Diaba%c-Dynamical Interac%on in the General Circula%on (lecture 2 of BLT&M-2)

Transcription

1 Diaba%c-Dynamical Interac%on in the General Circula%on (lecture 2 of BLT&M-2) The seasonal cycle of atmospheric temperature, determined by radia%on only, as a func%on pressure, la%tude and %me Radia%ve equilibrium state vs. radia%ve determined state. Thermal iner%a Isentropic density Aarnout van Delden Schedule of the BLT&M May: Introduc;on to radia;ve transfer; grey gas ; radia;ve equilibrium study sec)ons 12.1 and 12.2 (Introduc)on to the course), sec)ons & boxes (1) problem 12.1 (response )me) May: Radia;vely determined state study sec)ons and (2) problem 12.3 (radia)ve equilibrium/determined isentropic density) 3. 1 June: Poten;al vor;city inversion. study chapter 7 (3) In couples choose one project from the following list. List of projects: Problems 7.1, 7.3, 10.2, 10.3, 11.5, 11.6, 11.7, 12.5, June: Radia;ve-dynamical interac;on, with and without the water cycle study sec)on (again!)) and sec)ons (4) Essay June: Role of eddy-heat (mass) and momentum (vor;city) fluxes in the general circula;on study chapters 10 and 11 (also box 1.13, Dynamical Meteorology) (5) problem 12.6 & 7 (what-if-?-thought-experiment) June: Radia;ve-dynamical interac;on, with the water cycle and wave drag study sec)on June: Wave drag as a manifesta;on of the consequences of meridional PV-mixing. study box June: Presenta;ons of the project-results (no exam). 9. Hand in essay on Friday 6 July at the latest. 1

2 Zonal mean temperature ERA-40 Warm summer stratosphere h\p:// Tropical cold trap Zonal mean zonal wind ERA-40 Summer hemisphere Westward winds in the summer stratosphere h\p:// Winter hemisphere Subtropical jets Stratospheric winter jet 2

3 What is the cause of these features of the general circula;on? Radia)on (greenhouse effect, ozone) Water cycle (evapora;on, condensa;on) Wave stress (short for influence of meridional transport of ) Last week: Radia%ve equilibrium: full solu%on Atmospheric temperature: T = T skin ( δ +1) 1/4 Surface temperature: T S = T skin ( δ S + 2) 1/4 δ = σ a q a p / g T skin Q 4 2σ Q 1 4 S 0( 1 α p) σ a = 0.3 m 2 kg -1 ; r a = 390 ppmv BOX 2.4 α p = 0.3; S 0 =1366 W m -2 ; p s =1000 hpa δ S =1.81 3

4 Calcula%ng daily average Solar irradiance The daily average Solar irradiance, Q (expressed in W m-2), is calculated according to 2 Q= S0! dm $ # & ( ΔH sin φ sin δ + cos φ cos δ sin ΔH ) π"d % S0 represents the solar constant (=1366 W m-2), dm is the average distance between the Sun and the Earth, d represents the actual distance between the Sun and the Earth, φ is la%tude, δ is the declina%on angle of the Sun and ΔH is the length of the day in radians Box 2.1 Orbital parameters dm is the average distance between the Sun and the Earth, d represents the actual distance between the Sun and the Earth, φ is la%tude, δ is the declina%on angle of the Sun, ΔH is the length of the day in radians, e is the eccentricity and δmax is the axial %lt or obliquity ( ) d (t ) = dm 1+ esin {( 2π / 365) ( t )} dmin = dm (1 e); dmax = dm (1+ e) δ (t ) = (πδmax /180) sin {( 2π / 365) ( t )} e = eccentricity ΔH = arccos( tan φ tan δ ) Box 2.1 Axial ;lt or obliquity 4

5 Absorbed Solar radia%on Absorbed Solar radia;on (ASR) (indicated in W m -2 ) as a func;on of la;tude and ;me for a planet with a uniform albedo equal to 0.3. Contour interval is 25 W m -2. Thick contour corresponds to 250 W m -2. α p = 0.3; S 0 =1366 W m -2 Sols;ce Fig 12.5 Radia%ve equilibrium temperature Atmosphere which is transparent to Solar radia;on and contains one well-mixed greenhouse gas. Contour interval is 2. The cyan contour represents the isotherm. Temperatures below are indicated by blue contours. Temperatures above freezing () are indicated by red contours. In the Polar night poleward of 66 S (right panel) the radia;ve equilibrium temperature is absolute zero Kelvin! T = T skin δ +1 ( ) 1/ 4 equinox sols;ce Fig

6 Radia%ve equilibrium temperature Summer pole warmer than tropics No tropical cold trap Polar night temperature: absolute zero K! equinox sols;ce Polar night: absolute zero Fig 12.6 Energy budget equa%on earth s surface? W m -2 TOA E B surface temperature absorbed Solar radia;on surface C dt s dt = Q + B σ B T s 4 heat capacity of the earth s surface Emi\ed (E) terrestrial radia;on (black body!) back-radia;on from atmosphere C is also called the thermal iner%a coefficient Large C: slow response to radia%ve imbalance: Q + B σ B T s 4 0 6

7 The influence of thermal iner%a Radia;ve determined state (sec;ons 2.9 & 12.3) Divide the atmosphere into a finite number of layers of equal mass Formulate radia;ve transfer equa;ons for each layer plus the earth s surface (see equa;on on previous slide) Integrate these ;me-dependent ordinary differen;al equa;ons numerically, imposing the seasonal cycle in Solar radia;on and assuming that the atmosphere is transparent to Solar radia;on This leads to the so-called radia%ve determined state Radia%ve determined temperature Radia;vely determined temperature [ C] as a func;on of la;tude and pressure for day 75 (let) and for day 165 (right) in an atmosphere, which is transparent to Solar radia;on and contains one well-mixed greenhouse gas. The cyan contour represents the isotherm. Temperatures below are indicated by blue contours. Temperatures above freezing () are indicated by red contours. The heat capacity of the Earth s surface is 10 7 J K -1 m equinox -10 sols%ce -8-8 Fig

8 Radia%ve determined temperature Summer pole colder than tropics No tropical cold trap Polar night temperature finite -10 equinox -10 sols%ce -8-8 Fig 12.7 Observed temperature distribu%on Observed (COSPAR Interna;onal Reference Atmosphere) monthly average zonal average temperature [ C] as a func;on of la;tude and pressure for March (let panel) and for June (right panel). Contour interval is 2. The cyan contour represents the isotherm. Temperatures below are indicated by blue contours. Temperatures above freezing () are indicated by red contours. cold equinox warm sols%ce cold -8 cold Fig

9 Absorbed Solar radia%on at TOA Day 170: Sols;ce Fig 12.5 Outgoing long-wave radia%on at TOA Radia;vely determined outgoing long wave radia;on at the top of the atmosphere (OLR-TOA) [W m -2 ] during the second year of integra;on of a radia;on model for a planet with a uniform albedo (0.3). Contour interval is 25 W m -2. The corresponding absorbed (Solar) radia;on is shown in the previous slide. Day 170: Sols;ce Day 225: Max OLR TOA Time lag: 55 days Fig

10 Net absorbed radia%on at TOA Radia%vely determined difference between absorbed Solar radia%on and outgoing long wave radia%on at the top of the atmosphere [W m-2] during the second year of integra;on of the radia;on model, for a planet with a uniform albedo (0.3). Contour interval is 25 W m-2. Heat is gained in spring and lost in Autumn. The radia;ve imbalance is largest in Spring over the Polar cap. It may be as large as 250 W m-2. gain loss The radia%vely determined state in the tropics is close to radia%ve equilibrium! Fig Radia%ve determined diaba%c hea%ng Radia;vely determined tendency of the poten)al temperature [K day-1] (also called crossisentropic flow) as a func;on of la;tude and pressure for day 75 (second year) (just before Equinox) (let panel) and for day 165 (second year) (just before Sols;ce) (right panel) in an atmosphere, which is transparent to Solar radia;on and contains one well-mixed greenhouse gas. Contour interval is 0.25 K day-1 (zero contour not drawn). equinox sols%ce Fig

11 Observed (reanalysis) diaba%c hea%ng June average isobars (dashed black lines[hpa]) and June average tendency of the poten)al temperature [K day -1 ] (contour interval: 0.5 K day -1 ), according to the ERA-40 reanalysis. The thick black line indicates the zonal mean posi;on of the Earth surface. Fig June period Observed (reanalysis) diaba%c hea%ng Observed pa\ern of cross-isentropic flow is very different from radia%vely determined paeern. Why? Isentropic density: σ = 1 p g θ Fig June period

12 Isentropic density σ = 1 p g θ σ ref = σcosφdφ cosφdφ (integral from 10 N to the North Pole) Isentropic density determines Poten%al Vor%city (PV): PV Z ζ + f σ Fig 7.6 Assignment 2 PROBLEM Comparison of the radia%ve equilibrium isentropic density to the radia%vely determined isentropic density Plot the radia;ve equilibrium isentropic density (eq ) as a func;on of poten;al temperature at the equator and at 60 N, on 20 March, 20 June, 20 September and 20 December (using eqs and and the defini;on of poten;al temperature), for the parameter values indicated in the cap;on of figure 12.12, and compare the outcome with the radia;vely determined isentropic density, shown in figure Use the formula s given in Box 2.1 to compute Q. Discuss the dynamical consequences of the differences (for this: you need to read chapter 7). Hand in answer to Assignment 2 on or before 13/6/2018, 17:00 12

13 Project Assignment 3 (project): In couples choose one project from the following list: problems 7.1, 7.3, 10.2, 10.3, 11.5, 11.6, 11.7, 12.5, Surf zone Tape recorder effect Balance - zonal mean state Isentropic tropopause Downstream development Northern Annular Mode Sudden stratospheric warmings Tropical cold trap Water cycle in the model Project, which will be presented on 29 June 2018 Please from couples and choose a project Next lecture Friday 1/6, 2016, 10:00-12:00, room 607 BBG Conserva%on of poten%al vor%city Thermal wind balance PV-inversion Piecewise PV-inversion: PV-anomalies induce the zonal mean wind. Read Chapter 7 13