Open problems in light scattering by ice particles

1. Open problems in light scattering by ice particles Chris Westbrook www.met.reading.ac.uk/radar

2. Overview of ice cloud microphysics:Cirrus

3. Overview of ice cloud microphysics:thick stratiform cloud

4. Need for good scattering models Need models to predict scattering from non-spherical ice crystals if we want to interpret radar/lidar data, particularly: Dual wavelength ratios ? size ? ice content Depolarisation ratio LDR Differential reflectivity ZDR

5. Radar wavelengths

6. Lidar Wavelengths Small ice particles from 5mm (contrails) to 10mm ish (thick ice cloud) Lidar wavelengths 905nm and 1.5mm Wavenumbers k=20 to k=70,000 Big span of kR ? need a range of methods

7. Current methodology:

8. Rayleigh scattering

9. Non-Rayleigh scattering Exact Mie expansion for spheres So approximate ice particle by a sphere Prescribe an �effective� permittivity Mixture theories: Maxwell-Garnett etc. Pick the appropriate �equivalent diameter� How do you pick equiv. D? Maximum dimension? Equal volume? Equal area?

10. Non-spherical shapes

12. Current approach for lidar:

13. Better methods: FDTD Solves Maxwell curl equations Discretise to central-difference equations Solve using leap-frog method (ie solve E then H then E then H�) Nice intuitive approach Very general But� Need to grid whole domain and solve for E and H everywhere Some numerical dispersion Fixed cubic grid, so complex shapes need lots of points Stability issues Very computationally expensive, kR~20 maximum

14. BEM Boundary element methods Has been done for hexagonal prism crystal E and H satisfy the Helmholtz equation Problem with sharp edges/corners of prism (discontinuities on boundary) Have to round off these edges & corners to get continuous 2nd derivs in E and H This doesn�t seem to affect the phase function much so probably ok.

15. T-matrix Expand incident, transmitted and scattered fields into a series of spherical vector wave functions, then find the relation between incident (a,b) and scattered (p,q) coefficients Once know transition matrix T then can compute the complete scattered field Elements of T essentially 2D integrals over the particle surface Easy for rotationally symmetric particles (spheroids, cylinders, etc) But� Less straightforward for arbitrary shapes Numerically unstable as kR gets big OK up to kR~50 if the shape isn�t too extreme

16. Discrete dipole approximation Recognise that a �point scatterer� acts like a dipole Replace with an array of dipoles on cubic lattice Solve for E field at every point dipole ? know scattered field

17. DDA continued�

21. DDA pros & cons Physical approach, conceptually simple Avoids discretising outer domain Can do any shape in principle Needs enough dipoles to 1. represent the target shape properly 2. make sure dipole separation << l Takes a lot of processor time, hard to //ise Takes a lot of memory ~ N3 (the real killer) Up to kR~40 for simple shapes

22. Rayleigh Random Walks Well known that can use random walks to sample electrostatic potential at a point. For conducting particles (e??) Mansfield et al [Phys. Rev. E 2001] have calculated the polarisability tensor using random walker sampling. Advantages are that require ~ no memory and easy to parallelise (each walker trajectory is an independent sample, so can just task farm it) Problems: how to extend to weak dielectrics (like ice)? Jack Douglas (NIST) Efficiency may be poor for small e ?

23. Conclusions Lots of different methods � which are best? Computer time & memory a big problem Uncertain errors Better methods? FEM, BEM�? Ultimately want parameterisations for scattering in terms of aircraft observables eg. size, density etc. Would like physically-motivated scheme to do this (eg. mean-field m.s. approx etc)