Post-flight analysis of detailed size distributions of warm cloud droplets, as determined in situ by cloud and aerosol spectrometers

Warm clouds, consisting of liquid cloud droplets, play an important role in modulating the amount of incoming solar radiation to Earth's surface and thus the climate. The size and number concentration of these cloud droplets control the reflectance of the cloud, the formation of precipitation and ultimately the lifetime of the cloud. Therefore, in situ observations of the number and diameter of cloud droplets are frequently performed with cloud and aerosol spectrometers, which determine the optical diameters of cloud particles (in the range of up to a few tens of micrometers) by measuring their forward-scattering cross sections in visible light and comparing these values with Mie theoretical computations. The use of such instruments must rely on a fast working scheme consisting of a limited pre-defined uneven grid of cross section values that corresponds to a theoretically derived uneven set of size intervals (bins). However, as more detailed structural analyses of warm clouds are needed to improve future climate projects, we present a new numerical post-flight methodology using recorded particle-by-particle sample files. The Mie formalism produces a complicated relationship between a particle's diameter and its forward-scattering cross section. This relationship cannot be expressed in an analytically closed form, and it should be numerically computed point by point, over a certain grid of diameter values. The optimal resolution required for constructing the diagram of this relationship is therefore analyzed. Cloud particle statistics are further assessed using a fine grid of particle diameters in order to capture the finest details of the cloud particle size distributions. The possibility and the usefulness of using coarser size grids, with either uneven or equal intervals, is also discussed. For coarse equidistant size grids, the general expressions of cloud microphysical parameters are calculated and the ensuing relative errors are discussed in detail. The proposed methodology is further applied to a subset of measured data, and it is shown that the overall uncertainties in computing various cloud parameters are mainly driven by the measurement errors of the forward-scattering cross section for each particle. Finally, the influence of the relatively large imprecision in the real and imaginary parts of the refractive index of cloud droplets on the size distributions and on the ensuing cloud parameters is analyzed. It is concluded that, in the presence of high atmospheric loads of hydrophilic and light-absorbing aerosols, such imprecisions may drastically affect the reliability of the cloud data obtained with cloud and aerosol spectrometers. Some complementary measurements for improving the quality of the cloud droplet size distributions obtained in post-flight analyses are suggested.