The General Circulation of the Atmosphere: A Numerical Experiment
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1 The General Circulation of the Atmosphere: A Numerical Experiment Norman A. Phillips (1956) Presentation by Lukas Strebel and Fabian Thüring
2 Goal of the Model Numerically predict the mean state of the atmosphere 2
3 Goal of the Model Numerically predict the mean state of the atmosphere Explore the validity of the geostrophic theory in explaining the general circulation 3
4 Goal of the Model Numerically predict the mean state of the atmosphere Explore the validity of the geostrophic theory in explaining the general circulation Investigate the energetics of the atmosphere 4
5 Governing Equations Quasi-geostrophic theory Beta-plane approximation Geostrophic wind dominates 5
6 Governing Equations Quasi-geostrophic theory Non-adiabatic heat changes and friction Beta-plane approximation Non-adiabatic Geostrophic wind dominates Friction Du Dt + A vr 2 u + 6
7 Governing Equations Quasi-geostrophic theory Non-adiabatic heat changes and friction 2-level geostrophic model Beta-plane approximation Non-adiabatic Geostrophic wind dominates Friction Du Dt + A vr 2 u + 7
8 2-level geostrophic model Equation of momentum and continuity (pressure coordinates) 8
9 2-level geostrophic model Thermodynamic energy equation 9
10 2-level geostrophic model Thermodynamic energy equation 10
11 2-level geostrophic model Vertical levels 11
12 2-level geostrophic model Vertical levels Vertical boundary conditions Vertical velocities 12
13 2-level geostrophic model Vertical levels Vertical boundary conditions Vertical velocities Frictional stresses 13
14 2-level geostrophic model Vertical levels Vertical boundary conditions Vertical velocities Frictional stresses 14
15 2-level geostrophic model Geometry 15
16 2-level geostrophic model Geometry Boundary conditions in x are periodic 16
17 2-level geostrophic model Geometry Boundary conditions in y are defined by walls 17
18 2-level geostrophic model Lateral boundary conditions in y are defined by walls 18
19 2-level geostrophic model Lateral boundary conditions in y are defined by walls Normal geostrophic velocity vanishes at the walls 19
20 2-level geostrophic model Lateral boundary conditions in y are defined by walls Normal geostrophic velocity vanishes at the walls Disturbed vorticity vanishes at the walls (arbitrary) 20
21 2-level geostrophic model Lateral boundary conditions in y are defined by walls Normal geostrophic velocity vanishes at the walls Disturbed vorticity vanishes at the walls (arbitrary) Integrating momentum equation w.r.t to BC 21
22 2-level geostrophic model Lateral boundary conditions in y are defined by walls Normal geostrophic velocity vanishes at the walls Disturbed vorticity vanishes at the walls (arbitrary) Integrating momentum equation w.r.t to BC 22
23 Further Assumptions No variation of vertical stability (2 const 23
24 Further Assumptions No variation of vertical stability (2 const will be interpreted as the average non-adiabatic heating dq dt 24
25 Further Assumptions No variation of vertical stability (2 layer model) const will be interpreted as the average non-adiabatic heating Release of latent heat 25
26 Further Assumptions No variation of vertical stability (2 layer model) const will be interpreted as the average non-adiabatic heating Release of latent heat Radiation 26
27 Further Assumptions No variation of vertical stability (2 layer model) const will be interpreted as the average non-adiabatic heating Release of latent heat Radiation Small scale lateral eddy diffusion 27
28 Quasi-geostrophic equations Quasi-geostrophic vorticity equation 28
29 Quasi-geostrophic equations Quasi-geostrophic vorticity equation 29
30 Quasi-geostrophic equations Quasi-geostrophic vorticity equation 30
31 Quasi-geostrophic equations Thermodynamic energy equation (at interface) 22
32 Quasi-geostrophic equations Thermodynamic energy equation (at interface) 22
33 Quasi-geostrophic equations Thermodynamic energy equation (at interface) 22
34 Quasi-geostrophic equations Thermodynamic energy equation (at interface) Geostrophic stream function Modified Rossby deformation radius 22
35 Quasi-geostrophic potential vorticity Define Quasi-geostrophic potential vorticity 35
36 Quasi-geostrophic potential vorticity Define Quasi-geostrophic potential vorticity Define prognostic equations for qi 36
37 Numerical Scheme (QGPV) Prognostic step 37
38 Numerical Scheme (QGPV) Prognostic step Diagnostic step 38
39 Numerical Scheme (QGPV) Prognostic step Diagnostic step 39
40 Numerical Scheme (QGPV) Finite Differences 40
41 Numerical Scheme (QGPV) Finite Differences 41
42 Numerical Scheme (QGPV) Finite Differences 42
43 Energy Transformation Kinetic energy of the mean zonal flow Kinetic energy of the disturbed flow Potential energy of the mean zonal flow Potential energy of the disturbed flow 43
44 Total change in energy 1. A loss of energy due to lateral eddy viscosity A 44
45 Total change in energy 1. A loss of energy due to lateral eddy viscosity A 2. A loss due to effect of surface friction 45
46 Total change in energy 1. A loss of energy due to lateral eddy viscosity A 2. A loss due to effect of surface friction 3. A change due to the non-adiabatic heating 46
47 Energy Flow Diagram Lateral eddy-viscosity Lateral eddy-viscosity Non-adiabatic heating Direct meridional circulation Loss by friction Poleward sensible heat transport Convergence of mean eddy momentum transport Vertical circulation Loss by friction Lateral eddy-viscosity Lateral eddy-viscosity 47
48 Development of the flow Experimental Setup Meridional extent km Zonal extent 6000 km Initial atmosphere at rest 130 day forecast without eddies 48
49 Development of the flow Experimental Setup Meridional extent km Zonal extent 6000 km Initial atmosphere at rest 130 day forecast without eddies Interpretation The wave moves eastward 1800 km /day The waves begins as a warm low Tilted troughs and ridges 49
50 Development of the flow Interpretation Indication of cold and warm fronts in 1000 mb contours 50
51 Development of the flow Interpretation Occlusion of cyclones Numerical instability after 26 days 51
52 Development of the flow Variation of u 1 at 250 mbs with latitude (j) and time. Unit are m sec -1. Regions of easterly winds are shaded 52
53 Development of the flow Variation of u 4 at 1000 mbs with latitude (j) and time. Unit are m sec
54 Energy transformation 54
55 Conclusion of the experiment + Easterly and westerly distribution of the surface zonal wind +Existence of a jet +Model achieves net poleward transport of energy +Qualitative agreement of the energy transformation processes 55
56 Conclusion of the experiment + Easterly and westerly distribution of the surface zonal wind +Existence of a jet +Model achieves net poleward transport of energy +Qualitative agreement of the energy transformation processes Same order of magnitude of trade winds and polar easterly Uncertainty of input parameters ( ) Instability of the numerics 56
57 Questions? 57
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