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ATS 621 Fall 2012 Lecture 3 H2O part of constant Chain Reaction Example “M” is any other molecule available for collisions UNITS Mixing ratio or mole fraction CX [mol mol-1] # moles of X CX mole of air Trace gases remains constant when air density changes e robust measure of atmospheric composition GAS MIXING RATIO (dry air) [mol mol-1] Nitrogen (N2) 0.78 Oxygen (O2) 0.21 Argon (Ar) 0.0093 Carbon dioxide (CO2) 365x10-6 Neon (Ne) 18x10-6 Ozone (O3) (0.01-10)x10-6 Helium (He) 5.2x10-6 Methane (CH4) 1.7x10-6 Krypton (Kr) 1.1x10-6 • Air also contains variable H2O vapor (10-6-10-2 mol mol-1) and aerosol particles • Trace gas concentration units: 1 ppmv = 1x10-6 mol mol-1 1 ppbv = 1x10-9 mol mol-1 1 pptv = 1x10-12 mol mol-1 Slide courtesy Colette Heald "Perfect Gas" Law PV = N' kT or PV = N RT N' = number of molecules in the air parcel N = number of moles; N' = N x Av k = Boltzmann constant R = Universal Gas Constant; R = k x Av ================================= (In meteorology texts: P = r RT - different "R“ = 287 J/kg/K) k = 1.3806503 × 10-23 m2 kg s-2 K-1 R = 8.31 J mole-1 K-1 Slide courtesy Colette Heald Number density nX [molecules cm-3] nX Proper measure for • reaction rates • optical properties of atmosphere # molecules of X unit volume of air Column concentration X = nX ( z )dz 0 nX and CX are related by the ideal gas law: Also define the mass concentration (g cm-3): rX Proper measure for absorption of radiation by atmosphere na = air density Av = Avogadro’s number P = pressure [Pa] R = Universal gas constant = Av k k=Boltzmann cnst T = temperature [K] MX= molecular weight of X [g/mol] mass of X unit volume of air Slide courtesy Colette Heald Partial pressure Px [Pa] Dalton’s law: PX C X P Proper measure for phase change (such as condensation of water vapour) Evaporation of liquid water from a pan: No lid: water molecules escape from pan to atmosphere (evaporation) Add a lid: • escaping water molecules collide on lid and return to surface; collision rate measures PH2O • eventually, flux escaping = flux returning : saturation (PH2O,SAT) • cloud formation in atmosphere requires PH2O > PH2O,SAT •T e PH2O,SAT Slide courtesy Colette Heald CLAUSIUS-CLAPEYRON EQUATION PH 2O , SAT 1 1 A exp[ B( )] T0 T A = 6.11 hPa (= Pvap at 0C) B = 5310 K To = 273 K PH2O,SAT (hPa) Vapour pressure increases sharply with temperature, due to the large latent heat. T (K) Slide courtesy Colette Heald PHASE DIAGRAM FOR WATER gas-liquid metastable equilibrium RH (%) 100 PH 2O PH 2O,sat (T ) triple point of water (n=0) Dew point: Temperature Td such that PH2O = PH2O,SAT(Td) Slide courtesy Colette Heald RUNAWAY GREENHOUSE EFFECT ON VENUS due to accumulation of water vapor from volcanic outgassing early in its history …did not happen on Earth because farther from Sun; as water accumulated it reached saturation and precipitated, forming the oceans EARTH Slide courtesy Colette Heald VENUS REGIONS OF THE ATMOSPHERE Troposphere: • generally homogeneous, characterized by strong mixing • decreasing T with increasing altitude from heat-radiating surface • near surface boundary layer exists (over the oceans ~1km depth), BL often cloud topped and can trap emissions Tropopause: • serves as a “barrier” that causes water vapor to condense to ice • “tropopause folding” where strat air intrudes into lower levels exchange mechanism Stratosphere: • increasing T with altitude due to OZONE causing heating from absorption of UV Mesosphere: • absence of high levels of radiation absorbing species and thus a T decrease • upper mesosphere and higher defines the exosphere from which molecules and ions can escape the atmosphere Thermosphere: • rarified gases reach temperatures as high as 1200C by absorption of high energy radiation VERTICAL PROFILES OF PRESSURE AND TEMPERATURE Mean values for 30oN, March Stratopause Tropopause Pressure is the weight exerted by the overlying atmosphere: P F A N units : 2 Pa m Average sea-level pressure (SLP): ≡101.325 kPa ≡1 atm ≡1.013 25 bar ≡1013.25 millibars (mbar, mb) or hectopascals (hPa) ≈760.001 mm-Hg, 0 °C ≡760 torr ≈1033.227 cm–H2O, 4 °C ≈14.695 948 psi MASS ma OF THE ATMOSPHERE P=F/A Mean pressure at Earth's surface: 984 hPa Radius of Earth: 6378 km ma 4R 2 PSurface g 5.129 10 kg 18 g = gravitational acceleration = 9.80665 m/s2 Total number of moles of air in atmosphere: ma Na 1.8 1020 moles Ma Mol. wt. of air: 29 g mole-1 = .029 kg mole-1 PRESSURE-GRADIENT FORCE Fp = [P(z)-P(z+dz)]A Fg = mg P(z+dz) P(z) Low Pressure High Pressure slab of surface area A Pressure gradient force goes from high to low pressure BAROMETRIC LAW (variation of pressure with altitude) • Consider elementary slab of atmosphere: P(z+dz) P(z) [ P( z ) P( z dz )] A r a gAdz unit area PM a ra RT Ideal gas law: dP Mag dz P RT dP ra g dz hydrostatic equation Assume T = constant, integrate: P( z ) P(0)e z / H RT with scale height H 7.4 km (T 250 K) Mag Barometric law na ( z ) na (0)e z / H Ma= .02897 kg/mole At high altitudes (low P) the mean free path is >> than mfp at sea level (e.g., 106 cm at 500 km; 10-6 cm at sea level) Source: Ahrens, Meteorology Today How (where) are species transported in the atmosphere? Planetary boundary layer (PBL) is the zone influenced by frictional drag at the surface • lowest ~500 m of the atmosphere • important zone for urban air pollution •Includes semipermanent high and low pressure areas that reside over oceans & continents •Affects pollutant long-range transport •Includes migratory high and low pressure fronts •Affects urban and regional pollutant transport •Examples: meandering & dispersion of chimney plume, flows around a building http://apollo.lsc.vsc.edu/classes/met130/notes/chapter9/scales.html idealized reality Idealized general circulation Midlatitudes: • westerlies caused by Coriolis force on winds moving across the subtropical latitudinal belts, and requirement of thermal wind balance (equator-to-pole T gradient) • at low levels, semistationary subtropical high P regions pump anti-cyclonically moving air into the midlatitudes • Coriolis force pushes air toward east, producing westerly flow Idealized general circulation Midlatitudes: • Thermal wind invigorates westerly flow at midlats, esp in the winter hemisphere (equator-to-pole T gradient largest) • in NH, higher T in subtropics imply higher P and anti-cyclonic motion; lower T at high lats imply lower P and cyclonic motion • converge at midlats -westerly flow strongthen -e.g. jet stream Westerlies play large role in re-distribution of anthropogenic emissions from NH mid-lats: jet stream disperses to all parts of hemisphere Idealized general circulation Idealized general circulation Tropics: • Hadley Cell moves warm, moist air upwards into the tropical upper atmospheres and transports it across latitudinal belts to higher lats in both hemispheres • Sustained by solar input to equatorial lats results in strong, persistent convection • winter hemisphere is most vigorous • Inter-tropical Convergence Zone (ITCZ) is a band of low P, migrates seasonally (NH summer: closer to Northern midlats; NH winter, closer to, but somewhat north of, equator) Idealized general circulation • Ferrel Cell is weaker - transports cold air upward near poles and Ferrel warm air downward near midlats (opposite of natural tendency) Hadley • Monsoonal flow occurs in lowlatitude regions around the globe due to T gradients bewteen land and sea (solar heating during summer) • drives moist flow from ocean to land - strong convective currents induced by hot land surface lift air -- precipitation • currents typically oriented north-south - strong localized cross-equatorial flow •Interact with other features of the general circ (e.g. E. Pac. SST) Side view Note how species might get mixed; mixing relatively slow between hemispheres Characteristic mixing times Lower stratosphere 2 years Troposphere 50 years 1 year Planetary boundary layer 1 month 1 hour Surface mixed layer of ocean, 10 hours POLE EQUATOR 1 year 2.5 years POLE Mixing time scales More detail on air motion Geostrophic Wind winds balanced by the Coriolis and Pressure Gradient forces An air parcel initially at rest will move from high pressure to low pressure because of the pressure gradient force (PGF). However, as that air parcel begins to move, it is deflected by the Coriolis force to the right of the wind velocity in the northern hemisphere (to the left on the southern hemisphere). This is an apparent horizontal deflection force arising from Earth’s rotation; max at poles, zero at Equator. As the wind gains speed, the deflection increases until the Coriolis force equals the pressure gradient force. At this point, the wind will be blowing parallel to the isobars (lines of constant pressure). When this happens, the wind is referred to as geostrophic. Northern hemisphere: blows with lower P to LEFT and higher P to RIGHT The diagram above shows the two forces balancing to produce the geostrophic wind. Winds in nature are rarely exactly geostrophic, but can be close, at altitudes above the PBL and away from low or high pressure centers. This is because winds are only considered truly geostrophic when the isobars are straight and there are no other forces acting on it. Vg= velocity of geostrophic wind f = Coriolis parameter rho = air density delta P = pressure difference between isobars d = spacing between isobars Gradient wind • Near high or low pressure centers, isobars are curved and centripetal acceleration is important. Resulting wind is termed the gradient wind. Line of constant pressure L Fp Fcor Vgradient L Fcentrifugal cyclone Cyclonic and anticyclonic flows Near the surface, the frictional force slows wind velocity - This decreases the Coriolis force (=f(windspeed)) - wind then turns toward low pressure until the frictional force is sufficient to account for the decreased Coriolis force - effect is strongest near surface (reason that wind direction rotates with height) L As as result, wind in cyclonic flow converges toward low, leading to rising motion in center. CYCLONES and ANTICYCLONES are transient waves, with periods of 3-7 days Cyclone: low-P center Divergence aloft; rising Air flows toward the center at the surface Produces cloudy, inclement weather Anticyclone: high-P center Convergence aloft; sinking (subsidence) Air flows outward from the center at the surface Produces sunny, dry conditions H Subsidence Inversion • Subsidence associated with high-pressure systems produces stable air aloft, which can trap pollutants near the surface • Covers hundreds of thousands of square kms and can persist for days • Los Angeles is at the eastern edge of the semi-permanent North Pacific ant-cyclone – frequently experiences pollutant trapping from subsidence • Short-lived anticyclones can lead to episodic pollution trapping in affected areas More detail on Earth’s energy budget Earth’s Energy Balance Sunlight (Shortwave, visible radiation) 235 Watts per square meter (W/m2) Perturbations to energy balance are known as “radiative forcings” 45 Heat (Longwave, infrared radiation) 235 Watts per square meter (W/m2) Global energy budget 350-195 = 155+67+24+78 = 324 Extra stuff (mostly from Prof. Heald, and in Jacob text) Chapter 2. ATMOSPHERIC PRESSURE “SEA LEVEL” PRESSURE MAP http://weather.unisys.com SEA-LEVEL PRESSURE CAN’T VARY OVER MORE THAN A NARROW RANGE: 1013 ± 50 hPa Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz: P(x) P(x+dx) dF ( P( x) P( x dx))dydz 1 P Acceleration r x Pressure-gradient force Vertical area dydz For DP = 10 hPa over Dx = 100 km, ~ 10-2 m s-2 a 100 km/hr wind in 1 h! Effect of wind is to transport air to area of lower pressure a dampen DP On mountains, however, the surface pressure is lower, as the pressure-gradient force along the Earth surface is balanced by gravity: P(z+Dz) P-gradient gravity P(z) aThis is why weather maps show “sea level” isobars; a The fictitious “sea-level” pressure at a mountainous site assumes an isothermal air column to be present between the surface and sea level (at T of surface site) BAROMETRIC LAW: THE SEA-BREEZE EFFECT reminder : H RT Mag ~1 km ~10 km VERTICAL TRANSPORT: BUOYANCY Imagine object of same density as fluid: P-gradient r r' z+Dz Fluid (r’) FP FG r 'Vg Object (r) z Gravity Now look at force imbalance when density of object differs from surrounding fluid: rr FB FP FG r 'Vg rVg B r ' r g r If object is lighter than fluid accelerate upwards Note: Barometric law assumed a neutrally buoyant atmosphere with T = T’ T T ' r r ' buoyant acceleration