Cool Science Convection.. Take away concepts and ideas. State Properties of Air

Transcription

1 Thermal Structure of the Atmosphere: Lapse Rate, Convection, Clouds Cool Science 2007 Lamont Open House Saturday, October 4th 10am - 4pm Free Shuttle buses to / from Amsterdam & 118th: 9:30am, every 30 mins. Take away concepts and ideas Heat convection vs. conduction Atmospheric lapse rate Pressure as a function of altitude Convection in a dry vs. wet atmosphere Atmospheric heat transport Atmosphere Very poor conductor Very good convection Important radiation properties Why does water in a kettle heat up to boil? Why is air on the ceiling warmer than the floor? Why does smoke rise? Why does lava ooze out of cracks on the ocean floor? How do clouds form? Convection.. State Properties of Air The interdependence of air temperature, pressure, and density 1

2 Temperature and Pressure profiles of the atmosphere Thermodynamic properties of Dry Air Assume (for now) the atmosphere has no water. Dry air pressure (P), Temperature, and Density all linked through Ideal Gas Law Hydrostatic balance A. Ideal Gas Law P V = n R T Ideal Gas Law = Equation of State (just perfect gas with no other phases, like water) n / V = density = ρ; so rewrite as: P = ρ R T P = ρ R T or P V = n R T R = constant Pressure (P, force exerted by gas molecular motion) Temperature (T, energy of molecular motion) Density (ρ, number of atoms per unit volume, n/v) Q1: Fun with the ideal gas law P = ρ R T If you increase temperature but keep pressure constant what happens to density? A. Pressure increases B. Pressure decreases C. Density increases D. Density decreases E. R decreases Q2: More fun Which of the following rearrangements of the Ideal Gas law explains why, when you pump up a tire, a bicycle pump heats up? A. T = P/ (ρ R) B. P = ρ R T C. R = P / (ρ T) D. ρ = P / (RT) Adiabatic (no heat added/taken away, the P is doing the work) 2

3 constant P = ρ R T Rigid walls ρ = constant Flexible walls P = constant Cooling a balloon in liquid nitrogen (- T) increases the density (+ ρ) Link B. Hydrostatic Balance The atmosphere under gravity - hydrostatic balance Gravity pushes down the atmosphere pushes back When equal, this is Hydrostatic balance equation Δp = - ρ g Δz where g = grav. accel. (9.8 m/s 2 ) Impress your friends! Deriving the dry adiabatic lapse rate (rate at which the atmosphere cools with altitude): Easy as 1 2 3: 1) 1st Law of Thermodynamics Heating = internal energy + work Q = U + W (conservation of energy, signs are right here) No heating for an adiabatic process, therefore: 0 = U + W 2) 0 = U + W 0 = (change in temperature * air heat capacity) + (pressure * change in volume) 0 = n c v T + P V Combining, 0 = C p T + P/ρ (C p is heat cap of air) Rearranging, T/ P = -1 / ( C p ρ) Now, substitute into hydrostatic equation ( P = - ρ g z) You ve derived the Dry Adiabatic Lapse Rate equation Rearrange T/ z = g / C p T/ z = (9.8 m/s 2 ) / (1004 J/kg/K) = 9.8 K per km <-- Dry Lapse Rate!! Q3: Hiking You re planning a hike in some desert mountain range and the temperature at basecamp is 20 C. What is the temperature at the summit (2000m elevation higher)? A. 10 C B. 0 C C. -10 C D. -20 C E. Can t tell 3

4 Atmospheric temperature profile: Now just add water Wet Convection So far we ve just considered a dry atmosphere Dry adiabatic lapse rate: -9.8 C/km Heat transfer by DRY convection = 9.8 C / km Surface warming By conduction Adiabatic = No heat is lost or gained within a parcel of air Diabatic = Heat is lost or gained within a parcel of air typical adiabatic lapse rate: - 6 to -7 C/km why aren t they the same? Water vapor! Dry Air and Dry Convection Thermodynamic properties of moist air Think of a parcel of air If the air is heated, how does its density change? P = ρ R T The atmosphere in most places isn t dry. Energetics of water phase changes: Liquid --> Vapor needs 540 cal/gram H 2 O Is the parcel stable or unstable relative to adjacent parcels? dry air convection! (no clouds just yet ) 7 C/km 9.8 C/km (Latent heat of evaporation; takes heat AWAY) Vapor --> Liquid releases 540 cal/gram H 2 O (Latent heat of condensation; ADDS heat) Phase changes of water Temperature Controls Water Vapor Saturation in Air Direction of phase change going to lower energy phase (vapor->liquid->ice) Examples: rain, ice-formation going to higher energy phase (ice->liquid->vapor) Examples: Ice-melting, evaporation Thermodynamic effect heat is released (warms air) heat is absorbed (cools air) Warm air holds A LOT more water than cold air. What is saturation? Saturation water vapor content increases exponentially with temperature Clausius-Clapeyron relation --> 4

5 Moisture affects stability Consider a rising parcel of air, but this time it has water vapor (typically 0.5% by weight) Air parcel rises starts to cool Follows DRY ADIABATIC lapse rate until 1st condensation (cloud) 1st condensation --> release of latent heat of condensation inside of parcel Warming in parcel offsets cooling, so Rising parcel no longer follows dry adiabatic lapse rate of -9.8 C/km, but follows the MOIST ADIABATIC lapse rate of -6-7 C/km Tropical atmosphere follows MOIST adiabat Polar atmosphere follows DRY adiabat unstable -7 C/km stable -6.5 C/km -7 C/km MOIST PARCEL rising in warm environment Comparing the dry and moist lapse rates -9.8 C/km DRY PARCEL rising in warm environment California Coastal Range Coast Desert down Moist adiabatic lapse rate = 7 C/km up Dry adiabatic lapse rate = 9.8 C/km unstable 5

6 Why Hurricanes are so powerful CISK = Convective Instability of the Second Kind Galveston, TX: Hurricane of