Physics of the Atmosphere Physik der Atmosphäre WS 2014/15 Ulrich Platt Institut f. Umweltphysik SR 108/110 , INF 229, Mi, 09:15 - 10:45 Übungen zur Atmosphärenphysik (MVEnv1.2) SR 108/110, INF 229, Mi, 11:00 - 12:00 [email protected] Last Week • The Navier-Stokes Equation describes the conservation of momentum in fluids • Frontal zones and fronts are an important phenomenon in the Earth‘s atmosphere • Fronts are strongly tilted Formula of Margules • High- and low pressure systems form in the descending and ascending branch of baroclinc waves Contents 15.10.2014 Introduction – Literature, Structure of the atmosphere 22.10.2014 Atmospheric Radiation: Basics, Scattering 29.10.2014 Atmospheric radiation: Energy budget of the atmosphere - Climate 5.11.2014 Global circulation (Fronts, Rossby Waves) 12.11.2014 The Atmospheric Boundary Layer 19.11.2014 The Global Hydrological Cycle 26.11.2014 The Carbon Cycle 3.12.2014 Atmospheric Aerosol 10.12.2014 Gas-Phase Chemistry: Reaction Kinetics 17.12.2014 Ozone and Free Radicals 14.01.2015 Nitrogen, Sulfur, and Halogen Cycles 21.01.2015 The Stratosphere: Physics (Radiation and Circulation) 28.01.2015 The Stratosphere: Chemistry – 1 (Chapman Cycle + Extensions) 4.02.2015 11.02.2015 The Stratosphere: Chemistry – 2 (Ozone Hole) Measurement Techniques for Atmospheric Composition Characterisation of the Planetary Boundary Layer (PBL) • General definition of the PBL: The layer which is influenced by surface friction In this layer the shear stress τ is nearly constant with altitude • The PBL is the part of the atmosphere which is in direct contact to the • • • • • Earth‘s (or ocean) surface Here the exchange of scalar and vectorial tracers (heat, momentum, gases) between surface and atmosphere occurs The lowermost layer (thickness in the order of mm) is governed by molecular diffusion Molecular-viscous layer Above the molecular-viscous layer, turbulence is the dominant transport process Size of turbulent „eddies“ increases with altitude Questions: What is the flux from the surface to the free atmosphere above the PBL? How does it depend on: – Shear stress – Temperature profile and vertical stability (vertical temperature gradient) – Surface roughness Boundary Layer in a Wind Tunnel Seeds Dispersed in Olive Oil http://efd.safl.umn.edu/research/wind_tunnel/ Boundary Layer on the Wing of an Aircraft Evolution of the Atmospheric Boundary Layer The Structure of the Planetary Boundary Layer Classification by shear stress: 104 Free atmosphere 0 103 z [m] • Molecular-viscous layer (z ~ mm): – v(z=0) = 0 – τ = -ρ ∂vx/ ∂z ≡ const • Prandtl layer (z~10-100 m): – τ = -ρ K ∂vx/ ∂z = -ρ u*2 ≡ const; K = K(z) • Ekman layer (z ~ 1 km): – τ linearly decreasing with altitude, change in wind direction • Free atmosphere (z > 1 km): – τ≈0 Ekman - layer 102 101 100 Prandtl - layer const 0 10-1 10-2 10-3 Molecular – viscous layer Planetary Boundary Layer Wind Profile in the PBL (1) low p • Fp In the free atmosphere (free of friction), the wind is geostrophic (i.e., parallel to isobars due to the vg balance between pressure gradient and Coriolis force) • high p low p Close to the surface, friction will cause a FC Fp vr deviation of the wind direction from geostrophic solution (flow from high to low pressure) FR vg high p FC • Consequences: – wind speed increases with altitude – wind direction canges with altitude 165 m 330 m 500 m 0 m in form of a spiral, the so-called Ekman Spiral 750 m 950 m V g e o s tro p h is ch Wind Profile in the PBL (2) Close to the surface friction reduces the wind speed to levels well below the geostrophic speed vg. Since (Fc v) the influence of the Coriolis force is reduced. The direction of the friction force is opposite to the direction of the wind the, therefore close to the ground the wind will turn into the direction of the pressure gradient. FC A FP FR v FF B FC C FC FP v FF FC FP v FC A) Close to the ground the friction force is relatively large, v points approximately in the direction of pressure gradient force. B) In intermediate altitudes there is already a considerable angle between FP and v. C) In the geostrophic case (at several 100 m altitude) the friction force can be neglected and FC is anti parallel to FP. The air parcel moves at right angle to the pressure gradient force. Vertical Wind Profile in the Boundary Layer - Neutral Conditions Very close to the surface the wind velocity is determined by molecular friction (kinematic viscosity υ), the velocity profile is linear. Shear Stress: xz dv x dv x const dz dz Inspecting the dimension of the expression we find that (Velocity)2 2 2 N dv x kg m kgm kg m m kg m 3 2 2 2 2 3 2 3 dz m s s m m s m m s s m v2 2 xz Calling this velocity „Friction Velocity“ u* we may write: xz dv x u *2 const u * dz 2 dv x dv u u2* x * v x (z) dz dz const z dv 0 x dz dz z u2* 0 dz u2* z How to Measure the Shear Stress No Wind Wind force Turbulence near the Surface From z few mm turbulence sets in: In the turbulent regime we set: xz dv x K z u *2 dz 2 vx z 5 m Re z 1000, 1.5 10 s 5 3 103 Re 0.003m 1000 5 1.5 10 Laminar regime for comparison: xz dv x dz The “Turbulent Diffusion Constant” Kz=Kz(z) will certainly increase with height, since close to the surface only small eddies can exist (c.f. Kolmogorow – theory). We thus assume: K z z u* z with 0.4 von Kármán constant Laminar regime for comparison: const. Vertical Wind Profile in the Boundary Layer - 2 Vertical wind velocity – profile: dv x u*2 u*2 u* dz K z u* z z After integration we obtain vx(z) under the assumption that τ = ρ u*2 = const: log. profile transition region z u* u* z v x ( z) dz ln z z0 z0 with the Roughness Parameter z0 depending on the surface properties. For aerodynamically smooth surfaces, z0 is given by z0 ≈ υ/9u* linear profile Vertical Wind Profile in the Boundary Layer - 3 • Usually the surface wind is driven by the wind in the free atmosphere • Assume that the velocity vr(zr) at a refererence altitude zr is known (e.g., geostrophic wind) • Thus we have: u * zr u* z v r ( zr ) ln and v x ( z) ln z0 z0 • With u* = const this yields: ln z / z 0 v ( z) v r ln zr / z 0 Wind Profiles for Different Surface Roughness Rough surfaces: 1) Earth surface no longer reference height Zero Point displacement d 2) Interpret integration constant as „Roughness Parameter“ z0 u* z d v z ln z 0 Surface z0 /mm snow 0.1 - 1 grass 1 - 10 cereals 50 - 100 forest 500-1000 city 1000-5000 z0=10-2 mm z0=1 mm z0=100 mm Transition of Wind Profiles Change of vertical wind profile at the boundary rough smooth surface rough smooth • An ‚inner boundary layer‘ forms as a transition between both wind profiles • The upward propagation of this inner boundary can be described by turbulent diffusion • Height of boundary given by implicit equation (see Roedel): x ( x) const ln ( x) z0 The non-neutral PBL • For the neutral PBL, measurement of wind profile is sufficient for a complete description of dynamics • This is not valid anymore if the PBL is – Unstable: increased vertical exchange, larger diffusion coefficients, smaller gradients – Stable: reduced vertical exchange, stronger gradients, eventually (during strong inversions) complete surpression of turbulent mixing • In these cases, the buoancy of air parcels in relation to shear forces needs to be considered Influence of Water Vapour on Vertical Stability • So far, we have only considered the release of latent heat on vertical stability • Even without condensation water vapour also influences vertical stability because moist air is less dense than dry air • Ratio of molar masses of air and water vapour: M air 1.61 Mw • Density fluctuations under consideration of water vapour with density ρw: M air d d ' ' ' w ' 1 d d w MW ' w ' 0.61 ' w Influence of Water Vapour on Vertical Stability • The density fluctuations of moist air lead to energy production due to buoyancy forces: A g ' v ' z g ' v ' z 0.61 ' w v ' z • The first term in brackets describes the flux of sensible heat, for which we had already inferred H ' v 'z cp • The last term in brackets describes the turbulent flux of latent heat with the evaporation heat L: Hl ' w v ' z L • Thus the turbulent energy production rate becomes H Hl A g ' v ' z 0.61 c L p • • Over land: Hl ≈ H, contribution of water vapour to production of turbulent energy only several percent Over ocean: Hl ≈ 9H, contribution of water vapour to production of turbulent energy similar to contribution of thermal convection Transport of Trace Species in the Atmospheric Boundary Layer Trace Gas Flux JC: J C K z D JC dc K z D dz dc dz Integration and Division by JC yields: z2 c z 2 c z1 R12 JC dz z K z D 1 where R12 denotes the transfer resistance for trace gas transport between the altitude levels z2, z1. Its reciprocal is the transfer velocity: 1/R12 = v12 (or „piston velocity“) Transfer resistances are additive: z2 z 3 dz dz R12 R23 K z D z2 K z D z1 z3 dz z K z D R13 1 The Trace Gas Profile The trace species –Vertical profile at a given (height independent) vertical flux of the trace species JC : At sufficient distance from the ground (at neutral layering) we have: K = u*z + D u*z z2 c z 2 c z1 z 2 dz dz JC z 2 JC JC ln u z u* z 1 K z D z1 z1 * thus c(z) ln(z) The transfer resistance R12 between two altitude layers (z1, z2): R12 c z 2 c z1 JC z2 ln z1 u* The Transfer Resistance R10, 100 R1, 10 R0.1, 1 Each decade in z (0.1 – 1m, 1m – 10m, ...) represents the same resistance for the trace species. Thus Rges = ? R0.01, 0.1 R0.001, 0.01 Rlaminar RG Flux Measurements 1) Determine Transfer resistance from: R10, 100 R1, 10 c(z2) v(z2) c(z1) v(z1) R0.1, 1 R0.01, 0.1 z ln 2 c z 2 c z1 z R12 1 JC u* v ( z1 ) v ( z 2 ) 2) Calculate flux: c z 2 c z1 c JC R12 R12 R0.001, 0.01 Rlaminar RG u * z2 v ( z1 ) v ( z 2 ) ln u* z1 z2 ln z1 u* c z2 ln z1 v ( z1 ) v ( z 2 ) 2 z2 ln z1 z ln 2 z1 c v ( z1 ) v ( z 2 ) 2 z2 ln z1 2 c Vertical Flux – Example: NO2 C. Volpe Horii, J.W. Munger, and S.C. Wofsy, M. Zahniser, D. Nelson, and J. B. McManus (2004), Fluxes of nitrogen oxides over a temperate deciduous forest, J. Geophys. Res. 109, D08305, doi:10.1029/2003JD004326. Gas Exchange Atmosphere - Ocean Basic Gas Flux Equation Gas Flux (outward is positive): F = kL (Cl - Cg) kL: Cl: Cg: : Gas transfer velocity, also called piston velocity, gas exchange coefficient or deposition velocity. kL = 1/RL Concentration in water near the surface Concentration in air near the surface Solubility of the gas in water (Cl/Cg)equilibrium Time Scale considerations: - Characteristic time scale of gas transfer ( = h/k) is on order of weeks - Forcing function change on order of hours. In order to quantify gas fluxes on a regional or global scale we must have synoptic and co-located estimates of gas concentrations and forcing function. Conceptual view of air-sea gas exchange of inert gases Rick Wanninkhof Basic Conceptual Model Gas Phase: F= kg(Csg-Cg) Cg Csg Csl Cl Csg=Csl Water Phase: F=kl(Cl-Csl) Conceptual view of air-sea gas exchange of inert gases Rick Wanninkhof Air/water Resistance Magnitude of typical Ostwald solubility coefficients: He ≈ 0.01 O2 ≈ 0.03 CO2 ≈ 0.7 DMS ≈ 10 CH3Br ≈ 10 PCB's ≈ 100-1000 H2O ≈ ∞ Water side resistance Air and water side resistance of importance Air side resistance Conceptual view of air-sea gas exchange of inert gases Rick Wanninkhof Global CO2 Budget 1990-2000 (PgC a-1) Fossil Emissions +6.3 ± 0.4 Atmospheric Increase +3.1 ± 0.1 Ocean -1.9 ± 0.7 Net Land -1.2 ± 0.8 Emissions from Changes in Land Use +0.5 - +3.0 Residue ("Missing Sink") -0.9 - -5.0 Positive values: flux into atmosphere IPCC-TAR, Prentice et al., 2001 Oceanic Carbon Cycle Transport Mechanisms: • Advection and mixing through ocean currents (“Solubility Pump”) Marine biological “pumps”: • Organic carbon • Carbonates ‘AEOLOTRON’ – The Heidelberg Wind-Wave Facility circular wind-wave flume Institute of Environmental Physics, University of Heidelberg: • Diameter: 10 m (Perimeter: 29.2 m) • Width: 0.6 m B. Jähne, • Height: 2.4 m M. Schmidt. R. Rocholz • Water depth: 1.2 m (2005), 2 • Surface area: 18.4 m • Water volume: 21000 l • Wind speed up to 14 m/s • • • • • • Thermal imaging: passive und active, spectroscopy Fourier-Transform-Spectroscopy ( FTIR ) Gas Chromatography ( He, H2 ) Mass balance methods ( CO2, CH4, F12, N2O ) Wind waves (slope) Water- and wind current, temperature, humidity Setup for the Wave State Measurement at the AELOTRON Imaging Slope / Height Gauge digital image processing wave state: slope refraction at the surface height absorption in the water body area extended light source B. Jähne, M. Schmidt and R. Rocholz (2005), Combined optical slope/height measurements of short wind waves: principle and calibration, Meas. Sci. Technol. 16,1937-1944. B. Jähne, M. Schmidt. R. Rocholz (2005), Measures of the Wave State y x water surface reconstruction slope in x S= y/x • slope saturation spectra: slope in y plus height information • surface roughness • <s2> as a better parameter for gas transfer velocities Parameters influencing air sea gas exchange B. Jähne, M. Schmidt. R. Rocholz (2005), wind turbulence wind waves bubbles surfactants in order to improve the parameterizations and the models of gas exchange, the different transport mechanisms have to be understood in detail and quantitatively measured. Scaling Parameters of Transport Processes Across the Sea-Surface Microlayer flux scale F m k C s vertical space z D k scale Typical microlayer thickness: ~ 20 – 200 m for diffusive sublayer (gas) ~ 400 m – 2 mm thermal sublayer (heat) ~ 0.5 – 5 mm viscous sublayer (momentum) time scale z D t 2 k k All concepts (transport models, scaling, parameters) apply for transport of momentum, heat, and mass due to similarity of transport equations B. Jähne, M. Schmidt. R. Rocholz (2005), experimentally extreme difficult (e.g. wavy surface) typical time scale: 0.1 – 10 sec Parameterizations of the gas transfer velocity Wanninkhof, [1992]: Wanninkhof & McGillis, [1999]: Nightingale, [2000]: Quadratic fit of natural 14C disequilibrium and bomb 14C inventory methods. Cubic fit for transfer rates GASEX 1998 CO2 covariance methods. Best fit (quadratic) to North Sea 92, 93, Georges Banks 97, 98 data, 3He/SF deliberate tracer studies. 6 Parameterizations versus measurements Wind speed is not the only parameter influencing air-sea gas transfer: • Transfer rate is correlated with mean square slope of short wind waves, e.g. in [Jähne, 1980] • Surface films lead to strong decrease in transfer rate, e.g. in [Frew et al., 1990] • Fetch conditions have to be taken into account to infer from the wind speed to the sea state e.g. in [Woolf, 2005] • Bubble mediated transport: air entrainment due to wave breaking, e.g. in [Woolf, 1987] Global Air – Sea Flux of CO2 Estimation of the global exchange rate between ocean and atmosphere utilizing radar backscatter Cooperation with D. M. Glover, N. M. Frew, and S. J. McCue, Woods Hole Oceanographic Institution, Woods Hole, MA, USA: “Estimating regional and global air-sea gas exchange rates using the dual-frequency TOPEX and JASON-1 altimeters” Estimation of the Global gas transfer velocity based on parameterization with mean square slope of short wind waves. Summary • • • • The planetary boundary layer is the layer where surface friction has an impact (τ ≠ 0). It can be subdivided into different regimes: – Molecular-viscous layer governed by molecular diffusion – Prandl- layer, where shear stress is constant with altitude – Ekman- layer, where shear stress decreases with altitude (until it is zero in the free atmosphere) Basic assumption: Turbulent diffusion coefficient is proportional to altitude Logarithmic wind profile Water vapour has an impact on vertical stability not only due to the release of latent heat, but also due to its lower density The transport of scalar tracers in the boundary layer can be parameterised with the transfer resistance R or the piston velocity v12: z2 R 12 z1 • • • dz z) K( or v 12 1 R 12 In the turbulent regime, the transfer resistance is proportional to the logarithmic ratio of the altitude difference Air/sea gas exchange is a very important issue in the chemistry and climate of the atmosphere (how much anthropogenic CO2 is taken up by the oceans?) It can be investigated using wind-wave facilities, such as the Aelotron at the IUP The non-neutral PBL Bouyant forces • Buoyant forces Fb due to turbulence are caused by density fluctuations: ' and thus Fb ' g and dW g ' dz ' • Thus the turbulent power density (per volume) due to buoancy is: dW dz ' A g ' g ' v ' z dt dt • Density fluctuations are caused by: – Temperature fluctuations – Fluctuations in water vapour content (due to the smaller density of moist air, not due to the release of latent heat!) The non-neutral PBL Bouyant forces • Express density fluctuations as fluctuations of the potential temperature ' • Since ρ = const/θ , we have ' • Thus the turbulent power density becomes: g ' v ' z gH A g ' v ' z cp with the turbulent heat flux: H cp ' v 'z The non-neutral PBL Shear stress • Work done due to shear stress per unit area is dW = τ dx • Thus the power per unit area (= Energy flux) is dW dx v x u*2 v x dt dt • The negative divergence of the energy flux yields the power (energy production) per volume due to shear stress: d2 W 2 dv x s u* dt dz dz The non-neutral PBL Shear stress • For neutral conditions, we had (logarithmic wind profile) dv x u* dz z • For the general case of non-neutral conditions, a correction function Φ(H, u*, z) is introduced: dv x u* (H, u* , z) dz z with current gradient of wind velocity (H, u* , z) gradient of wind velocity for neutral conditions • Thus the energy production due to shear stress becomes: 3 dv u s u*2 x * (H, u* , z) dz z The non-neutral PBL Richardson Number and Monin-Obuchow Length • The Flux-Richardson number is defined as the negative ratio of energy production rates due to thermal forces and due to shear stress: A Rf s • Sign of Rf: – Rf > 0 for stable conditions – Rf = 0 for neutral conditions – Rf < 0 for labile conditions • It has been shown empirically that Rf and Φ only depend on altitiude z and a scale length called Monin-Obuchow Length L*: z Rf L * (z / L * ) • L* is (in first approximation) independent from altitude Monin-Obuchow length as a function of 10 m wind speed and turbulent heat flux The non-neutral PBL Richardson Number • The Flux-Richardson number is (or rather was) difficult to measure (simultaneous measurement of heat flux and shear stress). • A quantity more easy to measure (only temperature and wind speed profile necessary) is the Richardson-Number, given by Ri g d / dz dv x / dz 2 • The Richardson-Number is related to the Flux-Richardson number vial the ratio of turbulent diffusion coefficients for heat and momentum, KH and K, respectively: RF Ri KH K Labile Stable The non-neutral PBL Richardson Number as a Funciton of z/L* The non-neutral PBL Turbulent Diffusion Coefficient • The diffusion coefficient for momentum can be obtained from the definition of shear stress u 2* dv x K dz and the vertical wind profile: dv x u * (z / L * ) dz z yielding: u*z K (z / L * ) Labile Stable Characterisation of Vertical Exchange Convective Energy Produktion Rate A Turbulent Heat Flux H Monin-Obuchow-Length L* Richardson-Number Rf, Ri Stratification stable neutral labile 0 + 0 + + + 0 -

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