Michael Kahnert^{1,2} and Emma Andersson^{2}
^{1}Research Department, Swedish Meteorological and Hydrological Institute,
Folkborgsvägen 17, 601 76 Norrköping, Sweden

^{2}Department of Earth and Space Science,
Chalmers University of Technology, 412 96 Gothenburg, Sweden

Received: 10 Oct 2016 – Discussion started: 10 Nov 2016

Revised: 09 Feb 2017 – Accepted: 11 Feb 2017 – Published: 09 Mar 2017

Abstract. We theoretically and numerically investigate the problem of assimilating multiwavelength lidar observations of extinction and backscattering coefficients of aerosols into a chemical transport model. More specifically, we consider the inverse problem of determining the chemical composition of aerosols from these observations. The main questions are how much information the observations contain to determine the particles' chemical composition, and how one can optimize a chemical data assimilation system to make maximum use of the available information. We first quantify the information content of the measurements by computing the singular values of the scaled observation operator. From the singular values we can compute the number of signal degrees of freedom, *N*_{s}, and the reduction in Shannon entropy, *H*. As expected, the information content as expressed by either *N*_{s} or *H* grows as one increases the number of observational parameters and/or wavelengths. However, the information content is strongly sensitive to the observation error. The larger the observation error variance, the lower the growth rate of *N*_{s} or *H* with increasing number of observations. The right singular vectors of the scaled observation operator can be employed to transform the model variables into a new basis in which the components of the state vector can be partitioned into signal-related and noise-related components. We incorporate these results in a chemical data assimilation algorithm by introducing weak constraints that restrict the assimilation algorithm to acting on the signal-related model variables only. This ensures that the information contained in the measurements is fully exploited, but not overused. Numerical tests show that the constrained data assimilation algorithm provides a solution to the inverse problem that is considerably less noisy than the corresponding unconstrained algorithm. This suggests that the restriction of the algorithm to the signal-related model variables suppresses the assimilation of noise in the observations.

**Citation:**
Kahnert, M. and Andersson, E.: How much information do extinction and backscattering measurements contain about the chemical composition of atmospheric aerosol?, Atmos. Chem. Phys., 17, 3423-3444, doi:10.5194/acp-17-3423-2017, 2017.