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We theoretically and numerically investigate the problem of assimilatingmultiwavelength lidar observations of extinction and backscatteringcoefficients of aerosols into a chemical transport model. More specifically,we consider the inverse problem of determining the chemical composition ofaerosols from these observations. The main questions are how much informationthe observations contain to determine the particles' chemical composition,and how one can optimize a chemical data assimilation system to make maximumuse of the available information. We first quantify the information contentof the measurements by computing the singular values of the scaledobservation operator. From the singular values we can compute the number ofsignal degrees of freedom, Ns, and the reduction in Shannonentropy, H. As expected, the information content as expressed by eitherNs 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 errorvariance, the lower the growth rate of Ns 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 intosignal-related and noise-related components. We incorporate these results ina chemical data assimilation algorithm by introducing weak constraints thatrestrict the assimilation algorithm to acting on the signal-related modelvariables only. This ensures that the information contained in themeasurements is fully exploited, but not overused. Numerical tests show thatthe constrained data assimilation algorithm provides a solution to theinverse problem that is considerably less noisy than the correspondingunconstrained algorithm. This suggests that the restriction of the algorithmto the signal-related model variables suppresses the assimilation of noise inthe observations

How much information do extinction and backscattering measurements contain about the chemical composition of atmospheric aerosol?