New representation of water activity based on a single solute specific constant to parameterize the hygroscopic growth of aerosols in atmospheric models

Abstract. Water activity is a key factor in aerosol thermodynamics and hygroscopic growth. We introduce a new representation of water activity (a_w), which is empirically related to the solute molality (μ_s) through a single solute specific constant, ν_i. Our approach is widely applicable, considers the Kelvin effect and covers ideal solutions at high relative humidity (RH), including cloud condensation nuclei (CCN) activation. It also encompasses concentrated solutions with high ionic strength at low RH such as the relative humidity of deliquescence (RHD). The constant ν_i can thus be used to parameterize the aerosol hygroscopic growth over a wide range of particle sizes, from nanometer nucleation mode to micrometer coarse mode particles. In contrast to other a_w-representations, our ν_i factor corrects the solute molality both linearly and in exponent form x · a^x. We present four representations of our basic a_w-parameterization at different levels of complexity for different a_w-ranges, e.g. up to 0.95, 0.98 or 1. ν_i is constant over the selected a_w-range, and in its most comprehensive form, the parameterization describes the entire a_w range (0–1). In this work we focus on single solute solutions. ν_i can be pre-determined with a root-finding method from our water activity representation using an a_w−μ_s data pair, e.g. at solute saturation using RHD and solubility measurements. Our a_w and supersaturation (Köhler-theory) results compare well with the thermodynamic reference model E-AIM for the key compounds NaCl and (NH₄)₂SO₄ relevant for CCN modeling and calibration studies. Envisaged applications include regional and global atmospheric chemistry and climate modeling.