LECTURE 3 Basics of atmospheric composition and physics AOSC 434 AIR POLLUTION Russell R. Dickerson

Ib. ATMOSPHERIC PHYSICS Seinfeld & Pandis: Chapter 1 Finlayson-Pitts: Chapter 2 1.Pressure: exponential decay 2.Composition 3.Temperature The motion of the atmosphere is caused by differential heating, that is some parts of the atmosphere receive more radiation than others and become unstable.

VERTICAL PROFILES OF PRESSURE AND TEMPERATURE Mean values for 30 o N, March Tropopause Stratopause

N2N2 O2O2 Ar O3O3 Inert gasesCO 2 H2H2 ←SO 2, NO 2, CFC ’ s, etc PM CO CH 4 N2ON2O Composition of the Earth ’ s Troposphere

Banded iron formation. Smithsonian in DC

About 3E9 years ago, cyanobacteria began producing O 2 in photosynthesis; initially consumed by iron and organic matter in oceans. O 2 is toxic to anaerobic organisms – the first great extinction. (Range of P O2 estimates)

Units of pressure: 1.00 atm. = 14.7 psi = 1,013 mb = 760 mm Hg (torr) = 33.9 ft H ₂ O = 29.9 ” Hg = Pa A Pascal is a Nm ⁻ ² (kg m s -2 m -2 ) thus hPa = mb. Units of Volume: liter, cc, ml, m³ Units of temp: K, °C Units of R: L atm mole -1 K J mole -1 K -1 R ’ = R/M wt = J g -1 K -1 For a mole of dry air which has the mass 29 g. Problem for the student: calc Mwt. Wet (2% H ₂ O vapor by volume) air.

1A. Derive Hypsometric Equation Start with The Ideal Gas Law PV = nRT or P = ρR ’ T or P = R ’ T/α Where R ’ = R/Mwt Mwt = MOLE WT. AIR ρ = DENSITY AIR (g/l) α = SPECIFIC VOL AIR = 1/ρ We assume that the pressure at any given altitude is due to the weight of the atmosphere above that altitude. The weight is mass times acceleration. P = W = mg But m = Vρ For a unit area V = Z P = Zρg

For a second, higher layer the difference in pressure can be related to the difference in height. dP = − g ρ dZ But ρ = P/R ’ T dP = − Pg/R ’ T * dZ For an isothermal atmosphere g/R ’ T is a constant. By integrating both sides of the equation from the ground (Z = 0.0) to altitude Z we obtain:

Where H ₀ = R ’ T/g we can rewrite this as: *HYPSOMETRIC EQUATION* Note: Scale Height: H ₀ ~ 8 km for T = 273K For each 8 km of altitude the pressure is down by e ⁻ ¹ or one “ e-fold. ” Problems for the student: Derive an expression for pressure as a function of altitude using base two and base ten instead of base e. Calculate the scale height for the atmospheres of Venus and Mars. Ans. base 2 = H ₀ *ln(2) = 5.5 km base 10 = H ₀ *ln(10) = 18 km

1B. TEMPERATURE LAPSE RATE Going to the mountains in Shenandoah National Park the summer is a nice way to escape Washington ’ s heat. Why? Consider a parcel of air. If it rises it will expand and cool. If we assume it exchanges no heat with the surroundings (a pretty good assumption, because air is a very poor conductor of heat) it will cool “ adiabatically. ” Calculating the dry adiabatic lapse rate. First Law Thermodynamics * : dU = đ Q – đ W Or đ Q = dU + đ W = dU + PdV *watch out for work done by the system or on the system.

WHERE U = Energy of system (also written E) Q = Heat across boundaries W = Work done by the system on the surroundings H = Internal heat or Enthalpy ASSUME: a)Adiabatic (dQ = dH = 0.0) b)All work PdV work (remember α = 1/ρ) dH = Cp dT – α dP CpdT = α dP dT = (α/Cp) dP

Remember the Hydrostatic Equation OR Ideal Gas Law Result: This quantity, -g/C p, is a constant in a dry atmosphere. It is called the dry adiabatic lapse rate and is given the symbol γ ₀, defined as −dT/dZ. For a parcel of air moving adiabatically in the atmosphere:

Where Z ₂ is higher than Z ₁, but this presupposes that no heat is added to or lost from the parcel, and condensation, evaporation, and radiative heating can all produce a non-adiabatic system. The dry adiabatic lapse rate,  0, is a general, thermodynamic property of the atmosphere and expresses the way a parcel of air will cool on rising or warm on falling, provided there is no exchange of heat with the surroundings and no water condensing or evaporating. The environmental lapse rate, , is seldom equal to exactly the dry adiabatic lapse rate because radiative processes and phase changes constantly redistribute heat. The mean lapse rate is about 6.5 K/km. Problem left to the students: Derive a new expression for the change in pressure with height for an atmosphere with a constant lapse rate,

2. STABILITY AND THERMODYNAMIC DIAGRAMS Gray lines – thermodynamic property Black lines – measurements or soundings Three days  a < γ ₀ stable  b = γ ₀ neutrally stable  c > γ ₀ unstable On day a a parcel will cool more quickly than surroundings – air will be cooler and return to original altitude. On day b a parcel will always have same temperature as surroundings – no force of buoyancy. On day c a parcel will cool more slowly than surroundings – air will be warmer and rise.

17 Convective Instability dry air cb a

Example 1, early morning Pressure, mbTemp., °CDew point, °C Tropopause Inversion layer Saturated air (T = T D )

Example 2, mid-day Pressure, mbTemp., °CDew point, °C Tropopause Frontal Inversion layer

Skew-T handout Very important for air pollution and mixing of emissions with free troposphere. Formation of thermal inversions. In the stratosphere the temperature increases with altitude, thus stable or stratified. DFN: Potential temperature, θ : The temperature that a parcel of air would have if it were brought to the 1000 hPa level (near the surface) in a dry adiabatic process. You can approximate it quickly, or a proper derivation from dq = C p dT –  dp = 0 yields: θ z = T ( 1000 hPa/P z ) R’/Cp = T ( 1000 hPa/P z ) 0.286

DIURNAL CYCLE OF SURFACE HEATING/COOLING: z T 0 1 km MIDDAY NIGHT MORNING Mixing depth Subsidence inversion NIGHTMORNINGAFTERNOON

Copyright © 2013 R. R. Dickerson & Z.Q. Li 22 If the parcel reaches saturation, the condensation of water adds heat, and the rising air cools at a new, slower rate,  s. For details, see Wallace and Hobbs. Since  s <  d, we must also consider conditions between the two stability criteria for dry and saturated.  = parcel lapse (thermodynamically determined) rate.  = environment (observed) lapse rate.

Plume looping, Baltimore ~2pm.

Plume Lofting, Beijing in Winter ~7am.

High levels of air pollution in Beijing contain a large quantity of PM 2.5. © iStockPhoto.com/beijingstory. Marshall J PNAS 2013;110: ©2013 by National Academy of Sciences

Chinese Y12 (Twin Otter) for the airborne campaign over NE China April 2005

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~ 100 μg m -3 ↓ ↑ ~ 15 μg m -3

← Shenyang, 5 April 2005 ← NE USA median

Washington, DC ✪ Washington, DC Baltimore, MD  DISCOVER-AQ Case Study MODIS true color image 21 July 2011 Bay breeze: Winds veer w/ alt

Hot (Tmax > 100 o F) Humid, rel stable PBL. UMD Cessna

PM2.5 ~ 40  g m -3 

UMD Cessna

Copyright R. R. Dickerson Atmospheric Circulation and Winds

Copyright R. R. Dickerson ITCZ

Copyright R. R. Dickerson Mid latitude cyclone with fronts

Copyright R. R. Dickerson Fig Warm Front

Copyright R. R. Dickerson Fig Cold front

Copyright R. R. Dickerson Fig. 1-17, p. 21

Copyright R. R. Dickerson Fig. 1-16, p. 19

Copyright R. R. Dickerson Fig. 1-16, p. 19

Copyright R. R. Dickerson Detailed weather symbols