Precipitation efficiency

Precipitation efficiency is an important physical parameter for measuring the interaction between convection and its environment (Doswell et al., 1996; Ferrier et al., 1996; Tao et al., 2004). Its definition may vary. For large-scale applications involving cumulus parametrization (e.g. Kuo, 1965, 1974), the precipitation efficiency is defined as the ratio of the surface rain rate to the sum of the surface evaporation and vertically integrated moisture convergence, and is referred to as large-scale precipitation efficiency (LSPE). LSPE is similar to the precipitation efficiency defined by Braham (1952). For cloud-resolving models with cloud-microphysical parametriza-tion schemes (e.g. Li et al., 1999), the precipitation efficiency can be defined as the ratio of the surface rain rate to the sum of the vertically integrated condensation and deposition rates. This is referred to as cloud microphysics precipitation efficiency (CMPE). CMPE is similar to the precipitation efficiency defined by Weisman and Klemp (1982) and Lipps and Hemler (1986).

Li et al. (2002a) analyzed the domain-mean CMPE and found that the LSPE could be more than 100%, whereas the CMPE is less than 100%. The statistical analysis shows that the ratio of the CMPE to the LSPE is 1.2. The precipitation efficiency may depend on the environmental conditions and the strength of convection. Ferrier et al. (1996) showed that wind shear and updraft structure play an important role in determining the precipitation efficiency. Li et al. (2002a) showed that the CMPE increases with increasing mass-weighted mean temperature and surface rain rate. This suggests that precipitation processes are more efficient for the heavy rain regime in a warm environment.

Since the LSPE and the CMPE are expected to be the same based on physical considerations, the difference in Li et al. (2002a) is attributed in Sui et al. (2005) to the horizontal hydrometeor advection that is excluded in the domain-mean CMPE due to the cyclic lateral boundary condition. Sui et al. (2005) analyzed the grid data from the two-dimensional cloud-resolving simulations with the imposed TOGA COARE forcing and the three-dimensional MM5 cloud-resolving simulation of Typhoon Nari (Yang and Huang, 2004). The analysis of two-dimensional grid data through the root-mean-square differences and linear correlation coefficients shows that the sum of vapor condensation and deposition rates is approximately balanced by the sum of surface evaporation and vertically integrated moisture convergence. This relation leads to the statistical equivalence between the CMPE and the LSPE.

Analysis of the two-dimensional simulation further shows that the additional hydrome-teor converging into the atmospheric column would make the precipitation efficiency larger. When the hydrometeor convergence becomes the dominant term in the cloud budget, the CMPE can be larger than 100%, as found in light-rain conditions (<5mmh-1). On the other hand, a loss of clouds due to hydrometeors diverging out to the neighboring columns would make the CMPE smaller. This occurs mostly in heavy-rain conditions (>5mmh-1). The three-dimensional simulation of Typhoon Nari (2001) with more intense precipitation (compared to the TOGA COARE tropical convection) generally supports the two-dimension results.

Sui et al. (2007b) revisited the issue using the same two-dimensional cloud-resolving model simulation. They proposed more complete definitions of precipitation efficiency based on either the moisture budget (LSPE2) or the hydrometeor budget (CMPE2), which include all sources related to surface rainfall processes. They reached the following conclusions:

(1) LSPE2 and CMPE2 range from 0 to 100%;

(2) LSPE2 and CMPE2 are highly correlated;

(3) LSPE2 and CMPE2 are insensitive to the spatial scales of averaged data, and moderately sensitive to the time period of averaged data; (4) the simplified precipitation efficiencies of LSPE1 and CMPE1 appear to be good enough measures of precipitation efficiency in the heavy-rain conditions. CMPE2 (or CMPE1) is a physically more straightforward definition of precipitation efficiency than LSPE2 (or LSPE1). But the former can only be estimated in models with explicit parametrization of cloud mi-crophysics which is model dependent, while the latter may be estimated based on currently available assimilation data of satellite and sounding measurements.

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