Assumptions made in the analysis of both Raman lidar measurements of aerosol extinction and differential absorption lidar (DIAL) measurements of an absorbing species are tested. Statistical analysis techniques are used to enhance the estimation of aerosol extinction and aerosol extinction error that is usually handled using a linear model. It is determined that the most probable extinction value can differ from that of the linear assumption by up to 10% and that differences larger than 50% can occur in the calculation of extinction error. Ignoring error in the number density alters the calculated extinction by up to 3% and that of extinction error by up to 10%. The preceding results were obtained using the least-squares technique. The least-squares technique assumes that the data being regressed are normally distributed. However, the quantity that is usually regressed in aerosol extinction and DIAL calculations is not normally distributed. A technique is presented that allows the required numerical derivative to be determined by regressing only normally distributed data. The results from this technique are compared with the usual procedure. The same concerns raised here regarding appropriate choice of a model in the context of aerosol extinction calculations should apply to DIAL calculations of absorbing species such as water vapor or ozone as well because the numerical derivative that is required is identical.
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