By Jerry M. Straka
This ebook focuses in particular on bin and bulk parameterizations for the prediction of cloud and precipitation at numerous scales - the cloud scale, mesoscale, synoptic scale, and the worldwide weather scale. It presents a heritage to the elemental rules of parameterization physics, together with methods inquisitive about the creation of clouds, ice debris, liquid water, snow mixture, graupel and hail. It offers complete derivations of the parameterizations, permitting readers to construct parameterization programs, with various degrees of complexity in accordance with details within the ebook. Architectures for a number of dynamical types are given, within which parameterizations shape an important software for investigating huge non-linear numerical structures. version codes can be found on-line at www.cambridge.org/9780521883382. Written for researchers and complex scholars of cloud and precipitation microphysics, this e-book can also be a worthwhile reference for all atmospheric scientists thinking about types of numerical climate prediction.
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Additional info for Cloud and Precipitation Microphysics: Principles and Parameterizations
Nearly two decades after the empirical data in Fig. 8 R = 1 (mm hr -1) 100 0 1 2 D (mm) 3 4 Fig. 10. Distribution of number versus diameter for raindrops recorded at Ottawa, summer 1946. 0 mm hr 1. NDdD is the number of drops per cubic meter, of diameter between D and D þ dD. g. Feng and Beard 1991; Beard et al. 1991; Tokay and Beard 1996; Bringi et al. 1998; and Andsager et al. 1999). Nevertheless, for diameters greater than 1 mm, drops become increasingly oblate with size. Raindrops generally fall with their minor axis oriented in the vertical, though a rare few drops might be temporarily elongated vertically, possibly because of oscillations, collisions, or both.
LnðDx =Dnx Þ2 dDx 2s2x ! : ½lnðDx =Dnx Þ2 dDx 2s2x ð2:144Þ Dividing by Dnx gives 1 Ð Dx Dnx Deff ¼ Dnx 0 1 Ð Dx 0 2 exp exp Dnx ½lnðDx =Dnx Þ2 2s2x ½lnðDx =Dnx Þ2 2s2x d DDnxx : d DDnxx ð2:145Þ 44 Foundations of microphysical parameterizations Now letting u ¼ Dx/Dnx, 1 Ð Deff ¼ u2 exp Dnx 01 Ð u exp 0 ðln uÞ2 2s2x ðln uÞ2 2s2x du : ð2:146Þ du By letting y ¼ ln(u), u ¼ exp(y), du/u ¼ dy, so 1 Ð 1 Deff ¼ Dnx 1 Ð expð3yÞ exp expð2yÞ exp 1 y2 2s2x y2 2s2x dy ; ð2:147Þ dy where the limits of the integral change as stated above.
Finally it is necessary that f(D) needs to be readily normalizable. The spectral number density function n(D) is the concentration of particles per unit size interval from D to DD. The total number concentration is usually written as NT, and results from integrating the spectral density function over a given size interval such as zero to infinity. But it can, in theory, be any 19 20 Foundations of microphysical parameterizations interval of positive definite numbers. The slope intercept of a spectral number density function is given as N0.
Cloud and Precipitation Microphysics: Principles and Parameterizations by Jerry M. Straka