Statistical estimation of stratospheric particle size distribution by combining optical modelling and lidar scattering measurements J. Jumelet, S. Bekki, C. David, and P. Keckhut UPMC Paris 6, Service d'Aéronomie du CNRS/IPSL, Paris, France
Abstract. A method for estimating the stratospheric particle size distribution from
multiwavelength lidar measurements is presented. It is based on matching
measured and model-simulated backscatter coefficients. The lidar backscatter
coefficients measured at the three commonly used wavelengths 355, 532 and
1064 nm are compared to a precomputed look-up table of model-calculated
values. The optical model assumes that particles are spherical and that
their size distribution is unimodal. This inverse problem is not trivial
because the optical model is highly non-linear with a strong sensitivity to
the size distribution parameters in some cases. The errors in the lidar
backscatter coefficients are explicitly taken into account in the
estimation. The method takes advantage of the statistical properties of the
possible solution cluster to identify the most probable size distribution
parameters. In order to discard model-simulated outliers resulting from the
strong non-linearity of the model, solutions farther than one standard
deviation of the median values of the solution cluster are filtered out,
because the most probable solution is expected to be in the densest part of
the cluster. Within the filtered solution cluster, the estimation algorithm
minimizes a cost function of the misfit between measurements and model
Two validation cases are presented on Polar Stratospheric Cloud (PSC) events
detected above the ALOMAR observatory (69° N – Norway). A first
validation is performed against optical particle counter measurements
carried out in January 1996. In non-depolarizing regions of the cloud (i.e.
spherical particles), the parameters of an unimodal size distribution and
those of the optically dominant mode of a bimodal size distribution are
quite successfully retrieved, especially for the median radius and the
geometrical standard deviation. As expected, the algorithm performs poorly
when solid particles drive the backscatter coefficient. A small bias is
identified in modelling the refractive index when compared to previous works
that inferred PSC type Ib refractive indices. The accuracy of the size
distribution retrieval is improved when the refractive index is set to the
value inferred in the reference paper.
Our results are then compared to values retrieved with another similar
method that does not account for the effect of the measurements errors and
the non-linearity of the optical model on the likelihood of the solution.
The case considered is a liquid PSC observed over northern Scandinavia on
January 2005. An excellent agreement is found between the two methods when
our algorithm is applied without any statistical filtering of the solution
cluster. However, the solution for the geometrical standard deviation
appears to be rather unlikely with a value close to unity (σ≈1.04).
When our algorithm is applied with solution filtering, a more
realistic value of the standard deviation (σ≈1.27) is
found. This highlights the importance of taking into account the non
linearity of the model together with the lidar errors, when estimating
particle size distribution parameters from lidar measurements.
Citation: Jumelet, J., Bekki, S., David, C., and Keckhut, P.: Statistical estimation of stratospheric particle size distribution by combining optical modelling and lidar scattering measurements, Atmos. Chem. Phys., 8, 5435-5448, doi:10.5194/acp-8-5435-2008, 2008.