1. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Photon path length distributions and detailed microphysical parameterisations Marc Schröder Institut für Weltraumwissenschaften, Freie Universität Berlin, Berlin, Germany

2. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Overview Effect of different LWC profiles on absorption intensities Adiabaticity and mixing schemes LWC profiles Results Parameterisation of mean photon path Approach Dependence on sun zenith Results Radiative transfer based on cloud dropet number spectra Data and approach Problems Results Conclusions and outlook

3. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 The change of the cloud droplet distribution, n(r), with increasing droplet growth corresponds to a translation in the squared radius, r 2 (Brenguier, 1991). Assuming adiabaticity,  2 can be determined (Schueller et al., 2004). 1000 bins for r between 0.3 and 31.6 microns 22 Schueller et al. (2003) Effect of different LWC(z) on absorption intensities Adiabaticity

4. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Effect of different LWC(z) on absorption intensities LWC profiles constant liquid water path

5. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 How can deviations of LWC LES from the adiabatic LWC ad be interpreted to derive microphysical properties? Turbulent mixing of entrained dry air and cloudy parcels may result in two extreme cases: I) Homogeneous mixing: The mixing is faster than the droplet evaporation. All droplet are exposed to the same water vapor deficit. II) Heterogeneous mixing: The droplet evaporation is faster than the mixing. The droplets exposed to the entrained air are totally evaporated. I)I) II ) Effect of different LWC(z) on absorption intensities Mixing scheme

6. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Mixing Scheme I) Homogeneous: Effective radius, r eff, changes while N = const h = LWC LES / c w II) Heterogeneous:r eff = const and N changes Define f = LWC LES / LWC ad, then  = f *  ad with  being the volume extinction coefficient. Single scat- tering albedo, phase function, and  ad are defined by h = LWC ad / c w. An explicit knowledge of the cloud base is required for this procedure.

7. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Photon path length Each photon is traced until it gets absorbed or until it hits a boundary without being reflected. If the photon reaches the detector, the travelled path is stored: P(l) P(l) h 2 h cos(  ) 2 1 **

8. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Effect on absorption

9. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Parameterisation of mean photon path Approach Use adiabatic model of Schueller et al., 2004 Define a set of optical thicknesses  and droplet number concentrations N:  : 1, 2, 5, 10, 20, 50, 100 N: 50, 100, 200, 400 cm -3 Utilise Monte Carlo simulations to determine mean photon path length: = l P(l) dl 

10. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Interim result H: geometrical cloud thickness

11. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Parameterisation of mean photon path length In addition to optical thickness, depends significantly on effective radius. N

12. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Dependence on sun zenith

13. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Dependence on surface albedo A = 0.4 A = 0 = 1.33 km = 0.47 km

14. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Parameterisation of mean photon path length Dependence on LWC profile adiab cten rad cool subad heterogeneous 0.365 0.426 0.370 0.405 homogeneous0.365 0.422 0.380 0.416 Mean photon path length with N = 200 cm -3 and  = 11 maximum impact of ~14%

15. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 3D RT simulations based on cloud droplet numbers cloud droplet number spectra, n(r), from M. Leporini, LaMP, CNRS detailed microphysical model DECAM (Flossmann, 1985) 3D non-hydrostatic mesoscale model (Clark et al., 1996)  3D cloud model with warm microphysics 39 cloud droplet bins cover a radius range form 1.25 to 100.8 microns

16. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Problem Validation of Monte Carlo model shows a need for highly resolved phase functions (100,000 bins for the scattering angle): The phase function depends on radius, so that each droplet spectrum may result in a different phase function, in total 127,000. That amounts to 51 Gbyte working space.

17. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Solution Bin properties of all phase functions: 30 bins each 900 phase functions 20 10 2 8 20

18. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 2D averaging based on RT simulations directly from n(r)homogeneous 2.57 3.20 0.16 0.12 directly from n(r) homogeneous mixing

19. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Explanation Different microphysical models between the homogeneous mixing and the cloud droplet approach (recall the number of bins and ranges for the radius) Surface albedo A=0 mean optical thickness low red: homogeneous black: n(r)

20. Marc Schröder, FUB Tutorial, De Bilt, 10.´04 Conclusions Extinction at cloud top strongly affects the signal at absorbing channels. Significant to strong dependence of the mean photon path on cloud optical depth AND effective radius.  Potential improvements for retrieval schemes, either through direct simulation or subsequent adjustments.  It may increase the accuracy of gas absorption estimation in GCMs. The microphysical properties, in particular the phase function, can have strong effects on the overall reflectance and absorption intensity.