so at a slower rate than the Dry Adiabatic Lapse rate. The rate at which rising air inside a cloud cools is called the Saturated Adiabatic Lapse Rate (SALR).

Pat Arnott The Saturated Adiabatic Lapse Rate (SALR) The derivation of the equation for the SALR begins with a form of the First Law of Thermodynamics dq = c p dT - αdp What would we do here to get the dry adiabatic lapse rate?

Pat Arnott The Saturted Adiabatic Lapse Rate (Cont.) In this case the energy gained, dq, is equal to the latent energy released when water vapor condenses inside the cloud. dq = -L v dw s where L v is the latent heat of vaporization, and dw s is the change of specific humidity of the air parcel when water vapor condenses

Pat Arnott The SALR (Cont.) Substitute for dq in the First Law of thermodynamics to get -L v dw s = c p dT – αdp Add –c p dT + L v dw s to both sides to get

Pat Arnott The SALR (Cont.) -c p dT = -αdp + L v dw s Divide by c p dz to get -c p dT = -αdp + L v dw s c p dz c p dz c p dz Since α = 1/ρ we can write this as

Pat Arnott The SALR (Cont.) -dT = - 1 dp + L v dw s dz c p ρ dz c p dz From the hydrostatic approximation -1 dp = g ρ dz

Pat Arnott The SALR (Cont.) Substitution results in -dT = g + L v dw s = Γ s dz c p c p dz SALR = cooling due to work of expansion + warming due to latent energy released during condensation Γ dry Γ s = Γ dry + L v dw s c p dz

Pat Arnott The SALR (Cont.) The saturated adiabatic lapse rate is always less than the dry adiabatic lapse rate because the cooling caused by adiabatic expansion is partially offset by the release of latent energy during condensation.

Pat Arnott The SALR (Cont.) The saturated adiabatic lapse rate is quite variable!! The magnitude of the SALR is determined by the amount of water vapor that condenses.

Pat Arnott The SALR (Cont.) When warm moist air rises in a cloud, more water vapor condenses and the SALR is smaller. When cooler, drier air rises inside a cloud, less water vapor condenses and the SALR is larger.

Pat Arnott cooler drier air warmer moister air SALR = 0.9°C/100m less water vapor condenses more water vapor condenses SALR = 0.5°C/ 100 m

Pat Arnott Unsaturated air rises and cools at the DALR Lifting Condensation Level (LCL) Saturated air rises inside the cloud and the release of latent energy during condensation causes it to cool at the SALR

Pat Arnott Stability Cases for Clouds (1) When the environmental lapse rate (ELR) is greater than the SALR, then the air inside the cloud is unstable. Unstable air moves vertically and we tend to get tall, vertical clouds like cumulus and cumulonimbus. z ELRSALR T(z) O T lifted > T env T env

Pat Arnott Stability Cases for Clouds (Cont.) cumulus cumumlo- nimbus

Pat Arnott Stability Cases for Clouds (Cont.) (2) When the ELR is equal to the SALR, then the air inside the cloud is neutral. (3) When the ELR is less than the SALR, then the air inside the cloud is stable. z ELRSALR T(z) O T lifted < T env T lifted

Pat Arnott Stability Cases for Clouds (Cont.) There is much less vertical motion when air is neutral or stable. Thus, when air inside the clouds is neutral or stable, the clouds tend to have a flat, layered appearance. These types of layered clouds are called stratus clouds.

Pat Arnott Stability Cases for Clouds (Cont.) stratus

Pat Arnott Stability Cases for Clouds (Cont.) There is a special stability case that occurs when the Environmental Lapse Rate is between the Dry Adiabatic Lapse Rate and the Saturated Adiabatic Lapse Rate.

Pat Arnott Stability Cases for Clouds (Cont.) For example, what if DALR = 1.00°C/100 m ELR = 0.75°C/100 m SALR = 0.50°C/100 m If the air is unsaturated ELR SALR and the air is unstable.

Pat Arnott Stability Cases for Clouds (Cont.) This special case is called conditionally unstable, because the air must be lifted until it becomes saturated in order for it to become unstable

Pat Arnott 0000 m T = 28°C, T d = 20°CT env = 28°C LCL = 800 m T = 20C°, T d = 20°C T env = 22°C Air is stable 1600 m T = 16°C, T d = 16°C T env = 16°C Air is neutral 2000 m T = 14°C, T d = 14°C T env = 13°C Air is unstable DALR = 1°C/100 m ELR = 0.75°C/100 m SALR = 0.5°C/100 m

Pat Arnott Stability Cases in Clouds (Cont.) When the atmosphere is conditionally unstable it can lead to the rapid development of thunderstorms when a cold front or other weather feature lifts warm moist air in the spring.

Pat Arnott Stability Cases in Clouds (Cont.) The air is stable as long as it isn’t lifted high enough, but if it is lifted until the parcel is warmer than the environment, then the air instantaneously becomes unstable and starts rising on its own. Then thunderstorms can form rapidly.

Pat Arnott The Effect of Topography on Precipitation Patterns Precipitation patterns in mountainous regions tend to be closely related to the prevailing wind direction. Much higher precipitation amounts fall on the side of the mountains where the air is rising and it is much drier on the side where the air is sinking.

Pat Arnott The Effect of Topography on Precipitation Patterns (Cont.) The process where air is forced to rise up the side of a mountain is sometimes called orographic lifting.

Pat Arnott 0 meters T = 26°C, T d = 16°C Air rises and cools at DALR T = 16°C, T d = 16°C LCL 1000 m Air rises and cools at SALR = 0.5°C/ 100 m 3000 m T = 6°C, T d = 6°C Air sinks and warms at the DALR = 1°C/100 m 500 m T = 31°C, T d = 6°C Air is warm and dry Windward side Leeward side wind direction

Pat Arnott The Effect of Topography on Precipitation Patterns (Cont.) Rising motion causes clouds and precipitation on the windward side of the mountain range. Sinking motion causes warm, dry conditions on the leeward side of the mountain. The dry area on the leeward side of the mountain is called the rain shadow.

Pat Arnott The Effect of Topography on Precipitation Patterns (Cont.) Since the prevailing wind direction in the middle latitudes is from the west, the western sides of the mountains along the west coast of the U.S. are the rainy sides and the rain shadows occur along the eastern slopes of the mountains.

Pat Arnott

Find the LCL for a surface parcel: find Tw, the wet bulb temperature.

Pat Arnott Evaporative Cooler: Swamp Cooler.

Pat Arnott

NASA satellite image (MODIS imager on board the Terra satellite) of a wave cloud forming off of Amsterdam Island in the far southern Indian Ocean. Image taken on December 19, 2005.

Pat Arnott