**6. References**

70 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

critical dimensions of the ice embryo are several micrometers, and such process is not favoured. However, the droplet can contain impurities, and some of them may promote collection of water droplets into an ice-like structure to form a ice-like embryo with dimension already beyond the critical size for glaciations. Such particles are termed *ice nuclei* and the process they start is termed *heterogeneous freezing*. Such process can start not only within the droplet, but also upon contact of the ice nucleus with the surface of the droplet (*contact nucleation*) or directly by deposition of ice on it from the water vapour phase (*deposition nucleation*). Good candidates to act as ice nuclei are those particle with molecular structure close to the hexagonal ice crystallography. Some soil particles, some organics and even some bacteria are effective nucleators, but only one out of 103-105 atmospheric particles can act as an ice nucleus. Nevertheless ice particles are present in clouds in concentrations which are orders of magnitude greater than the presence of ice nuclei. Hence, ice multiplication processes must be at play, like breaking of ice particles upon collision, to

Ice particles can grow from the vapour phase as in the case of water droplets. In a mixed phase cloud below 0°C, a much greater supersaturation is reached with respect to ice that can reach several percents, than with respect to water, which hardly exceed 1%. Hence ice particles grows faster than droplets and, since this deplete the vapour phase around them, it may happen that around a growing ice particle, water droplets evaporate. Ice can form in a variety of shapes, whose basic habits are determined by the temperature at which they grow. Another process of growth in a mixed cloud is by *riming*, that is by collision with supercooled droplets that freeze onto the ice particle. Such process is responsible of the

A process effective in cold clouds is the *aggregation* of ice particles between themselves,

A brief overview of some topic of relevance in atmospheric thermodynamic has been provided, but much had to remain out of the limits of this introduction, so the interested reader is encouraged to further readings. For what concerns moist thermodynamics and convection, the reader can refer to chapters in introductory atmospheric science textbooks like the classical Wallace and Hobbs (2006), or Salby (1996). At a higher level of deepening the classical reference is Iribarne and Godson (1973). For the reader who seeks a more theoretical approach, Zdunkowski and Bott (2004) is a good challenge. Convection is thoughtfully treated in Emmanuel (1994) while a sound review is given in the article of Stevens (2005). For what concerns the microphysics of clouds, the reference book is Pruppacher and Klett (1996). A number of seminal journal articles dealing with the thermodynamics of the general circulation of the atmosphere can be cited: Goody (2003), Pauluis and Held (2002), Renno and Ingersoll (2008), Pauluis et al. (2008) and references therein. Finally, we would like to suggest the Bohren (2001) delightful book, for which a scientific or mathematical background is not required, that explores topics in meteorology

when they have different shapes and/or dimension, hence different fall speeds.

create ice splinterings that enhance the number of ice particles.

**4.5 Growth of ice particles** 

formation of hailstones.

and basic physics relevant to the atmosphere.

**5. Conclusion** 


**Thermodynamic Aspects of** 

<sup>1</sup>*Key Laboratory of Meteorological Disaster of Ministry of Education* 

Precipitation efficiency is one of important meteorological parameters and has been widely used in operational precipitation forecasts (e.g., Doswell et al., 1996). Precipitation efficiency has been defined as the ratio of precipitation rate to the sum of all precipitation sources from water vapor budget (e.g., Auer and Marwitz, 1968; Heymsfield and Schotz, 1985; Chong and Hauser, 1989; Dowell et al., 1996; Ferrier et al., 1996; Li et al., 2002; Sui et al., 2005) after Braham (1952) calculated precipitation efficiency with the inflow of water vapor into the storm through cloud base as the rainfall source more than half century ago. Sui et al. (2007) found that the estimate of precipitation efficiency with water vapor process data can be more than 100% or negative because some rainfall sources are excluded or some rainfall sinks are included. They defined precipitation efficiency through the inclusion of all rainfall sources and the exclusion of all rainfall sinks from surface rainfall budget derived by Gao et

In additional to water vapor processes, thermal processes also play important roles in the development of rainfall since precipitation is determined by environmental thermodynamic conditions via cloud microphysical processes. The water vapor convergence and heat divergence and its forced vapor condensation and depositions in the precipitation systems could be major sources for precipitation while these water vapor and cloud processes could give some feedback to the environment. Gao et al. (2005) derived a water vapor related surface rainfall budget through the combination of cloud budget with water vapor budget. Gao and Li (2010) derived a thermally related surface rainfall budget through the combination of cloud budget with heat budget. In this chapter, precipitation efficiency is defined from the thermally related surface rainfall budget (*PEH*) and is calculated using the data from the two-dimensional (2D) cloud-resolving model simulations of a pre-summer torrential rainfall event over southern China in June 2008 (Wang et al., 2010; Shen et al., 2011a, 2011b) and is compared with the precipitation efficiency defined from water vapor related surface rainfall budget (Sui et al., 2007) to study the efficiency in thermodynamic

The impacts of ice clouds on the development of convective systems have been intensively studied through the analysis of cloud-resolving model simulations (e.g., Yoshizaki, 1986;

al. (2005), which fixed precipitation efficiency to the normal range of 0-100%.

aspect of the pre-summer heavy rainfall system.

**1. Introduction** 

*Nanjing University of Information Science and Technology 2NOAA/NESDIS/Center for Satellite Applications and Research* 

**Precipitation Efficiency** 

Xinyong Shen1 and Xiaofan Li2

*1China 2USA* 

Zdunkowski W. & Bott A., (2004), *Thermodynamics of the Atmosphere: A Course in Theoretical Meteorology*, Cambridge University Press, Cambridge. **3** 
