ATMOSPHERIC CHEMISTRY CHEM 5151
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This 19 page Class Notes was uploaded by Guiseppe Bednar on Friday October 30, 2015. The Class Notes belongs to CHEM 5151 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/232188/chem-5151-university-of-colorado-at-boulder in Chemistry at University of Colorado at Boulder.
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Date Created: 10/30/15
Lecuue4ChmnkmlTnnmpo in thcrAnnnosphcre Suggested Reading SP Chapter I 7 Atmospheric ChemistIy CHEM5151 ATOC5151 Spring 2005 Prof Brian Toon PAOS The Aerosol Continuity Eguation A transgort The change in the concentration of a chemical often can be written ngP LC amp Here L is the loss rate P is the production rate and C is the species concentration per unit volume How do we account for the effects oftransport on C An observer standing at a fixed point in space measures changing concentrations d d The observer must account for the chemical sources and sinks as well as forthe Al U A I 7 motion ofthe air This is u u M called an Eulerian measurement since it is at a wind Mum point AW i Wmammm The flux of material into the upwind side of the box is chu particles per cm2 per sec The total number of particles being added per second is UuCudydz particles per second where dydz is the area of the open face of the box Therefore considering that material is also leaving the box on the downwind side the total amount of material added to the box per second divided by the volume of the box so that we have the particles added cm393 squot is chu 7 Ucdx idUCdx Considering all three directions and adding the sources and sinks we arrive at the flux form of the continuity equation g dUC dvclc iwq 7 PLC d aquot 6 amp This is often called the total derivative in d CP7LC dt Example of flux based Eulerian transport oAssume the wind speed is U10 kmhI p constant at 10 km hrquot oAssume the concentration declines by 1012 molecules cm393 km1 in the wind 1 km direction lt gt oAssume the concentration I 10 mol cm 3 hrquot declines by 1013 molecules cm393 hr391 due to a chemical sink 1013 mol cm 3 9x1012 mol cm 3 The rate of change in the concentration at the fixed downwind position is km 9X1012 710 mol ac 7 R W 1 EH 710 3mF01410 Hence in this example the advection by the wind completely masks the ongoing chemical loss of the material The Lagrangian form of the continuity equation n observer moving with the 1U U A d wind so that the same air parcel is always observed only has to account for physical and chemical changes within the air parcel and not for air motions to understand how the mixing k LL ratio varies The Lagrangian form of the continuity equation Since neither air molecules nor the species being observed can be lost from within the parcel the ratio of the species concentration to the air density is not changed no matter how winds distort the volume of the air parcel P LCp dC p dt NOAANESDIS EDGE IMAGE DISPLAY O 57 LAT lQQKM GLOBAL ANALYSIS NCAA16 18 l79 LON ESESQS 666 651563 Zlm 169 HOURS A view of aerosol transport There were large res in Russia prior to this time period and dust storms in Africa Can you tell the source and sink regions just by glancing at the distributions and knowing the Winds 1 Transport of forest re smoke in July 2002 from V Seawifs fov sulfuric acid nucleation n the stratosphere Evidence i No sun and Rosen wing ratios can identify GRL 2 l3 l985 source and smk regions a kelalsaiener 27a 1650 1555 urns The diffusion approximation in the continuity equation Brownian Diffusion occurs due to the relative random es motions of air molecu The Brownian diffusion equation can be derived from THE KINETIC THEORY OF GASES equations similar to those from Brownian diffusion Thnrnfnrn r theory which is referred to as eddy diffusion I a circulation Still it is widely used The diffusive flux in analogy to thermodynamics is pKX There is no diffusive flux if the mixing ratio is independent of location The diffusive flux is often referred to as being quotdown the gradientquot which means diffusion causes a positive flux in the direction of decreasing mixing ratio oHence diffusion produces a uniform mixing ratio by transporting material from regions where the mixing ratio is high into regions where the mixing ratio is low 100 Altitude km The diffusion coefficient 2 10 3 10 4 10 5 2 0 Diffusion Coef cient cm s39 A typical eddy diffusion coefficient used in one dimensional models of the atmosphere The Brownian diffusion coefficient is much smaller than the eddy diffusion coefficient below 100 km Three views of transport Example descent into the polar vortex During polar night air descends from the mesopause into the lower stratosphere How can we think about this process 1 The Eulerian view 29km 27km Polar v ottex WCtop lt95 27 km 25 km South pole WCbottom WCtopgt WCbottom Three views of transport 2 the Lagrangian View dP1mbar 39 50 km dz10km 418mb dP1mbar dz15 km Ambar dP1mbar dz 300m Three views of transport 3 The diffusion view 50m Ozone ang muo Aa osol Mxxmg muo 50km 25km The ADVANTAGE OF THE DIFFUSION EQUATION IS THAT IT CAN BE SOLVED RELATIVELY EASILY CONSIDER THE FOLLOWING SIMPLE TRANSPORT AND CHEMISTRY PROBLEM 1 ASSUME THAT THE CONCENTRATION OF A MATERIAL IS HELD CONSTANT AT THE SURFACE 2 ASSUME THAT VERTICAL TRANSPORT BY EDDY DIFFUSION ACTS AGAINST A CONSTANT ALTITUDE INDEPENDENT CHEMICAL LOSS RATE 3 THE STEADY STATE EQUATION TO BE SOLVED IS a C WKZM 5ZZLC 0 2 The LOSS RATE IS THE INVERSE OF THE CHEMICAL LIFETIME QUL The AIR DENSITY IS A SIMPLE FUNCTION OF ALTITUDE IF THE ATMOSPHERE IS ISOTHERMAL Z 2 ex p p0 p H SO WE CAN REWRITE THE EQUATION AS 520 1 ac C 03922 H z KT THE SOLUTION TO THE EQUATION IS C Co 1 E Z ip Uexp H 025KTE 05 The chemical time constant appears in a ratio with another time constant for vertical transport H2 K Z Td The dynamical lifetime 1d H2KZ for several fixed values of diffusion coefficient and for a typical altitude dependent diffusion coefficient 100 80 4cm2571103cm251 60 40 VariableK 20 0 I I 2 001 01 1 10 10 Dynamics time constantyrs The vertical variation of the mixing ratio assuming a unit mixing ratio at the surface for simplicity for various values of the ratio of the chemical lifetime to the dynamical lifetime When the chemical lifetime is m l 100 times larger than 1 dynamical lifetime materials I i will have an almost constant mixing ratio to nearly 100 km altitude However when the chemical lifetime is 1 of the dynamical lifetime the mixing 39 ratio falls very rapidly in the 3 1 72 1039 1 troposphere mixing mm Numerical and analytical solutions of the diffusion Allmdz m eq atIon I and in x u n m x mm 1 Expunznml llamath m l l 39 j T quot39 Exwmnmlhfenme J Week I 39 mm ma 1 Solid redchemical lifetime is ten times the dynamical lifetime 2 Dotted black the chemical lifetime is held constant but the transport is done with the vertically varying diffusion coefficient 3 Green constant diffusion coefficient of 104 cm2 s4 but the chemical lifetime decrea Where H7 km ses exponentially with altitude using a scale height of 4H 4Dashed red the diffusion coefficient varies with altitude and the chemical lifetime decreases exponentially with altitude Material Atmospheric observations Lifetimes of some interesting materials Mb Abundance Tg Pb Source tn Lifetime Tgyr 1 3x107 5x105 0 025 5x103 515 10 5 2 i 2 4 3 o 670 9 200 003V 005 2 5x103 1221 120 6 2 o 25 5o 10 3 o 37 102 5 3 5 i 5 3 6 1300 o 003 METE OROL OGICAL T RACERS IT IS VERY USEFUL TO HAVE METEOROLOGICAL TRACERS SO THAT THE TH WHICH AIR PARCELS MOVE CAN BE lDENTIFIED CONSIDER THE FIRST LAW OF DYNAMICS REWRITTEN WITH THE IDEAL GAS LAW 1 dQ din T Raunp M dt T d1 IF WE CONSlDER ADIABATIC TRANSPORT IN WHICH NO HEATING OCCURS THEN WE CAN INTEGRATE THE TEMPERATURE OVER GET YIELDING R e T1000mm Mc P eIS CALLED THE POTENTIAL TEMPERATURE 1T ls TlE TEMPERATURE THAT AN A PARCEL WOULD HAVE IE IT WERE TAKEN ADIABATICALLY To A PRESSURE OF 1000 MBARS 9 IS A CON SERVED TRACER TAKING THE IDGAR ITHM B DIFFERENTIATlNG WITH RESPECT TO THVIE AND USING THE FIRST OF THERMODYNAMICS YIEIDS THE LAGRANGIAN FORM OF THE CONTINUITY EQUATION FOR THE POTENTIAL TENIPERATURE iidi dt c T dt eIS CONSERVED BY AIR PARCEIS WHICH DO NOT EXPERIENCE ANY EXTERNAL HEATlNG OVER SHORT TIME SCALES OFTEN SEVERAL DAYS EXTERNAL HEATlNG DUE TO TENIP T SURFA ES CAN BE OU39ND FROM ANALYSES OF T STRUCTURE 1ND ON THESE SURFACES CHEMISTRY SO THE RECOGNITION OF CONSTANT POTENTIAL TENIPERATURE SURFACES CONVERTS THE THREE CHEMICAL TRANSPORT eM39EASURES THE STABILITY OF THE ATMOSPHERE FROM THE FERST LAW OF THERMODYNAMICS AND THE CONT JNUITY EQUATION FOR 9 WE ET RT as d C dTr dPTC Q P M P e USING THE HYDROSTATIC EQUATION AND DIVIDJNG BY Csz 1de ldT RT7 dz 1 537 RTpg r Z Mp Cpsz M SD gt0 Stable dz d9 0 neutral dz d9 lt 0 unstable dz m s y Wm mm mummarl a w mm M m m w momW m POTENTIAL VORTICITY ANOTHER USEFUL METEOROIDGICAL TRACER IS POTENTIAL VORTICITY IT IS ANA IDGOUS TO ANGULAR MOMENTUM J 1R2 21 9 D w N THE POTENTIAL VORTICITY PV OBEYS 69 MW dg f 0 dt dt 39 IF THE FLOW IS ADIABATIC AND FRICTIONLESS IE DIFFUSION ISN T IMPORTANT DUE TO SMALL SCALE TRANSPORT SO PV AND 0 ARE CONSERVED UNDER THE SAME COND ITION S PV HAS UNITS OF K CM2 G39I S39I ae PV g f 0p sin 1 IS A MEASURE OF THE ROTATION OF AN AIR PARCEL DUE TO ITS LOCATION ON THE IT S IS THE VERTICAL COMPONENT OF THE RELATIVE VORTICITY OF THE FLUID A MEASURE OF THE MICROSCOPIC TENDENCY OF THE FLUID TO ROTATE DUE TO WINDS AND HAS UNITS OF S71 o 9 im giA gt0 A or gaxay U6xV 6x6y 7U 6y6er6y ay or Q Gr 0X IE U 5 gt 1 VJ R E lt gt I 5y THE FHVAL PART OF THE DEFHVITION OF POTENTIAL VORTICITV IS THE VERTICAL GRADIENT OF 0 THIS AS A MEASURE OF THE DEPTH OF THE FLUH EXAMPLE CONSIDER A UNIFORM NO GRADIHVTS HI THE HORIZONTAL DHIECTIONS WESTERLY FLOW OF AHI OVER A CHAHV OF MOUNTAINS HI THE NORTHERNHEMISPHERE H I i L E WI II OQP munJEs39cu rm c U SHVCE THE AHI FLOW IS ASSUNIED TO BE UNIFORNI HVITIALLY IT HAS NO RELATIVE VORTICITY PV WILL BE POSITIVE DUE TO THE COMOLIS TERM THE 9 SURFACE AT THE BASE OF THE FLOW MUST RISE AS THE AIR MOVES OVER THE MOUNTAHVS SO THE DEPTH OF THE FLUID IS DECREASED AND THE GRADIENT OF 0 WITH PRESSURE IS HVCREASED THUS THE CHANGE HI THE TERM HI PV HVVOLVING U WILL BE HI THE SENSE TO HVCREASE PV TO CONSERVE PV THE RELATIVE VORTICITY OF THE FLUID MUST BECOME NEGATIVE SO THAT IT CAN REMOVE SOME OF THE PV DUE TO THE CORIOLIS TERM FOR THE RELATIVE VORTICITY TO BECOME NEGATIVE THE AIR MUST TURN TOWARD THE SOUTH AS THE AIR LEAVES THE MOUNTAINS TH G OE BWILL DECREASE AS THE DEPTH OF THE AIR PARCEL INCREASES THEN THE AIR WILL SWING BACK TOWARD E NORTH H NCE CONSERVATION OE PV REQUIRES AN OSCILLATORY MOTION BE INDUCED AS AIR ELOWS OVER A MOUNTAIN RANGE SUCH OSCILLATIONS ARE SEEN ON DAILY WEATHER MAP WHERE AIR ELOWS OVER EXTENDED MOUNTAIN RANGES SUCH AS THE ROCKIES Ilmmn I II I HAde w I IIV NUIIIHIIHVNH W 11 wawmmau N W W lt quot397 I quotwequot vv 7 1 1 mo 7 5w cu Ionmm 1 unmqu 300 r war Imam m m w mu IN 1qu Pom Lanna m uummcm an In quumptmr uupmphm mm HIL39 impupumc H mm lw Ihr IImI um Iqu um m mumm m mm m mm Imupu um mm IIIthIII mum 4mm mum I I u Imm cumme In Impulm I Imn Kw mu k IIIImI u m IImInnm Inn yum uhcn Iwmnmn mIIIm pan 11quot unlmpmm I I HIc n um I I l L II M I musmImII mums Imc mmnupml pump I Im um ILIIIIIIEAIILndL d mum IIImu Imnqmu m mm mum 1mIIIILIIIIIIIIupImIIIppuI Impmmmm Imnglu ImI III I I anIcllmIIuII quotmumuuuc LIIImIprIlhInCIIIIIIIIgInIdxuIIIIvIAImIIII um I Igllu JI rm mum I mu Inc mu IHII an ImI mm u quot1me Im um JV wlIImcln hmm Iwu mmme In Ilw nlm may ImuIInmn mu I IImLn bx um IIKMI UPI39II pump WI39 IUII U H 39 39 39 39 HI39LUL KIN JIM k IIIlmL I III m unIInl m Iu I39II IM nmqumnI k wl urn 5 mIumw mum rIw IIIIIIr quot1 mm u mums m L MIDIInn 39 v I I I 5 I I I1 In u V39IIHIIWEHHII humAI HIIU Ilr IIm II L m II I Wm WM I llII ml quotI um I Iqu mm up In I Im In M Tracertracer plots are useful u I mm m
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