Inverse modelling of Köhler theory – Part 1: A response surface analysis of CCN spectra with respect to surface-active organic species
Authors: Lowe Samuel , Partridge Daniel , Topping David , Stier Philip 
Published: February 2016

Abstract. In this study a novel framework for inverse modelling of CCN spectra is developed using Köhler theory. The framework is established by carrying out an extensive parametric sensitivity analysis of CCN spectra using 2-dimensional response surfaces. The focus of the study is to assess the relative importance of aerosol physicochemical parameters while accounting for bulk-surface partitioning of surface active organic species. By introducing an Objective Function (OF) that provides a diagnostic metric for deviation of modelled CCN concentrations from observations, a novel method of analysing CCN sensitivity over a range of atmospherically relevant supersaturations, corresponding to broad range of cloud types and updraft velocities, is presented. Such a scalar metric facilitates the use of response surfaces as a tool for visualising CCN sensitivity over a range of supersaturations to two parameters simultaneously. Using response surfaces, the posedness of the problem as suitable for further study using inverse modelling methods in a future study is confirmed. The organic fraction of atmospheric aerosols often includes surface-active organics. Partitioning of such species between the bulk and surface phases has implications for both the Kelvin and Raoult terms in Köhler theory. As such, the analysis conducted here is carried out for a standard Köhler model as well more sophisticated partitioning schemes seen in previous studies. Using Köhler theory to model CCN concentrations requires knowledge of many physicochemical parameters some of which are difficult to measure in-situ at the scale of interest. Therefore, novel methodologies such as the one developed here are required to probe the entire parameter space of aerosol-cloud interaction problems of high dimensionality and provide global sensitivity analyses (GSA) to constrain parametric uncertainties. In this study, for all partitioning schemes and environments considered, the accumulation mode size distribution parameters, surface tension σ, organic:inorganic mass ratio α, insoluble fraction and solution ideality ϕ were found to have significant sensitivity. In particular, the number concentration of the accumulation mode N2 and surface tension σ showed a high degree of sensitivity. The complete treatment of bulk-surface partitioning is found to model CCN spectra similar to those calculated using classical Köhler theory with the surface tension of a pure water drop, as found in traditional sensitivity analysis studies. In addition, the sensitivity of CCN spectra to perturbations in the partitioning parameters K and Γ was found to be negligible. As a result, this study supports previously held recommendations that complex surfactant effects might be neglected and continued use of classical Köhler theory in GCMs is recommended to avoid additional computational burden. In this study we do not include all possible composition dependent processes that might impact CCN activation potential. Nonetheless, this study demonstrates the efficacy of the applied sensitivity analysis to identify important parameters in those processes and will be extended to facilitate a complete GSA using the Monte Carlo Markov Chain (MCMC) algorithm class. As parameters such as σ and ϕ are difficult to measure at the scale of interest in the atmosphere they can introduce considerable parametric uncertainty to models and therefore they are particularly good candidates for a future parameter calibration study that facilitates a global sensitivity analysis (GSA) using automatic search algorithms.