1. 1 Atmospheric Radiation – Lecture 8 PHY2505 - Lecture 8 Radiative Transfer Band Models

2. 2 Atmospheric Radiation – Lecture 8 Outline Equivalent width Weak line/strong line approximations Band models Curtis-Godson approximation MODTRAN

3. 3 Atmospheric Radiation – Lecture 8 Equivalent width Consider a homogenous atmospheric layer. Here the spectral absorption coefficient does not depend on path length. The spectral transmittance T for a band of width  v is And spectral absorptance, A Equivalent width, W [cm -1 ]: a measure of absorptance, A, over the spectral interval  v

4. 4 Atmospheric Radiation – Lecture 8 Equivalent width of a Lorentz line

5. 5 Atmospheric Radiation – Lecture 8 Equivalent width of a Lorentz line

6. 6 Atmospheric Radiation – Lecture 8 “Weak line” limit

7. 7 Atmospheric Radiation – Lecture 8 “Strong line” limit

8. 8 Atmospheric Radiation – Lecture 8 Strong/weak line: limits of validity Can find experimentally from “curves of growth”

9. 9 Atmospheric Radiation – Lecture 8 Band models A band is a spectral interval of a width Dv small enough to use a mean value of the Planck function B v (T) but large enough to contain several absorption lines Band models are introduced to simplify computation of spectral transmittance Now we have found out how to calculate the equivalent width of a single line, need to consider how we deal with a band of many lines Two main cases: 1)Lines with regular positions 2)Lines with random positions

10. 10 Atmospheric Radiation – Lecture 8 Regular Elasser band model See Liou p139-141 for derivation This gives

11. 11 Atmospheric Radiation – Lecture 8 Principle of statistical band models

12. 12 Atmospheric Radiation – Lecture 8 Principle of statistical band models where  is the mean spacing For multiple lines, transmission is exponential in W

13. 13 Atmospheric Radiation – Lecture 8 Goody statistical model

14. 14 Atmospheric Radiation – Lecture 8 Goody statistical model: weak and strong line limits

15. 15 Atmospheric Radiation – Lecture 8 Correlated k distribution Here, the spectral lines are rearranged over a given spectral interval and a histogram produced Absoprtion coefficient for representative lines is multiplied by a weighting function representing frequency of occurance of this type of line Typically useful to use 4 divisions per decade on log scale … See Liou section 4.3 for a discussion of the limits of validity for this approximation Liou, FIG 4.5

16. 16 Atmospheric Radiation – Lecture 8 Curtis – Godson approximation

17. 17 Atmospheric Radiation – Lecture 8 Curtis – Godson approximation

18. 18 Atmospheric Radiation – Lecture 8 Curtis – Godson approximation

19. 19 Atmospheric Radiation – Lecture 8 Curtis – Godson approximation

20. 20 Atmospheric Radiation – Lecture 8 MODTRAN4 A. Berk *, G.P. Anderson #, P.K. Acharya *, J.H. Chetwynd #, M.L. Hoke #,L.S. Bernstein *, E.P. Shettle ^, M.W. Matthew *, and S.M. Adler-Golden # US Air Force Research Laboratory *Naval research Laboratory Atmosphere: gas profiles, temperature, pressure profiles, aerosol/cloud type & vertical distribution Surface type & measurement geometry Select calculation methods: eg. correlated K method, scattering (DISTORT ) 2cm -1 resolution

21. 21 Atmospheric Radiation – Lecture 8 Who still uses band models (MODTRAN)? UV/VIS atmospheric instruments where scattering important Eg. SCISAT-1 MAESTRO McElroy, C.T., A spectroradiometer for the measurement of direct and scattered solar spectral irradiance from on-board the NASA ER-2 high-altitude research aircraft, Geophys. Res. Lett., 22, 1361-1364 (1995). Multispectral imagers cloud, ozone, water vapour retrieval Eg. MODIS Justice, C.et al, The Moderate Resolution Imaging Spectroradiometer (MODIS): Land remote sensing for global change research, IEEE Trans. Geosci. Remote Sens., 36, 1228-1249 (1998). Hyperspectral imagers for atmospheric corrections Eg. AVIRIS Berk, A, et al, MODTRAN Cloud and Multiple Scattering Upgrades with Application to AVIRIS, Remote Sens. Environ., 65, 367-375 (1998).

22. 22 Atmospheric Radiation – Lecture 8 MODTRAN dialogue windows