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METR 5970.002 Advanced Atmospheric Radiation

METR 5970.002 Advanced Atmospheric Radiation. Dave Turner Lecture 2. Warren Wiscombe. Atmospheric Radiation Measurement (ARM) Scientific Leaders. 2010. Circa 1980. Tom Ackerman 2 nd Chief Scientist. Bob Ellingson Lead Author of ARM Proposal to DOE. Gerry Stokes

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METR 5970.002 Advanced Atmospheric Radiation

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  1. METR 5970.002Advanced Atmospheric Radiation Dave Turner Lecture 2

  2. Warren Wiscombe Atmospheric Radiation Measurement (ARM) Scientific Leaders 2010 Circa 1980 Tom Ackerman 2nd Chief Scientist Bob Ellingson Lead Author of ARM Proposal to DOE Gerry Stokes 1st Chief Scientist Warren Wiscombe 3rd Chief Scientist 1997

  3. The Radiative Transfer Equation

  4. Primary Gas Absorption Bands in IR

  5. Upwelling LW Radiance at Top of the Atmosphere

  6. Upwelling LW Radiance at Top of the Atmosphere Downwelling LW Radiance at the Surface

  7. Upwelling LW Radiance at Top of the Atmosphere Downwelling LW Radiance at the Surface Water Vapor Water Vapor CO2 O3 Trace gases (CFC, CH4, etc) absorb in various regions

  8. Upwelling LW Radiance at Top of the Atmosphere Downwelling LW Radiance at the Surface Water Vapor Water Vapor CO2 O3 Clouds Aerosols Trace gases (CFC, CH4, etc) absorb in various regions

  9. RT Basics X I0 I M4 M3 M2 M1 is the transmittance from height z to the “instrument” Local Thermodynamic Equilibrium Absorption = Emission Transmission to the surface Emission from the layer

  10. Downwelling Clear Sky Case (Example 1a) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 T2=272 K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Downwelling radiance: (1-exp(-0. 2))*(41.2+55.0)/2*exp(-(0. 8+3.2+12.5+50)) + (1-exp(-0. 8))*(55.0+71.2)/2*exp(-(3.2+12.5+50)) + (1-exp(-3.2))*(71.2+89.9)/2*exp(-(12.5+50)) + (1-exp(-12.5))*(89.9+111.0)/2*exp(-50) + (1-exp(-50))*(111.0+134.4)/2 = 122.7 RU Caveat

  11. Downwelling Cloudy Sky Case (Example 1b) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 Τcloud3 = 10, Fcld= 1.0 T2=272 K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Downwelling radiance: (1-exp(-0. 2))*(41.2+55.0)/2*exp(-(0. 8+13.2+12.5+50)) + (1-exp(-0. 8))*(55.0+71.2)/2*exp(-(13.2+12.5+50)) + (1-exp(-13.2))*(71.2+89.9)/2*exp(-(12.5+50)) + (1-exp(-12.5))*(89.9+111.0)/2*exp(-50) + (1-exp(-50))*(111.0+134.4)/2 = 122.7 RU Caveat

  12. Example 1a vs Example 1b: Why ? Τgas5 = 0.2 Τgas5 = 0.2 Τgas4 = 0.8 Τgas4 = 0.8 Τgas3 = 3.2 Τtotal3 = 13.2 Τgas2 = 12.5 Τgas2 = 12.5 Τgas1 = 50.0 Τgas1 = 50.0 Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Downwelling Radiance: 122.7 RU Downwelling Radiance: 122.7 RU Caveat

  13. Downwelling Clear Sky Case (Example 1c) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 T2 is 270 instead of 272 K T2=270K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Example 1a (T2=272K): Downwelling Radiance: 122.7 RU Example 1c (T2=270K): Downwelling Radiance: 122.7 RU Example 1c (T2=270K): Downwelling Radiance: ?? RU Caveat

  14. Downwelling Clear Sky Case (Example 1d) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 T2=272 K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0 is 302 instead of 300 K T0=302 K, B(T)=137.9 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Example 1a (T0=300K): Downwelling Radiance: 122.7 RU Example 1d (T0=302K): Downwelling Radiance: 124.5 RU Example 1d (T0=302K): Downwelling Radiance: ?? RU Caveat

  15. Downwelling Clear Sky Case (Example 1e) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 All optical depths are 100x smaller T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Example 1a (large tau): Downwelling Radiance: 122.7 RU Example 1e (small tau): Downwelling Radiance: 57.1 RU Example 1e (small tau): Downwelling Radiance: ?? RU Caveat

  16. Downwelling Clear Sky Case (Example 2a) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Downwelling radiance: (1-exp(-0.002))*(41.2+55.0)/2*exp(-(0.008+0.032+0.125+0.5)) + (1-exp(-0.008))*(55.0+71.2)/2*exp(-(0.032+0.125+0.5)) + (1-exp(-0.032))*(71.2+89.9)/2*exp(-(0.125+0.5)) + (1-exp(-0.125))*(89.9+111.0)/2*exp(-0.5) + (1-exp(-0.500))*(111.0+134.4)/2 = 57.1 RU Caveat

  17. Upwelling Clear Sky Case (Example 2b) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Upwelling radiance: 152.5*1.0 * exp(-(0.5+0.125+0.032+0.008+0.002)) + (1-exp(-(0.500))*(134.4+110.0)/2*exp(-(0.125+0.032+0.008+0.002))) + … (1-exp(-(0.002))*(55.0+41.2)/2 = 133.6 RU Caveat

  18. Down and Upwelling Cloudy Sky Case #1 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 1.0 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = ? RU R = ? RU

  19. Down and Upwelling Cloudy Sky Case #2 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 0.5 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = ? RU R = ? RU

  20. Down and Upwelling Cloudy Sky Case #3 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 Τcloud4 = 1, Fcld= 0.25 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 0.5 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = ? RU R = ? RU

  21. Answers

  22. Down and Upwelling Cloudy Sky Case #1 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 1.0 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = 100.0 RU R = 108.2 RU Caveat

  23. Down and Upwelling Cloudy Sky Case #2 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 0.5 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = 104.0 RU R = 102.1 RU Averaging optical depth for clear and cloudy scenes Caveat

  24. Down and Upwelling Cloudy Sky Case #2 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 0.5 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = 116.80 RU R = 82.67 RU Independent Column Approximation (ICA) (This is much more accurate than the previous) Caveat

  25. Down and Upwelling Cloudy Sky Case #3 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 Τcloud4 = 1, Fcld= 0.25 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 0.5 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = 110.96 RU Maximum overlap R = 82.76 RU Caveat

  26. Down and Upwelling Cloudy Sky Case #3 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 Τcloud4 = 1, Fcld= 0.25 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 0.5 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = 105.67 RU Minimum overlap R = 87.79 RU Caveat

  27. The Caveat Linear in tau approximation (Suggested by Wiscombe in JQSRT 1976) • 0 as tau  ∞ • 0.5 as tau 0 Log10(Optical Depth)

  28. Downwelling Clear Sky Case (Example 1a) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 T2=272 K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Downwelling radiance: (1-exp(-0. 2))*(41.2+55.0)/2*exp(-(0. 8+3.2+12.5+50)) + (1-exp(-0. 8))*(55.0+71.2)/2*exp(-(3.2+12.5+50)) + (1-exp(-3.2))*(71.2+89.9)/2*exp(-(12.5+50)) + (1-exp(-12.5))*(89.9+111.0)/2*exp(-50) + (1-exp(-50))*(111.0+134.4)/2 = 122.7 RU Correct Answer = 133.9 RU Including linear-in-tau approximation

  29. Downwelling Cloudy Sky Case (Example 1b) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 Τcloud3 = 10, Fcld= 1.0 T2=272 K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Downwelling radiance: (1-exp(-0. 2))*(41.2+55.0)/2*exp(-(0. 8+13.2+12.5+50)) + (1-exp(-0. 8))*(55.0+71.2)/2*exp(-(13.2+12.5+50)) + (1-exp(-13.2))*(71.2+89.9)/2*exp(-(12.5+50)) + (1-exp(-12.5))*(89.9+111.0)/2*exp(-50) + (1-exp(-50))*(111.0+134.4)/2 = 122.7 RU Correct Answer = 133.9 RU Including linear-in-tau approximation

  30. Downwelling Clear Sky Case (Example 1c) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 T2 is 270 instead of 272 K T2=270K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Example 1a (T2=272K): Downwelling Radiance: 122.7 RU Example 1c (T2=270K): Downwelling Radiance: 122.7 RU Example 1c (T2=270K): Downwelling Radiance: ?? RU Correct Answer = 133.9 RU Including linear-in-tau approximation

  31. Downwelling Clear Sky Case (Example 1d) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.2 T4=244 K, B(T)=55.0 RU Τgas4 = 0.8 T3=258 K, B(T)=71.2 RU Τgas3 = 3.2 T2=272 K, B(T)=89.9 RU Τgas2 = 12.5 T1=286 K, B(T)=111.0 RU Τgas1 = 50.0 T0 is 302 instead of 300 K T0=302 K, B(T)=137.9 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Example 1a (T0=300K): Downwelling Radiance: 122.7 RU Example 1d (T0=302K): Downwelling Radiance: 124.5 RU Example 1d (T0=302K): Downwelling Radiance: ?? RU Correct Answer = 137.4 RU Including linear-in-tau approximation

  32. Downwelling Clear Sky Case (Example 1e) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 All optical depths are 100x smaller T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Example 1a (large tau): Downwelling Radiance: 122.7 RU Example 1e (small tau): Downwelling Radiance: 57.1 RU Example 1e (small tau): Downwelling Radiance: ?? RU Correct Answer = 57.4 RU Including linear-in-tau approximation

  33. Upwelling Clear Sky Case (Example 2b) T5=230 K, B(T)=41.2 RU Calculation at 800 cm-1 which is 12.5 µm RU = 1 mW/(m2sr cm-1) Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 Upwelling radiance: 152.5*1.0 * exp(-(0.5+0.125+0.032+0.008+0.002)) + (1-exp(-(0.500))*(134.4+110.0)/2*exp(-(0.125+0.032+0.008+0.002))) + … (1-exp(-(0.002))*(55.0+41.2)/2 = 133.6 RU Correct Answer = 133.1 RU Including linear-in-tau approximation

  34. Down and Upwelling Cloudy Sky Case #1 T5=230 K, B(T)=41.2 RU Τgas5 = 0.002 T4=244 K, B(T)=55.0 RU Τgas4 = 0.008 T3=258 K, B(T)=71.2 RU Τgas3 = 0.032 T2=272 K, B(T)=89.9 RU Τgas2 = 0.125 Τcloud2 = 4, Fcld= 1.0 T1=286 K, B(T)=111.0 RU Τgas1 = 0.500 T0=300 K, B(T)=134.4 RU Tsfc=310 K, B(Tsfc)=152.5 RU, Emissivity=1 R = 100.0 RU Correct R = 94.4 RU R = 108.2 RU Correct R = 111.9 RU Including linear-in-tau approximation

  35. Other Things • Non-vertical view angles • Non-black surface

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