Inversion of aerosol-microphysical properties from lidar data

Motivation

One of the main topics in understanding the effect of aerosols on climate is the investigation of the spatial and temporal variability of microphysical properties of particles. These parameters are, for instance, mean (effective) radius, volume and surface-area concentration, and complex refractive index. Single-scattering albedo which is one of the key input parameters in climate forcing studies is derived from such microphysical parameter sets.

Data inversion algorithms are used to retrieve these parameters from the optical parameters which are derived from the lidar observations. The difficulty in developing such algorithms lies in the fact that the input optical data are connected to the investigated microphysical parameters through non-linear integral equations of the first kind (Fredholm equations), which cannot be solved analytically.

The numerical solution of these equations leads to the so called ill-posed inverse problem. Such problems are characterized by a strong sensitivity of the solution space toward uncertainties of the input data, the non-uniqueness of the solution space, and the incompleteness of the solution space. The solution space may still be correct in a mathematical sense, but might not necessarily reflect the physical conditions.

Basic equations

Fredholm integral equations of the first kind

Input of optical data

  • Input for inversion of optical data into microphysical parameters: Particle backscatter coefficients at 355, 400, 532, 710, 800, 1064 nm
  • Particle extinction coefficients at 355, 532 nm

 

Base functions

...are used to reconstruct the investigated particle size distribution (very simplified picture)

 

Kernel functions

  • … contain information on particle size and particle refractive index
  • backscatter efficiencies are highly structurized
  • backscatter efficiencies are much more dependent on complex refractive index than extinction efficiencies

Inversion

Therefore regularization (= stabilization) is needed

  • introduce constraints, such as smoothness and positivity of the particle size distribution
  • regularization reduces oscillation of solution

Output

The Algorithm delivers the following paramters:

  • effective particle radius - reff
  • particle volume size distribution - v(r)
  • total surface-area concentration - s
  • total number concentration - n
  • total volume concetration - v
  • refractive index (real part and imaginary part)
  • single-scattering albedo

 

Publications

Veselovskii, I., Kolgotin, A., Griaznov, V., Müller, D., Franke, K. and Whiteman, D. 2004. Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution. Appl. Optics, 43, 1180-1195.

Veselovskii, I., Kolgotin, A., Griaznov, V., Müller, D., Wandinger, U. and Whiteman, D. 2002. Inversion with regularization for the retrieval of tropospheric aerosol parameters from multiwavelength lidar sounding. Appl. Optics, 41, 3685-3699.

Müller, D., Wandinger, U., Althausen, D. and Fiebig, M. 2001. Comprehensive particle characterization from 3-wavelength Raman-lidar observations: Case study. Appl. Optics, 40, 4863-4869.

Müller, D., Wagner, F., Wandinger, U., Ansmann, A., Wendisch, M., Althausen, D. and Hoyningen-Huene von, W. 2000. Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: Experiment. Appl. Optics, 39, 1879-1892.

Müller, D., Wandinger, U. and Ansmann, A. 1999. Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: Simulation. Appl. Optics, 38, 2358-2368.

Müller, D., Wandinger, U. and Ansmann, A. 1999. Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: Theory. Appl. Optics, 38, 2346-2357.

Müller, D., Wandinger, U., Althausen, D., Mattis, I. and Ansmann, A. 1998. Retrieval of physical particle properties from lidar observations of extinction and backscatter at multiple wavelengths. Appl. Optics, 37, 2260-2263.