The method to derive aerosol size distributions from in situ stratospheric measurements from the University of Wyoming is modified to include an explicit counting efficiency function (CEF) to describe the channel-dependent instrument counting efficiency. This is motivated by Kovilakam and Deshler's (2015, ) discovery of an error in the calibration method applied to the optical particle counter (OPC40) developed in the late 1980s and used from 1991 to 2012. The method can be applied to other optical aerosol instruments for which counting efficiencies have been measured. The CEF employed is the integral of the Gaussian distribution representing the instrument response at any one aerosol channel, the aerosol counting efficiency. Results using the CEF are compared to previous derivations of aerosol size distributions (Deshler et al., 2003, ) applied to the measurements before and after Kovilakam and Deshler's correction of number concentration for the OPC40 calibration error. The CEF method is found, without any tuning parameter, to reproduce or improve upon the Kovilakam and Deshler's results, thus accounting for the calibration error without any external comparisons other than the laboratory determined counting efficiency at each aerosol channel. Moments of the new aerosol size distributions compare well with aerosol extinctions measured by Stratospheric Aerosol and Gas Experiment II and Halogen Occultation Experiment in the volcanic period 1991-1996, generally within 40%, the precision of OPC40 moments, and in the nonvolcanic period after 1996, generally within 20%. Stratospheric Aerosol and Gas Experiment II and Halogen Occultation Experiment estimates of aerosol surface area are generally in agreement with those derived using the new CEF method. Plain Language Summary Since 1971, balloon-borne instruments have been used to measure the size distribution of sub-micrometer-sized particles in the stratosphere. These particles, or aerosol, are important for two reasons: (1) They cool the planet by scattering sunlight back to space and (2) they facilitate chemical reactions, which destroy ozone. Ozone shields the Earth from harmful ultraviolet rays from the Sun. Stratospheric aerosol have also been measured from satellites since the 1980s using instruments which measure aerosol extinction, the extent to which sunlight is scattered or absorbed by stratospheric particles. The two measurement methods, satellite- and balloon-borne instruments, have had a long-standing discrepancy between satellite extinction measurements and balloon-borne measurements used to calculate extinction. This paper resolves that discrepancy through laboratory investigations of the counting efficiency of the balloon-borne instruments. When counting efficiency is included in the method to derive aerosol size distribution functions from the balloon-borne measurements, from which extinction and aerosol surface area can be calculated, the two measurement methods are in reasonable agreement. Resolving this discrepancy between the two instruments allows the local balloon-borne measurements to be used for testing the retrieval of aerosol surface area from the global satellite measurements. Stratospheric aerosol surface area is required for global climate models. Thus, this paper provides a basis to characterize the confidence, which can be placed in the global satellite estimates of aerosol surface area for the modeling community.
