By Jerry M. Straka
This ebook focuses particularly on bin and bulk parameterizations for the prediction of cloud and precipitation at a variety of scales - the cloud scale, mesoscale, synoptic scale, and the worldwide weather scale. It presents a heritage to the basic rules of parameterization physics, together with approaches fascinated about the construction of clouds, ice debris, liquid water, snow mixture, graupel and hail. It provides complete derivations of the parameterizations, permitting readers to construct parameterization programs, with various degrees of complexity in line with info within the publication. Architectures for a number of dynamical types are given, within which parameterizations shape an important device for investigating huge non-linear numerical platforms. version codes can be found on-line at www.cambridge.org/9780521883382. Written for researchers and complicated scholars of cloud and precipitation microphysics, this e-book is additionally a necessary reference for all atmospheric scientists interested by types of numerical climate prediction.
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Additional resources for Cloud and Precipitation Microphysics: Principles and Parameterizations
10 and Fig. g. Rauber et al. 1991; Young 1993; Sauvageot and Lacaux 1995; and Joss and Zawadski 1997). Even though the negative-exponential distribution functions fit observed raindrop distributions well, there is indication that gamma distributions may provide a better fit, especially for raindrops of sizes less than 1 mm in diameter (Fig. 10 and Fig. 11). Schoenberg-Ferrier (1994) also noted this and suggested using gamma distributions for parameterization of raindrop distributions. However, it should be stated that observations of raindrop distributions are highly variable (Ulbrich 1983).
11 The third moment, mixing ratio and characteristic diameter The mixing ratio Qx of a hydrometeor species is related to mass, which is related to volume, and is written in terms of the third moment. For a spherical hydrometeor and the complete gamma distribution, 1 Qx ¼ r 1 ð ax Dbx x 0 ! NTx anxx mx Dx nx mx 1 Dx m x Dx d : exp ax Àðnx Þ Dnx Dnx Dnx ð2:98Þ Dividing by Dnx produces NTx anxx mx Dbnxx Qx ¼ ax Àðnx Þ r 1 ð Dx Dnx bx Dx Dnx nx mx 1 exp ax Dx Dnx ! 5 Gamma distributions 37 for the gamma distribution, the mixing ratio is Qx ¼ ax NTx Dbnxx Àðnx þ bx Þ ; r Àðnx Þ ð2:102Þ and for the negative-exponential distribution, Qx ¼ ax NTx Dbnxx Àð1 þ bx Þ: r ð2:103Þ Notice that there is a characteristic diameter Dnx to the bx power in the equations, which for a spherical hydrometeor is equal to three.
3 Power laws For bulk microphysical parameterizations it is advantageous to use power laws for mass, density, terminal velocity, and other necessary variables if possible, as these are amenable to integration with the various forms of the gamma function and log-normal spectral density functions. With bin microphysical parameterizations, it is not so important that power laws be used because there are no spectral density functions used. g. collection growth) a mass diameter relationship is needed.