Abstract
Abstract. A parameterization for the collision–coalescence process is presented based on the methodology of basis functions. The whole drop spectrum is depicted as a linear combination of two lognormal distribution functions, leaving no parameters fixed. This basis function parameterization avoids the classification of drops in artificial categories such as cloud water (cloud droplets) or rainwater (raindrops). The total moment tendencies are predicted using a machine learning approach, in which one deep neural network was trained for each of the total moment orders involved. The neural networks were trained and validated using randomly generated data over a wide range of parameters employed by the parameterization. An analysis of the predicted total moment errors was performed, aimed to establish the accuracy of the parameterization at reproducing the integrated distribution moments representative of physical variables. The applied machine learning approach shows a good accuracy level when compared to the output of an explicit collision–coalescence model.
Highlights
Drop populations are represented using drop size distributions (DSDs)
Total mass remains constant during the entire simulation, with a proportional mass transfer between f1 and f2. These results demonstrate that the P-deep neural networks (DNNs) parameterization behavior is physically sound, with remarkable consistency between the different variables calculated, both bulk (N, r and liquid water contents (LWCs)) and DSD related
A hybrid parameterization for the process of collision–coalescence based on the methodology of basis functions employing a linear combination of two lognormal distributions was formulated and implemented
Summary
Drop populations are represented using drop size distributions (DSDs). The first attempt at characterizing drop spectra in space as opposed to distributions over a surface was made by Marshall and Palmer (1948), who employed exponential distributions based on drop diameter to describe the DSDs. More recently, the use of a three-parameter gamma distribution has shown good agreement with observations (Ulbrich, 1983). Lognormal distributions have shown a better squared-error fit to measurements of rain DSDs than gamma or exponential distributions (Feingold and Levin, 1986; Pruppacher and Klett, 2010). Some authors have employed this type of distribution function, which is lognormal, to parameterize cloud processes with promising results (Clark, 1976; Feingold et al, 1998; Huang, 2014)
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