Multiscatter: A fast, approximate multiple scattering algorithm

Lidar and radar are powerful tools for cloud remote sensing, especially when used in synergy, but both can be affected by multiple scattering which makes the returns more difficult to interpret. Lidar is affected by multiple scattering in any optically thick medium, particularly liquid clouds. Millimetre-wave radar is typically only affected when observing deep convective clouds from space. One approach to deal with this problem is to use a variational retrieval algorithm with a forward model that can represent multiple scattering while being both accurate and fast. This code is such a forward model, and consists of two algorithms, the backscatters from which are summed:

• PVC method (lidar only): the Photon Variance-Covariance method for quasi-small-angle multiple scattering shares several assumptions with the Eloranta (1998) formulation, but by the way it treats the outgoing and returning photon distributions is able to simulate high orders of scattering several orders of magnitude faster. Note that quasi-small-angle scattering only occurs for phase functions with strong forward scattering lobes, so typically for lidar but not radar. For further details see Hogan (2006, 2008) below.
• TDTS method (lidar and radar): the Time-Dependent Two-Stream method for wide-angle multiple scattering copes with the more difficult situation of pulse stretching by integrating a pair of coupled PDEs forward in time. It is described with benchmark calculations by Hogan and Battaglia (2008) below.

Papers

• Original PVC method (lidar only)
  Hogan, R. J., 2006: Fast, approximate calculation of multiply scattered lidar returns, Applied Optics, 45, 5984-5992: PDF file
• Faster PVC method (lidar only) with anisotropic phase functions near 180 degrees
  Hogan, R. J., 2008: Fast lidar and radar multiple-scattering models: Part 1: Small-angle scattering using the photon variance-covariance method. J. Atmos. Sci., 65, 3621-3635: PDF file
• TDTS method (lidar and radar)
  Hogan, R. J., and A. Battaglia, 2008: Fast lidar and radar multiple-scattering models: Part 2: Wide-angle scattering using the time-dependent two-stream approximation. J. Atmos. Sci., 65, 3636-3651: PDF file
  
• Example of the use of the PVC method in a retrieval algorithm
  Delanoe, J., and R. J. Hogan, 2008: A variational scheme for retrieving ice cloud properties from combined radar, lidar and infrared radiometer. J. Geophys. Res., 113, D07204, doi:10.1029/2007JD009000: PDF file

Presentations

• Talk at International Radiation Symposium, Brazil, Aug 2008 (PPT)
• Talk at EarthCARE workshop, ESA, May 2007 (PPT)

Source code

• Latest version: multiscatter-1.1.2.tar.gz (In C and tested on Linux - read the README file first).
• Older versions: multiscatter-1.0.tar.gz; multiscatter-0.9.3.tar.gz (PVC only).

Matlab interface

• multiscatter.m - a matlab function that has calls the multiscatter executable (you will need to edit the function to point it at the location of the executable). It has been tested on linux. Type "multiscatter" with no options at the matlab prompt to see usage information. Be sure to use the "-no-forward-lobe" option for radar cases.
• test_icesat_ms.m - an example of the use of multiscatter.m to calculate the multiple scattering for idealized clouds with different effective radius observed by the ICESat lidar. You will need the multiscatter_platt.m function, which estimates the backscattering using a much simpler method, for comparison. It should produce this figure.

See also

• Eloranta's model
• A pretty animation of the actinic flux as a pulse of light enters a cloud (calculated using the TDTS model):