Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Chapter 6: Blackbody Radiation: Thermal Emission "Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating. Eventual Absorption: Acts like a black body (classroom also?)

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Earth-Atmosphere Energy Balance Fig. 9.1

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Molecules as Billiard Balls

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Container of Photons: It really works! Radiation Pressure I=  T 4,  =5.67e-8 W m -2 K -4

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer DEFINITION OF THE BRIGHTNESS TEMPERATURE T B Measured Radiance at wavenumber v = Theoretical Radiance of a Black Body at temperature T B

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer FTIR Radiance: Atmospheric IR Window 13 microns 8 microns Ground, T s FTIR

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Ground, T s FTIR FTIR Brightness Temperatures

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Nimbus Satellite FTIR Spectrum FTIR Ground, T s

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Nimbus Satellite and Ground Based FTIR Spectrum FTIR Ground, T s FTIR TsTs ≈T s

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Planck Functions for Earth and Sun: Note some overlap (4 microns), but with log scale, can treat them separately for the most part.

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Eye Response Evolved to Match Solar Spectrum Peak? The answer depends on how you look at the distribution functions, wavelength or wavenumber. Seems to support it Seems not to support it.

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Blackbody Radiation: A look at the Forms:

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Blackbody Radiation: Another look at the Forms:

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Earth’s Surface Temperature T e Earth’s radiative temperature T s Sun’s radiative temperature R s Sun’s radius R se Sun to Earth distance a Earth’s surface solar reflectance t IR transmittance of Earth’s atmosphere.

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Simple Model for Earth’s Atmosphere: No Absorption of Sunlight by the Atmosphere.

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Simple Surface Temperature Calculation Assuming Solar Absorption only at the surface, IR emission by the atmosphere and Earth’s surface, and IR absorption by the Atmosphere. S 0 = 1376 W/m 2 =Solar Irradiance at the TOA and  =Stefan-Boltzmann constant

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Model with Atmosphere that absorbs solar radiation: Terrestrial IR=IR=LW, Solar = SW A = surface albedo≈0.3 a sw = Atmosphere absorption of solar radiation t sw = Transmission of solar by the atmosphere = (1-a sw ) a lw = Atmosphere absorption of IR radiation = Atmospheric Emissivity. t lw = Transmission of IR by the atmosphere = (1-a lw ) T s = surface temperature T a = atmosphere temperature  ≈ 1 = IR surface emissivity. Fluxes: F 1 =incident from sun F 2 = t sw F 1 = (1-a sw )F 1 F 3 =Solar reflected to space by the earth, atmosphere=F 4 transmitted by atmosphere. F 4 =Solar reflected by surface. F 8 =IR emitted by surface. F 7 =t lw F 8 =(1-a lw )F 8. F 5 =F 6 =IR emitted by atmosphere. Solar Flux Relationships: F 1 = S F 2 = t sw F 1 = (1-a sw ) F 1 = (1-a sw ) S F 4 =A F 2 = A (1-a sw ) S F 3 = (1-a sw ) F 4 = A(1-a sw ) 2 S IR Flux Relationships: F 5 = F 6 = a lw  T a 4 F 8 =   T s 4 =  T s 4 F 7 = (1-a lw ) F 8 = (1-a lw )  T s 4

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Radiative Equilibrium Relationships A = surface albedo≈0.3 a sw = Atmosphere absorption of solar radiation t sw = Transmission of solar by the atmosphere = (1-a sw ) a lw = Atmosphere absorption of IR radiation = Atmospheric Emissivity. t lw = Transmission of IR by the atmosphere = (1-a lw ) T s = surface temperature T a = atmosphere temperature  ≈ 1 = IR surface emissivity. Fluxes: F 1 =incident from sun F 2 = t sw F 1 = (1-a sw )F 1 F 3 =Solar reflected to space by the earth, atmosphere=F 4 transmitted by atmosphere. F 4 =Solar reflected by surface. F 8 =IR emitted by surface. F 7 =t lw F 8 =(1-a lw )F 8. F 5 =F 6 =IR emitted by atmosphere. F net,toa = F 3 +F 5 +F 7 -F 1 = Flux (Out-In)=0 F net,surface = F 4 +F 8 -F 2 -F 6 = Flux (Out-In)=0

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Sufficient Number of Equations to Solve for All Fluxes A = albedo ≈ 0.3 a sw = Atmosphere absorption of solar radiation t sw = Transmission of solar by the atmosphere = (1-a sw ) a lw = Atmosphere absorption of IR radiation = Atmospheric Emissivity. t lw = Transmission of IR by the atmosphere = (1-a lw ) T s = surface temperature T a = atmosphere temperature  ≈ 1 = IR surface emissivity. S 0 = 1360 W/m 2

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Resulting Temperate Example for the Simple Model

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Broad View of Model Predictions Surface Temperature (K) Atmosphere Temperature (K)

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a calm water surface. 55 deg IsIs IpIp

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude). Medium 2 Medium 1 ii tt

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Reflectivity of Water And Ice Brewster Angle Microwave =15,000 microns n r = n i = Mid Visible (green) =0.5 microns n r = n i = x

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Reflectivity of Water And Ice: Normal Incidence What drives the reflectivity?

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Fresnel Reflection Coefficients: What is the magnitude of the light specularly reflected from a surface? (Also can get the transmitted wave magnitude). Medium 2 Medium 1 ii tt ICE Transmission & Absorption: T p =1-R p =a p =  p T s =1-R s =a s =  s a=absorption coefficient  =emissivity

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer Calculate the microwave radiant intensity (magnitude and polarization state) measured by a satellite above a calm water surface. The answer. 55 deg IsIs IpIp Is0Is0 Ip0Ip0 T ii tt What are the sources of I p 0 ? (same form for I s )

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer WHY? What if n i = 0? R p and R s are not 0 in that case. How could we get emission if n i =0? We have no absorption in that case! If n i =0, then  abs =4  n i / = 0!

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer The transmitted wave, with absorption k 2, diminishes. The total amount of radiation eventually absorbed in medium 2 is given by T p,s = (1 - R p,s ). No matter-filled medium exists where k 2 =0. 55 deg IsIs IpIp

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer See how it goes for normal incidence … Layer dz emits radiation dI at temperature T that transfers to the satellite. After emission, it is partially absorbed in distance z, and then transmitted out the boundary. dz z m

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer See how it goes for normal incidence … Layer dz emits radiation dI at temperature T that transfers to the satellite. After emission, it is partially absorbed in distance z, and then transmitted out the boundary. Interpretation of the terms. dz z emissivity boundary transmissivity medium propagator m

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer See how it goes for normal incidence … Layer dz emits radiation dI at temperature T that transfers to the satellite. After emission, it is partially absorbed in distance z, and then transmitted out the boundary. The total emission is determined by integration in the z direction. dz z m The main contribution to the emitted radiation comes from about a skin depth of the surface, /(4  n i ).

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer For problem 6.28, let I p,s 0 =0. Calculate for each frequency. 55 deg IsIs IpIp T ii tt (same form for I s ) N2N2 N1N1 Key for remote sensing: N 2 (T) (why?)

Pat Arnott, ATMS 749 Atmospheric Radiation Transfer AMSR Sensor: In support of the Earth Science Enterprise's goals, NASA's Earth Observing System (EOS) Aqua Satellite was launched from Vandenberg AFB, California on May 4, 2002 at 02:54:58 a.m. Pacific Daylight Time. The primary goal of Aqua, as the name implies, is to gather information about water in the Earth's system. Equipped with six state-of-the-art instruments, Aqua will collect data on global precipitation, evaporation, and the cycling of water. This information will help scientists all over the world to better understand the Earth's water cycle and determine if the water cycle is accelerating as a result of climate change. The Advanced Microwave Scanning Radiometer - EOS (AMSR-E) is a one of the six sensors aboard Aqua. AMSR-E is passive microwave radiometer, modified from the Advanced Earth Observing Satellite-II (ADEOS-II) AMSR, designed and provided by JAXA (contractor: Mitsubishi Electric Corporation). It observes atmospheric, land, oceanic, and cryospheric parameters, including precipitation, sea surface temperatures, ice concentrations, snow water equivalent, surface wetness, wind speed, atmospheric cloud water, and water vapor. NASA A-Train