Thermodynamic Aspects of Precipitation Efficiency

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 al. (2005), which fixed precipitation efficiency to the normal range of 0-100%. 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 aspect of the pre-summer heavy rainfall system. 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;


Introduction
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 al. (2005), which fixed precipitation efficiency to the normal range of 0-100%.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., 2011aShen et al., , 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 aspect of the pre-summer heavy rainfall system.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;74 Nicholls, 1987;Fovell and Ogura, 1988;Tao and Simpson, 1989;McCumber et al., 1991;Tao et al., 1991;Liu et al., 1997;Grabowski et al., 1999;Wu et al., 1999;Li et al., 1999;Grabowski and Moncrieff, 2001;Wu, 2002;Grabowski, 2003;Gao et al., 2006;Ping et al., 2007).Wang et al. (2010) studied microphysical and radiative effects of ice clouds on a pre-summer heavy rainfall event over southern China during 3-8 June 2008 through the analysis of sensitivity experiments and found that microphysical and radiative effects of ice clouds play equally important roles in the pre-summer heavy rainfall event.The total exclusion of ice microphysics decreased model domain mean surface rain rate primarily through the weakened convective rainfall caused by the exclusion of radiative effects of ice clouds in the onset phase and through the weakened stratiform rainfall caused by the exclusion of ice microphysical effects in the development and mature phases, whereas it increased the mean rain rate through the enhanced convective rainfall caused by the exclusion of ice microphysical effects in the decay phase.Thus, effects of ice clouds on precipitation efficiencies are examined through the analysis of the pre-summer heavy rainfall event in this chapter.Precipitation efficiency is defined in section 2. Pre-summer heavy rainfall event, model, and sensitivity experiments are described in section 3. The control experiment is discussed in section 4. Radiative and microphysical effects of ice clouds on precipitation efficiency and associated rainfall processes are respectively examined in sections 5 and 6.The conclusions are given in section 7.

Definitions of precipitation efficiency
The budgets for specific humidity (q v ), temperature (T), and cloud hydrometeor mixing ratio (q l ) in the 2D cloud resolving model used in this study can be written as qu q wq w q w q w q S txz z where Following Gao et al. (2005) and Sui and Li (2005), the cloud budget (1c) and water vapor budget (1a) are mass integrated and their budgets can be, respectively, written as where where H s is surface sensible heat flux.

Pre-summer rainfall case, model, and experiments
The pre-summer rainy season is the major rainy season over southern China, in which the rainfall starts in early April and reaches its peak in June (Ding, 1994).Although the rainfall is a major water resource in annual water budget, the torrential rainfall could occur during the pre-summer rainfall season and can lead to tremendous property damage and fatalities.
In 1998, for instance, the torrential rainfall resulted in over 30 billion USD in damage and over 100 fatalities.Thus, many observational analyses and numerical modeling have been contributed to understanding of physical processes responsible for the development of presummer torrential rainfall (e.g., Krishnamurti et al., 1976;Tao and Ding, 1981;Wang and Li, 1982;Ding and Murakami, 1994;Simmonds et al., 1999).Recently, Wang et al. (2010) and Shen et al. (2011aShen et al. ( , 2011b) conducted a series of sensitivity experiments of the pre-summer torrential rainfall occurred in the early June 2008 using 2D cloud-resolving model and studied effects of vertical wind shear, radiation, and ice clouds on the development of torrential rainfall.They found that these effects on torrential rainfall are stronger during the decay phase than during the onset and mature phases.During the decay phase of convection on 7 June 2008, the increase in model domain mean surface rain rate resulting from the exclusion of vertical wind shear is associated with the slowdown in the decrease of perturbation kinetic energy due to the exclusion of barotropic conversion from mean kinetic energy to perturbation kinetic energy.The increase in domain-mean rain rate resulting from the exclusion of cloud radiative effects is related to the enhancement of condensation and associated latent heat release as a result of strengthened radiative cooling.The increase in the mean surface rain rate is mainly associated with the increase in convective rainfall, which is in turn related to the local atmospheric change from moistening to drying.The increase in mean rain rate caused by the exclusion of ice clouds results from the increases in the mean net condensation and mean latent heat release caused by the strengthened mean radiative cooling associated with the removal of radiative effects of ice clouds.The increase in mean rain rate caused by the removal of radiative effects of water clouds corresponds to the increase in the mean net condensation.
The pre-summer torrential rainfall event studied by Wang et al. (2010) and Shen et al. (2011aShen et al. ( , 2011b) ) will be revisited to examine the thermodynamic aspects of precipitation efficiency and effects of ice clouds on precipitation efficiency.The cloud-resolving model (Soong and Ogura, 1980;Soong and Tao, 1980;Tao and Simpson, 1993) used in modeling the pre-summer torrential rainfall event in Wang et al. (2010) is the 2D version of the model (Sui et al., 1994(Sui et al., , 1998) ) that was modified by Li et al. (1999).The model is forced by imposed large-scale vertical velocity and zonal wind and horizontal temperature and water vapor advections, which produces reasonable simulation through the adjustment of the mean thermodynamic stability distribution by vertical advection (Li et al., 1999).The modifications by Li et al. (1999) include: (1) the radius of ice crystal is increased from m (Hsie et al., 1980) to 100m (Krueger et al., 1995) in the calculation of growth of snow by the deposition and riming of cloud water, which yields a significant increase in cloud ice; (2) the mass of a natural ice nucleus is replaced by an average mass of an ice nucleus in the calculation of the growth of ice clouds due to the position of cloud water; (3) the specified cloud single scattering albedo and asymmetry factor are replaced by those varied with cloud and environmental thermodynamic conditions.Detailed descriptions of the model can be found in Gao and Li (2008).Briefly, the model includes prognostic equations for potential temperature and specific humidity, prognostic equations for hydrometeor mixing ratios of cloud water, raindrops, cloud ice, snow, and graupel, and perturbation equations for zonal wind and vertical velocity.The model uses the cloud microphysical parameterization schemes (Lin et al., 1983;Rutledge andHobbs, 1983, 1984;Tao et al., 1989;Krueger et al., 1995) and solar and thermal infrared radiation parameterization schemes (Chou et al., 1991(Chou et al., , 1998;;Chou and Suarez, 1994).The model uses cyclic lateral boundaries, and a horizontal domain of 768 km with 33 vertical levels, and its horizontal and temporal resolutions are 1.In the control experiment (C), the model is integrated with the initial vertical profiles of temperature and specific humidity from NCEP/GDAS at 0200 LST 3 June 2008.The model is integrated with the initial conditions and constant large-scale forcing at 0200 LST 3 June for 6 hours during the model spin-up period and the 6-hour model data are not used for analysis.The comparison in surface rain rate between the simulation and rain gauge observation averaged from 17 stations over southern Guangdong and Guangxi reveals a fair agreement with a gradual increase from 3-6 June and a rapid decrease from 6-7 June (Fig. 2).Their RMS difference (0.97 mm h -1 ) is significantly smaller than the standard derivations of simulated (1.22 mm h -1 ) and observed (1.26 mm h -1 ) rain rates.The differences in surface rain rate between the simulation and observation can reach 2 mm h - 1 , as seen in the previous studies (e.g., Li et al., 1999;Xu et al., 2007;Wang et al., 2009).The differences may partially be from the comparison of small hourly local sampling of rain gauge observations over 35% of model domain over land and no rain gauge observations over 65% of model domain over ocean with large model domain averages of model data in the control experiment with imposed 6-hourly large-scale forcing.The convection may be affected by land-ocean contrast and orography; these effects are included in the largescale forcing imposed in the model.Fig. 2. Time series of surface rain rates (mm h -1 ) simulated in the control experiment (solid) and from rain gauge observation (dash).
Fig. 3. Time series of model domain means of (a) P SWV (dark solid), Q WVT (light solid), Q WVF (short dash), Q WVE (dot), Q CM (dot dash), and (b) P SH (dark solid), S HT (light solid), S HF (short dash), S HS (dot), S LHLF (long short dash), S RAD (long dash), and To investigate effects of ice clouds on precipitation efficiency, two sensitivity experiments are examined in this study.Experiment CNIR is identical to C except that the mixing ratios of ice hydrometeor are set to zero in the calculation of radiation.Experiment CNIR is compared with C to study radiative effects of ice clouds on rainfall responses to the largescale forcing.Experiment CNIM is identical to C except in CNIM ice clouds (the ice hydrometeor mixing ratio and associated microphysical processes) are excluded.The comparison between CNIM and CNIR reveals impacts of the removal of microphysical efficient of ice clouds on rainfall responses to the large-scale forcing in the absence of radiative effects of ice clouds.The hourly model simulation data are used in the following discussions of this study.

The control experiment: C
Model domain mean surface rain rate starts on 3 June 2008 with the magnitude of about 1 mm h -1 (Fig. 3), which corresponds to the weak upward motions with a maximum of 2 cm s -1 at 6-8 km (Fig. 1a).The rain rate increases to 2 mm h -1 as the upward motions increase up to over 6 cm s -1 on 4 June.When the upward motions weaken in the evening of 4 June and a weak downward motion occurs near the surface, the mean rainfall vanishes.As upward motions pick their strengths on 5 June, the mean rain rate intensifies (over 2 mm h -1 ).The mean rainfall reaches its peak on 6 June (over 4 mm h -1 ) as the upward motions have a maximum of over 20 cm s -1 .The upward motions rapidly weaken on 7 June, which leads to the significant reduction in the mean rainfall.Thus, four days (4, 5, 6, and 7 June) are defined as the onset, development, mature, and decay phases of the rainfall event, respectively.During 3-6 June, the mean rainfall is mainly associated with the mean water vapor convergence (Q WVF >0) in water vapor related surface rainfall budget and the mean heat divergence (S HF >0) in thermally related surface rainfall budget.Local atmospheric drying (Q WVT >0) and moistening (Q WVT <0) occur while the mean local atmospheric cooling (S HT <0) prevails.The mean hydrometeor loss/convergence (Q CM ) has small hourly fluctuations.The mean radiative heating during the daytime and mean radiative cooling during the nighttime have the much smaller magnitudes than the mean heat divergence and the mean local heat change do in thermally related surface rainfall budget.On 7 June, the mean water vapor related surface rainfall budget shows that the rainfall is associated with local atmospheric drying while water vapor divergence prevails.The mean thermally related surface rainfall budget reveals that the rainfall is related to heat divergence while the heat divergence cools local atmosphere.The calculation of precipitation efficiency using model domain mean model simulation data shows that PEWV generally is higher than PWH (Fig. 4a) because the rainfall source from the mean water vapor convergence in water vapor related surface rainfall budget is weaker than the rainfall source from the mean heat divergence in thermally related surface rainfall budget (Fig. 3).This suggests that the precipitation system is more efficient in the consumption of rainfall source from water vapor than in the consumption of the rainfall source from heat.The root-mean-squared (RMS) difference between PEWV and PEH is 24.4%.Both PEWV and PEH generally increase as surface rain rate increases (Fig. 5a).This indicates that the precipitation system generally is more efficient for high surface rain rates than for low surface rain rates.The ranges of PEWV and PEH are smaller when surface rain rate is higher than 3 mm h -1 (70-100%) than when surface rain rate is lower than 3 mm h -1 (0-100%).Units are % for PEWV and PEH and mm h -1 for P S .
Fig. 6.Time series of contributions of model domain mean of (a) P (dark solid), Q WVT (light solid), Q WVF (short dash), Q WVE (dot), Q CM (dot dash), and (b) P SH (dark solid), S HT (light solid), S HF (short dash), S HS (dot), S LHLF (long short dash), S RAD (long dash), and Q CM (dot dash) from convective regions in C. Unit is mm h -1 .
Model domain mean surface rainfall consists of convective and stratiform rainfall.
Convective rainfall differs from stratiform rainfall in four ways.First, convective rain rates are higher than stratiform rain rates.Second, convective rainfall is associated with stronger horizontal reflectivity gradients than stratiform rainfall.Third, upward motions associated with convective rainfall are much stronger than those associated with stratiform rainfall.Fourth, the accretion of cloud water by raindrops via collisions in strong updraft cores and the vapor deposition on ice particles are primary microphysical processes that are responsible for the development of convective and stratiform rainfall,respectively (Houghton 1968).The convective-stratiform rainfall partitioning scheme used in this study is developed by Tao and Simpson (1993) and modified by Sui et al. (1994).This scheme partitions each vertical column containing clouds in 2-D x-z framework into convective or stratiform based on the following criterion.Model grid point is identified as convective if it has a rain rate twice as large as the average taken over the surrounding four grid points, the one grid point on either side of this grid point, and any grid point with a rain rate of 20 mm h -1 or more.All non-convective cloudy points are considered as stratiform.In addition, grid points over stratiform regions are further checked and identified as convective when following conditions are met.Over raining stratiform regions, cloud water below the melting level is greater than 0.5 g kg -1 or the maximum updraft above 600 hPa exceeds 5 m s -1 , or over non-raining stratiform regions, cloud water mixing ratio of 0.025 g kg -1 or more exists or the maximum updraft exceeds 5 m s -1 below the melting level.Convective rain rate (Fig. 6) is much higher than stratiform rain rate (Fig. 7) and mainly accounts for model domain mean surface rain rate (Fig. 3).Over convective regions, rainfall is associated with water vapor convergence in water vapor related surface rainfall budget (Fig. 6a) and heat divergence in thermally related surface rainfall budget (Fig. 6b).Q CM is negative over convective regions whereas Q CM is positive over raining stratiform regions (Fig. 8), which indicates the transport of hydrometeor concentration from convective regions (Q CM <0) to raining stratiform regions (Q CM >0).The hydrometeor transport is associated with the local atmospheric drying (Q WVT >0) over convective regions because Q WVT and Q CM have similar magnitudes but opposite signs.The water vapor convergence, local atmospheric drying, and heat divergence are the rainfall sources whereas the local atmospheric cooling and the transport of hydrometeor concentration from convective regions to raining stratiform regions are the rainfall sinks.PEWV generally is higher than PEH (Fig. 4b) because the rainfall source from water vapor convergence in water vapor related surface rainfall budget is weaker than the rainfall source from heat divergence in thermally related surface rainfall budget (Fig. 6).PEWV is lower than PEH on 4 and 7 June because the rainfall source from water vapor convergence is stronger than the rainfall source from heat divergence.The RMS difference between PEWV and PEH is 12.5%.Both PWEV and PEH increase as convective rainfall intensifies (Fig. 5b).Precipitation efficiency ranges from 60% to 90% as convective rain rate is higher than 2 mm h -1 , whereas it ranges from 0 to 100% as convective rain rate is lower than 2 mm h -1 .
Over raining stratiform regions, rainfall is primarily associated with the transport of hydrometeor concentration from convective regions to raining stratiform regions because water vapor divergence dries local atmosphere on 3 and 7 June and water vapor convergence moistens local atmosphere on 4-6 June and heat divergence cools local atmosphere (Fig. 7).PWH is generally higher than PEWV on 3, 4, and 7 June whereas it is generally lower than PEWV on 5-6 June (Fig. 4c).The RMS difference between PEWV and PEH is 23.8%, which largely accounts for the RMS difference in the model domain mean calculations.The ranges of precipitation efficiencies for the surface rain rate of lower than 1 mm h -1 (0-100%) are larger than those for the surface rain rate of higher than 1 mm h -1 (45-100%).

Radiative effects of ice clouds: CNIR versus C
The calculations of model domain mean simulation data show that PEWV is insensitive to radiative effects of ice clouds on 4 June, whereas the exclusion of radiative effects of ice clouds decreases PEH (Table 1).
Fig. 1.Temporal and vertical distribution of (a) vertical velocity (cm s -1 ) and (b) zonal wind (m s -1 ) from 0200 LST 3 June -0200 LST 8 June 2008.The data are averaged in a rectangular box of 108-116 o E, 21-22 o N from NCEP/GDAS data.Ascending motion in (a) and westerly wind in (b) are shaded.

Fig. 4 .
Fig. 4. Time series of PEWV (solid) and PEH (dash) calculated using (a) model domain mean data and data from (b) convective and (c) raining stratiform regions in C. Unit is %.

Fig. 5 .
Fig. 5. PEWV versus P S (cross) and PEH versus P S (open circle) calculated using (a) model domain mean data and data from (b) convective and (c) raining stratiform regions in C. Units are % for PEWV and PEH and mm h -1 for P S .

Table 2 .
The removal of radiative effects of ice clouds increases PEWV, but it barely affects PEH on 5 June.The elimination of radiative effects of ice clouds decreases PEWV and PEH on 6 June.The exclusion of radiative effects of ice clouds increases PEWV but it decreases PEH on 7 June.On 4 June, the water vapor realted surface rainfall budgets reveal that all rainfall processes contribute to rain rate in C and CNIR (Table2), which leads to 100% of PEWV in the two experiments.The thermally related surface rainfall budgets show that rainfall is associated with heat divergence and radiative cooling in the two experiments (Table3).Thus, local atmospheric cooling (S HT <0) makes PEH less than 100% in the two experiments.Water vapor related surface rainfall budget (P SWV , Q WVT , Q WVF , Q WVE , and Q CM ) averaged daily and over model domain, convective regions, and raining stratiform regions in C, CNIR, and CNIM.Unit is mm h -1 .The removal of radiative effects of ice clouds decreases PEH from C to CNIR through the enhanced local atmospheric cooling associated with the enhanced radiative cooling because of similar heat divergence in the two experiments.On 5 June, the elimination of radiative effects of ice clouds increases PEWV through the reduced local atmospheric moistening (Q WVT <0) associated with the decreased water vapor convergence (Q WVF >0).The two experiments have similar PEH because of similar heat related rainfall processes.On 6 June, the exclusion of radiative effects of ice clouds decreases PEWV and PEH from C to CNIR through the enhanced hydrometeor gain (Q CM >0) because water vapor and heat processes have similar contributions to rainfall (Q WVT +Q WVF +Q WVE  S HT +S HF +S HS +S LHLF +S RAD ) in the two experiments.On 7 June, the removal of radiative effects of ice clouds increases PEWV through the decreased water vapor divergence, whereas it decreases PEH through the enhanced local atmospheric cooling associated with the enhanced radiative cooling.Over convective regions, the exclusion of radiative effects of ice clouds decreases PEWV and PEH through the intensified transport of hydrometeor concentration from convective regions to raining stratiform regions (Q CM <0) because water vapor and heat processes have similar contributions to rainfall in the two experiments on 4 June.Similar magnitudes of rainfall sources associated with water vapor, heat, and cloud processes lead to similar