Atmospheric Structure I

Transcription

1 Atmospheric Structure I Required Reading: Jacob Chapter 2 Atmospheric Chemistry ATOC-5151 / CHEM-5151 Spring 2013 Prof. Jose-Luis Jimene 1 Review Questions 1. Oxygen has a constant mixing ratio in the atmosphere. How would you expect its number density in surface air to vary between day and night? 2. Give a rough order of magnitude for the number of molecules present in a typical 1 micrometer aerosol particle. 3. Does it make sense to talk about the mixing ratio of aerosol particles in air? To express the concentration of soot aerosol in units of ppbv? From Heald 2 1

2 Atmosphere is a thin planetary skin Radius = 6000 km Atm = 12 km Radius/atm = 500 Radius = 75 mm skin = 0.5 mm Radius/skin= 150 From Tolbert Atmosphere is locally flat For most practical purposes, lower atmosphere can be regarded as flat. Earth curvature only needs to be considered in very special cases. Earth does drag a veil of gas with itself ( exosphere ) with the sie of approximately 10,000 km, however it is extremely dilute. For reference, space km above the Earth surface Figure from Brasseur & Jacob 4 2

3 Atmospheric Pressure Measurement of atmospheric pressure with the mercury barometer: Atmospheric pressure P = P A = P B = Hg gh vacuum h A B Mean sea-level pressure: P = 1.013x10 5 Pa = 1013 hpa = 1013 mbar (mb) = bar = 1 atm = 760 mm Hg (Torr) From Jacob Sea Level Pressure Map Q1: is P in Boulder correct? A.Yes B. No C. It depends D. I don t know Q2: why is P variation relatively small? A. Because T is also small B. Because of storms C. Because of winds D. Because it is an El Niño year E. I don t know Adapted from Jacob 3

4 Sea-Level P can only vary over a narrow range Consider a pressure gradient at sea level operating on an elementary air parcel dxdyd: Vertical area dyd P(x) P(x+dx) Pressure-gradient force df ( P( x) P( xdx)) dyd Acceleration 1 dp dx For P = 10 hpa over x = 100 km, a ~ 10-2 m s km/h wind in 3 h! Effect of wind is to transport air to area of lower pressure and dampen P On mountains, however, the surface pressure is lower, and the pressure-gradient force along the Earth surface is balanced by gravity: P(+D) P-gradient gravity P() This is why weather maps show sea level isobars; The fictitious sea-level pressure at a mountain site assumes an air column to be present between the surface and sea level From Jacob Vertical Structure I Questions: Physical basis for P variation? Physical basis for T variation? 8 4

5 Vertical Structure II From Tolbert Troposphere: 0 15 km Greek tropo = turning Strong vertical motions (days/hrs) T decreases with altitude Air mostly transparent to visible radiation, not a lot of heating Sun heats surface: warm air below cold Creates buoyancy and convection Adapted from Tolbert 5

6 Stratosphere: km Latin stratus = layered Slow vertical mixing - years T increases w/ altitude, warm above cold Stable, temperature inversion From Tolbert CQ: Where is the tropopause higher? a. Tropics b. Poles c. About equal in both places d. Tropics in summer and poles in winter e. I don t know Adapted from Tolbert 6

7 Mesosphere: km Temperature drops off again This is where small meteors burn up shooting stars T increases w/ altitude, warm above cold Stable, temperature inversion From Tolbert Thermosphere: > 80 km Air is heated by absorption of x-rays Highly ionied This class: Troposphere and Stratosphere T increases w/ altitude, warm above cold Stable, temperature inversion From Tolbert 7

8 AS II: Pressure Variation Write force balance for slab From Jacob 15 AS II: Pressure Variation Solution Newton's gad [ P( ) P( d)] A dp g d From ideal gas law : PM a RT Combining these two we get : dp gm a d P RT Assuming that T and M are independent of : a P( ) P(0) e laws : H Hydrostatic equation RT where H is "scale height" gm a CQ: H in troposphere? A: 7 km B: 7 K/km C: 2 km D: 0.5 atm E: dunno Adapted from Nidkorodov 8

9 Atmospheric Structure II Required Reading: Jacob Chapter Atmospheric Chemistry ATOC-5151 / CHEM-5151 Spring 2013 Prof. Jose-Luis Jimene 17 Business Items Dr. Christoph Knote (NCAR) will teach lecture on simple models He is an atmospheric modeler Tricky conceptually, if you haven t done this before Do the reading before the lecture if you can, and especially if you are having issues with the simple models in the problems (e.g. Radon problem in HW2.2, pollution problem in HW3.7) HW programming notes Pay attention to conventions of the course, points shall be taken off for not following them If a problem requires doing the same calculation for several time steps, you need to reuse the same code. It is inefficient (esp. on your time) to e.g. write a separate routine or loop for each time step 18 9

10 Mass of the Atmosphere from force balance Radius of Earth: 6380 km Mean pressure at Earth's surface: 984 hpa m Total number of moles of air in atmosphere: N a 2 4 RPSurface g m a 20 a moles M a kg Mol. wt. of air: 29 g mole -1 = kg mole -1 Clicker Q: approx. number of moles in the mesosphere? A: 1.8 x B: 1.8 x C: 1.8 x D: 1.8 x E: I don t know The sea breee circulation From Jacob section

11 Vertical Profile of Temperature Mean values for 30 o N, March Radiative cooling (ch.7) -3 K km -1 Altitude, km + 2 K km -1 Radiative heating: O 3 + ho 2 + O O + O 2 + M O 3 +M heat Radiative cooling (ch.7) -6.5 K km -1 Expansion cooling Convective Transport & Latent heat release Surface heating Heating by Absorption In the absence of local heating, T decreases with height Exceptions: Stratosphere: Chapman Cycle (1930s) O 2 + hv 2O O + O 2 + M O 3 (+ heat) O + O 3 2O 2 O 3 + hv O + O 2 (+ heat) Q: what is heat at the molecular level? Mesosphere: absorption by N 2, O 2, atoms 22 11

12 Adiabatic Lapse Rate For adiabatically expanding gas: ncvdt (internal energy) PdV (work) where cv is molar heat capacity of air at constant V. Combining this with ideal gas law, where c p (rate of temperature decrease with altitude) PV nrt we get: dt RT dp c P p is molar heat capacity of air at constant P. dt RT dp MW g d d c P d c p is called "dry adiabatic lapse rate" p Clicker Q: What is the approx. lapse rate for Earth if C p for air is 29.1 J mole -1 K -1? A.10 K/km B.1 K/km C.0.01 K/m D.10 km/atm E.Don t know Adapted from Nidkorodov Atmospheric (Vertical) Stability I Adiabatic Lapse Rate () vertical temperature profile when air ascends or descends adiabatically, i.e. w/o giving or receiving heat For Earth, = 9.8 K km -1 Buoyancy force on an air parcel that has rapidly (adiabatically) ascended or descended: F b = g g Figure from Jacob s book 24 12

13 Atmospheric (Vertical) Stability II adiabatic Actual Inversion T Q: which of the following profiles are stable? Stable: a small vertical motion is damped (Unstable: it is amplified) A: 1 & 2 B: 2 C: 3 D: 2 & 3 E: I don t know F: All of the above T T 25 Dilution of Power Plant Plumes Question: which plume dispersion corresponds to each T profile? From Jacob s book (problem 4.1) 26 13

14 How does the Temperature Profile Evolve? An atmosphere left to evolve adiabatically from an initial state would eventually tend to neutral conditions (-dt/d = ) at equilibrium Solar heating of surface and radiative cooling from the atmosphere disrupts that equilibrium and produces an unstable atmosphere: ATM T ATM T initial final T Initial equilibrium state: - dt/d = G Solar heating of surface/radiative cooling of air: unstable atmosphere buoyant motions relax unstable atmosphere back towards dt/d = G Fast vertical mixing in an unstable atmosphere maintains the lapse rate to. Observation of -dt/d >= is sure indicator of an unstable atmosphere. From Jacob Temperature Inversions in the Troposphere Condition under which temperature increases with altitude (negative lapse rate) instead of decreasing. CONSEQUENCE Air in the inversion layer is not mixed efficiently, which results in local trapping of pollutants. Atmospheric Boundary Layer Air contained below the inversion layer, where mixing is rapid. This layer is directly affected by the surface. Air pollutants emitted on the ground rapidly distribute through the boundary layer and accumulate in the inversion layer. From Nidkorodov 14

15 Diurnal Ventilation of Urban Pollution PBL depth Subsidence inversion MIDDAY 1 km Mixing depth NIGHT 0 MORNING T NIGHT MORNING AFTERNOON Potential Temperature I Potential temperature,, is the temperature an air parcel would assume if it were adiabatically compressed from its initial pressure P to some reference pressure P 0 (usually 1 atm). If the adiabatic approximation applies, we have 1 1 T P constant P0 where P0 is reference pressure ( 1 atm) CP 7 γ CV 5 The quantity P P T T P P 0 0 USEFULNESS is known as the "potential temperature" Air parcels approximately conserves its potential temperature and tend to move along lines of constant. Air parcels with constant can be assumed to be well mixed In other words, potential temperature is a convenient indicator of atmospheric stability: Adapted from Nidkorodov 15

16 Stability w/ Potential Temperature adiabatic Actual Q: which of the following profiles are stable? Stable: a small vertical motion is damped (Unstable: it is amplified) A: 1 & 2 B: 2 C: 3 D: 2 & 3 E: I don t know F: All of the above 31 Potential Temperature III d dt MW g 0 when d d d c well mixed atmosphere p d 0 d poorly mixed atmosphere Clicker Q: An air parcel has a temperature of 10 C and a pressure of 650 mbar. Is this parcel likely to have the same composition as the air at the ground level below it? A. Yes B. Only partially C. It depends on additional info D. No way Jose E. E. I don t know Adapted from Nidkorodov. Fig. from Jacob 16

17 In Cloudy Air T Latent heat release as H 2 O condenses Cloud deepens W 2-7 K km -1 W RH 100% RH > 100%: Cloud forms Cloud forms Air parcel 9.8 K km -1 Clicker Q: Does the stability criterion that we discussed based on q apply to cloudy air? A. Yes B. Only partially C. It depends on additional info D. No E. I don t know Adapted from Jacob cloud boundary layer A picture to illustrate. Not the same place/time, but the same phenomenon Discuss: why do the clouds start where they do? why do they stop? Air is turbulent (cf. airplane take off and landing) below the cloud base and inside the cloud and usually smooth above why? Adapted from Jacob 17

18 Clouds and Subsidence Inversions FT PBL typically 2 km Very common, otherwise air would rise to tropopause, precipitating along the way. Lateral distance between the point of ascent and descent for the air mass can be as short as several kilometers and as large as thousands of kilometers. Subsidence over subtropical cities (LA, Mexico City, Athens, Sao Paulo) adds to pollution. FT = Free Troposphere From Jacob & Nidkorodov Species Variation? H() = RT()/(MW air * g) Dalton s law: each component behaves as if it was alone in the atmosphere H i () = RT()/(MW i * g) O 2 at lower altitudes than N 2? Some scientists: CFCs could not cause stratospheric O 3 depletion; too heavy to rise to stratosphere Q: What s wrong with that picture? 36 18

19 Heterosphere: Above 100 km Diffusion faster than turbulent fluid mixing Gravitation separation based on MW Homosphere: Turbulent fluid mixing faster than diffusion From Tolbert Persistence of Planetary Atmospheres Molecules in the high velocity tail of the Maxwell- Botmann distribution can escape the atmosphere The molecules are held back by the gravitational pull of the planet. The critical parameter is the ratio of their gravitational and thermal energy (r = planet radius; G = m 3 /(kg s 2 ) = gravitational constant; M = planet mass; m = mass of the molecule; k = Boltmann constant) Escape rate per unit area per second can be estimated as (n c = density at the critical level). This is known as the Jeans escape formula. Escape velocity is the ratio of the escape rate and the gas concentration p MaxBolt m m ( ) exp 2 kt 2kT Epotential GMm E rkt thermal n c Rate (1 ) 2 V escape e Rate (1 ) e n 2 c 2kT m Planet Exospheric Temperature (K) H V escape (cm/s) Has atmosphere? Uranus Yes Venus Yes Earth Yes Moon No Io No Solve in class: Calculate O and V escape for the oxygen atom on Earth. The mass of the Earth is kg, and its radius is 6371 km. Do a similar calculation for the Moon, M = kg, r = 1738 km) Earth answer: O = 100; V escape = 0.00 cm/s Moon answer: O = 13.9; V escape = 0.24 cm/s 19

20 Spatial and Temporal Scales From S&P Tight link between spatial & temporal scales 39 20