The dependence of precipitation efficiency on rainfall type in a cloud resolving model

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011jd016117, 2011 The dependence of precipitation efficiency on rainfall type in a cloud resolving model Shouting Gao 1 and Xiaofan Li 2 Received 15 April 2011; revised 18 July 2011; accepted 22 August 2011; published 15 November [1] The rain microphysical precipitation efficiency (RMPE), the cloud microphysical precipitation efficiency (CMPE), and the large scale precipitation efficiency (LSPE) are analyzed using 21 day two dimensional cloud resolving model simulation data for the period of 18 December 1992 to 9 January 1993 in the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA COARE) for eight rainfall types separated by a partitioning scheme based on the surface rainfall budget. RMPE estimated from grid scale data is considered to be the reference precipitation efficiency. Mean versus gridded estimates of RMPE and CMPE show that they are not very sensitive to spatial scales for all rainfall types. The root mean square (RMS) differences between LSPE and RMPE are larger than the standard deviations of RMPE for five rainfall types, and the time mean LSPE estimates are lower than those of RMPE for six rainfall types, indicating that LSPE is not a good estimate for RMPE. Although the RMS differences between CMPE and RMPE are smaller or marginally smaller than the standard deviations of RMPE for all rainfall types, CMPE estimates are lower than those of RMPE for four rainfall types. Citation: Gao, S., and X. Li (2011), The dependence of precipitation efficiency on rainfall type in a cloud resolving model, J. Geophys. Res., 116,, doi: /2011jd Introduction [2] Precipitation efficiency is an important quantity for precipitation systems that measure what percentage of rainfall source is used to produce precipitation. Thus, precipitation efficiency is generally defined as the ratio of the precipitation rate to the precipitation source. One way to define the source is water vapor convergence plus surface evaporation, which is defined as the large scale precipitation efficiency (LSPE); Braham [1952], more than half a century ago, calculated precipitation efficiency with the inflow of water vapor into the storm through a cloud base as the rainfall source. LSPE has been widely used in modeling studies and operational forecasts [e.g., Auer and Marwitz, 1968; Heymsfield and Schotz, 1985; Chong and Hauser, 1989; Doswelletal.1996; Ferrier et al., 1996; Li et al., 2002a; Tao et al., 2004; Sui et al., 2005, 2007]. This definition does not directly consider the roles of clouds and associated microphysical processes in the production of precipitation. Another consideration for a rainfall source is the net condensation for models with a fine horizontal resolution, including a cloud microphysical parameterization 1 Laboratory of Cloud Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China. 2 Center for Satellite Applications and Research, National Environmental Satellite, Data, and Information Service, NOAA, Camp Springs, Maryland, USA. Copyright 2011 by the American Geophysical Union /11/2011JD scheme, whose definition is cloud microphysics precipitation efficiency (CMPE). CMPE directly accounts for the role of clouds and associated microphysical processes in producing precipitation and has been widely used in modeling studies [e.g., Weisman and Klemp, 1982; Lipps and Hemler, 1986; Ferrier et al., 1996; Li et al., 2002a; Sui et al., 2005, 2007]. [3] The measure of precipitation efficiency is not unique as the estimates of precipitation efficiency with LSPE and CMPE in previous studies showed significant differences. Recently, Gao and Li, [2011] argued that the precipitation efficiency should be defined only in the rain microphysical budget for tropical rainfall in which the precipitation rate is a diagnostic term and is estimated using grid scale simulation data. Thus, the precipitation efficiency defined in the rain microphysical budget (rain microphysical precipitation efficiency (RMPE)) estimated from grid scale simulation data serves as the reference for evaluating other precipitation efficiencies (e.g., CMPE and LSPE) defined from the other budgets. Calculations show that the root mean square (RMS) difference between LSPE and RMPE is large, which suggests that LSPE is not a valid estimate for RMPE. [4] Shen et al. [2010] developed a new rainfall partitioning scheme based on surface rainfall processes; they separated grid scale rainfall simulation data into eight rainfall types based on local atmospheric drying/moistening, water vapor convergence/divergence, and hydrometeor loss/convergence or hydrometeor gain/divergence in the surface rainfall budget proposed by Gao et al. [2005a]. Such a rainfall separation leads to spatial scale independence of LSPE for each rainfall type. Whether CMPE and RMPE are spatial scale dependent 1of8

2 for each rainfall type and to what degree LSPE and CMPE deviate from RMPE for each rainfall type will be addressed through the analysis of a two dimensional (2 D) cloudresolving model simulation during a selected 21 day period of the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA COARE). The partitioning scheme based on the surface rainfall budget proposed by Shen et al. [2010] will be used to separate the rainfall types. Thus, this paper follows on the work of Gao and Li [2011], but focuses on the dependence of precipitation efficiency on the rainfall type, partitioned based on the surface rainfall budget. In the next section, the cloud model, forcing, and experiment are described. The results are presented in section 3. The summary is given in section Model, Forcing, Experiment, and Methodologies [5] The cloud resolving model used in this study is the 2 D version of the Goddard Cumulus Ensemble Model. The model was originally developed by Soong and Ogura [1980], Soong and Tao [1980], and Tao and Simpson [1993] and was modified by Li et al. [1999, 2002b]. The model has prognostic equations for potential temperature, specific humidity, mixing ratios of five cloud species, and perturbation zonal wind and vertical velocity. The model includes cloud microphysical parameterization schemes [Lin et al., 1983; Rutledge and Hobbs, 1983, 1984; Tao et al., 1989; Krueger et al., 1995] and interactive solar and thermal infrared radiation parameterization schemes [Chou et al., 1991, 1998; Chou and Suarez, 1994]. The model uses cyclic lateral boundaries, a horizontal domain of 768 km, a horizontal grid resolution of 1.5 km, 33 vertical levels, and a time step of 12 s. Detailed model descriptions can be found in the work by Gao and Li [2008a]. [6] Because of a small model domain (768 km in this study), the model cannot simulate large scale circulations. Thus, large scale forcing is required to force the model. The large scale forcing in this study includes zonally uniform vertical velocity, zonal wind, and thermal and moisture advection constructed from the 6 hourly TOGA COARE observation data set within the intensive flux array (IFA) region and the hourly sea surface temperature data measured at the improved meteorological (IMET) surface mooring buoy (1.75 S, 156 E) [Weller and Anderson, 1996]. The model is integrated for 486 h from 0400 LST 18 December 1992 to 1000 LST 9 January Figure 1 shows the timeheight cross sections of the large scale vertical velocity and zonal wind and the time series of the sea surface temperature. These 21 day model simulation data have been used to study surface rainfall processes [Cui and Li, 2006; Gao et al., 2005a; Gao and Li, 2008b, 2010a, 2010b], ice microphysics [Gao et al., 2006], precipitation efficiency [Li et al., 2002a; Sui et al., 2005, 2007; Gao and Li, 2011], diurnal variation [Gao et al., 2009], cloud merging [Ping et al., 2008], cloud radiative and microphysical processes [Li et al., 2005; Sui and Li, 2005;Cui et al., 2007] and vorticity vectors [Gao et al., 2004, 2005b]. Hourly instantaneous grid scale model simulation data are used in the following discussions. [7] Gao et al. [2005a] and Cui and Li [2006] derived a diagnostic surface rainfall equation and showed that the surface rain rate (P s ) is determined by water vapor processes, including local atmospheric drying/moistening (Q WVT ), water vapor convergence/divergence (Q WVF ), and surface evaporation (Q WVE ), and cloud processes, including hydrometeor loss/convergence or hydrometeor gain/ divergence (Q CM ). The surface rain rate can be written as where P s ¼ X4 I¼1 HQ ð I ÞQ I ; ð1aþ Q I ¼ ðq WVT ; Q WVF ; Q WVE ; Q CM Þ; ð1bþ Q WVT ½ q vš ; Q WVF ¼ u @x uo þu Þq v qo v þq v v ð1dþ Q CM ½ q Q WVE ¼ E s ; uo þ u Þq 5 ; ð1fþ where q v is specific humidity; u and w are the zonal and vertical wind components, respectively; E s is the surface evaporation rate; q 5 (q c + q r + q i + q s + q g ) is the total hydrometeor mixing ratio; q c, q r, q i, q s, and q g are the mixing ratios of cloud water, raindrops,, snow, and graupel, respectively; overbars denote domain means; primes are perturbations from the model domain mean; [()] = R z t z b ()dz where z t and z b are the heights of the top and the bottom of the model atmosphere, respectively; and the superscript o is an imposed COARE observed value. Positive values of Q WVT, Q WVF, and Q CM are local atmospheric drying, water vapor convergence, and hydrometeor loss/ convergence. A partitioning scheme based on the surface rainfall budget proposed by Shen et al. [2010] is applied to the grid scale rainfall simulation data, separating the data into eight rainfall types: TFM, TFm, tfm, tfm, TfM, Tfm, tfm, and tfm (see the definitions for rainfall types in Table 1). Only seven of them analyzed in this paper because tfm has a negligibly small contribution to total rainfall. [8] The precipitation efficiencies RMPE, CMPE, and LSPE can be defined as the ratios of rain rate to rainfall sources in the rain microphysical budget, the cloud microphysical budget, and the surface rainfall budget, respectively. From the work of Gao and Li [2011], RMPE, CMPE, and LSPE can be expressed by RMPE ¼ CMPE ¼ P 12 I¼1 P 7 I¼1 P S ; ð2þ HðRP I ÞRP I þ HQ ð RM ÞQ RM LSPE ¼ P S ; ð3þ HP ð I ÞP I þ HQ ð CM ÞQ CM P 4 I¼1 P S ; ð4þ HQ ð I ÞQ I 2of8

3 Figure 1. Time height cross sections of (a) vertical velocity (cm s 1 ) and (b) zonal wind (m s 1 ), and (c) time series of sea surface temperature ( C) observed and derived from TOGA COARE for the 21 day period. Upward motions in Figure 1a and westerly winds in Figure 1b are shaded. where Q RM ½ q r ; RP I ¼ ð ½P SACW ðt > T o ÞŠ; ½P RAUT Š; ½P RACW Š; ½P GACW ðt > T o ÞŠ; ½P REVP Š; ½P RACS ðt > T o ÞŠ; ½P IACR ðt < T o ÞŠ; ½P GACR ðt < T o ÞŠ; ½P SACR ðt < T o ÞŠ; ½P GFR ðt < T o ÞŠ; ½P SMLT ðt > T o ÞŠ; ½P GMLT ðt > T o ÞŠÞ; ð5bþ P I ¼ ð½ P CND Š; ½P DEP Š; ½P SDEP Š; ½P GDEP Š; ½P REVP Š; ½P MLTG Š; ½P MLTS ŠÞ: ð5cþ H is the Heaviside function; H(F) = 1 when F > 0, and H(F) = 0 when F 0. T 0 = 0 C. RP I denotes rainfall source and sink terms from rain microphysical processes and P I denotes rainfall source and sink terms from cloud microphysical processes, which are all defined in Table Results [9] Since the rainfall sources count only the positive values of rainfall processes, calculating the area averaged grid scale data first and then taking positive terms (referred as to the mean data calculation hereafter) may be significantly smaller than accumulating positive rainfall source terms at each model grid first and then making an average (referred as to grid scale data calculation hereafter) because the rainfall sinks (the negative values of rainfall processes) offset the rainfall sources in the mean data calculation. The mean and the positive terms are denoted by the subscripts M and P in this paper. A comparison between the two calculations shows the spatial scale dependence of precipitation efficiency. 3of8

4 Table 1. Summary of Rainfall Types a Type TFM TFm tfm tfm TfM Tfm tfm tfm Description Water vapor convergence, local atmospheric drying, and hydrometeor loss/convergence Water vapor convergence, local atmospheric drying, and hydrometeor gain/divergence Water vapor convergence, local atmospheric moistening, and hydrometeor loss/convergence Water vapor convergence, local atmospheric moistening, and hydrometeor gain/divergence Water vapor divergence, local atmospheric drying, and hydrometeor loss/convergence Water vapor divergence, local atmospheric drying, and hydrometeor gain/divergence Water vapor divergence, local atmospheric moistening, and hydrometeor loss/convergence Water vapor divergence, local atmospheric moistening, and hydrometeor gain/divergence a T and t represent local atmospheric drying and moistening, respectively. F and f represent water vapor convergence and divergence, respectively. M and m represent hydrometeor loss or convergence and gain or divergence, respectively. [10] The two calculations for RMPE are compared in Figure 2. RMPE M is higher than RMPE P in the mean calculation for the entire rainfall area. Their RMS difference is 11.9% (Table 3), which is smaller than the standard deviation of RMPE P (17.6%, Table 4). The RMS differences are greatly reduced when RMPE is calculated for each rainfall type. The RMS is the smallest for TFM whereas they are over 5% for tfm, tfm, and TfM (Table 3); there is much less scatter in TFM compared with that of the other rainfall types. This indicates that the RMS difference calculated over the whole rainfall area results primarily from tfm, tfm, and TfM. [11] The RMS difference of CMPE (22.9%) is double that for RMPE in the calculations over the entire rain area; CMPE has a larger scatter than RMPE (Table 3 and Figures 2 and 3). Like RMPE, CMPE M is higher than CMPE P. Table 4 shows that the RMS difference for CMPE, unlike that for RMPE, is larger than the standard deviations of CMPE P (15.4%) and CMPE M (21.3%). This suggests that the calculation of CMPE is more spatial scale dependent than the calculation of RMPE. There are virtually no differences between the mean and grid scale data calculations of CMPE (CMPE P = CMPE M ) for TFM, TFm, tfm, and Tfm (Figure 3), indicating spatial scale independence for the calculations of CMPE for these rainfall types. Thus, the RMS difference of CMPE calculated over rainfall area comes mainly from tfm and Tf M, as indicated by their RMS differences in Table 3. The calculation for each rainfall type reveals that the RMS difference of CMPE is well below the standard deviations of CMPE P and CMPE M (Tables 2 and 3). [12] When CMPE M is compared with the reference precipitation efficiency (RMPE P ) over the entire rainy area, Figure 4 shows that CMPE M is generally higher than RMPE P. Their RMS difference is 11.9% (Table 3), which is smaller than the standard deviation of RMPE P (17.6%, Table 4). This implies that CMPE M calculated over the entire rainfall area can be used to represent the reference precipitation efficiency. TFM shows much less scatter than the other rainfall types do because only fewer than 30 hourly samples of CMPE M deviate from RMPE P (Figure 4). The RMS difference in TFM (4.5%) is much smaller than Table 2. List of Microphysical Processes and Their Parameterization Schemes a Notation Description Scheme P MLTG Growth of vapor by evaporation of RH84 liquid from graupel surface P MLTS Growth of vapor by evaporation of RH83 melting snow P REVP Growth of vapor by evaporation of RH83 raindrops P IMLT Growth of cloud water by melting of RH83 P CND Growth of cloud water by condensation TSM of supersaturated vapor P GMLT Growth of raindrops by melting of RH84 graupel P SMLT Growth of raindrops by melting of snow RH83 P RACI Growth of raindrops by the accretion of RH84 P RACW Growth of raindrops by the collection of RH83 cloud water P RACS Growth of raindrops by the accretion of RH84 snow P RAUT Growth of raindrops by the LFO autoconversion of cloud water P IDW Growth of by the deposition KFLC of cloud water P IACR Growth of by the accretion of RH84 rain P IHOM Growth of by the homogeneous freezing of cloud water P DEP Growth of by the deposition TSM of supersaturated vapor P SAUT Growth of snow by the conversion of RH83 P SACI Growth of snow by the collection of RH83 P SACW Growth of snow by the accretion of RH83 cloud water P SFW Growth of snow by the deposition of KFLC cloud water P SFI Depositional growth of snow from KFLC P SACR Growth of snow by the accretion of LFO raindrops P SDEP Growth of snow by the deposition of RH83 vapor P GACI Growth of graupel by the collection of RH84 P GACR Growth of graupel by the accretion of RH84 raindrops P GACS Growth of graupel by the accretion of RH84 snow P GACW Growth of graupel by the accretion of RH84 cloud water P WACS Growth of graupel by the riming of RH84 snow P GDEP Growth of graupel by the deposition of RH84 vapor P GFR Growth of graupel by the freezing of raindrops LFO a The schemes are from the works of Lin et al. [1983] (LFO); Rutledge and Hobbs [1983, 1984] (RH83, RH84); Tao et al. [1989] (TSM); and Krueger et al. [1995] (KFLC). 4of8

5 Table 4. Standard Deviations (%) of RMPE P, RMPE M, CMPE P, CMPE M, and LSPE Calculated Over Rainfall Regions (Mean) and Regions of Seven Rainfall Types RMPE P RMPE M CMPE P CMPE M LSPE Mean TFM TFm tfm tfm TfM Tfm tfm the standard deviations of RMPE P (12.0%) and CMPE M (10.7%). The other rainfall types have RMS differences of at least 13.0%. CMPE M is generally lower than RMPE P in TFm, tfm, Tfm, and tfm. In tfm and TfM, CMPE M and RMPE P are similar in many hourly samples, but CMPE M is much lower than RMPE P in some hourly samples, which Figure 2. RMPE P versus RMPE M.RMPE M is calculated from area mean data over rainfall regions (mean) and regions of seven rainfall types, whereas RMPE P is calculated from the accumulations of rainfall sources from each model grid over rainfall regions and regions of seven rainfall types. Diagonal lines denote RMPE P = RMPE M. Table 3. RMS Differences (%) Between RMPE P and RMPE M [RMS(RM)], CMPE P and CMPE M [RMS(CM)], RMPE P and CMPE M [RMS(RM,CM)], and RMPE P and LSPE [RMS(RM, LS)] Calculated Over Rainfall Regions (Mean) and Regions of Seven Rainfall Types RMS(RM) RMS(CM) RMS(RM,CM) RMS(RM,LS) Mean TFM TFm tfm tfm TfM Tfm tfm Figure 3. As in Figure 2 except CMPE P versus CMPE M. 5of8

6 (12.0%) and LSPE (0%). LSPE is generally lower than RMPE P in the six other rainfall types, and their RMS differences are over 16.0%, with the largest RMS difference up to 39.3% in TfM. The RMS differences in tfm, tfm, TfM, and Tfm are larger than the standard deviations of RMPE P and LSPE. The RMS differences are smaller than the standard deviations of RMPE P and are marginally smaller than the standard deviations of LSPE in TFm and tfm. Thus, LSPE often cannot be used to estimate RMPE over the rainfall area and for each rainfall type. [14] The time mean calculations over rainfall area in Table 5 reveal that CMPE M is similar to RMPE M but is higher than the reference precipitation efficiency (RMPE P ). LSPE is much higher than all other time mean estimates of precipitation efficiency. All time mean estimates of precipitation efficiency in TFM are higher than those in the six other rainfall types. In TFM, LSPE is 100% and other estimates are about 86.0%. All time mean estimates of LSPE in the six other rainfall types are well below those of Figure 4. As in Figure 2 except RMPE P versus CMPE M. makes their RMS differences similar to those of TFm, tfm, Tfm, and tfm. Although the RMS differences for the six rainfall types are well below the standard deviations of RMPE P (over 21.0%), they can be similar to the standard deviation of CMPE M (15.7%) for Tfm or even be larger than the standard deviation of CMPE M (14.5%) for tfm. These six rainfall types have similar contributions to the RMS differences in the calculations over the entire rainfall area. [13] Figure 5 reveals that LSPE is generally higher than the reference precipitation efficiency (RMPE P ) for the total rainfall area. LSPE can be up to 100%, whereas RMPE P is less than 100%. Their RMS difference of 31.0% is larger than the standard deviation of RMPE P (17.6%), but it is marginally smaller than the standard deviation of LSPE (32.5%). Because all of the rainfall processes contribute to surface rainfall in TFM, LSPE is always 100%. Meanwhile, RMPE P in TFM is generally lower than 100%, which leads to a large RMS difference (19.2%). The RMS difference in TFM is well above the standard deviations of RMPE P Figure 5. As in Figure 2 except RMPE P versus LSPE. 6of8

7 Table 5. Time Means of RMPE P, RMPE M, CMPE P, CMPE M, and LSPE Calculated Over Rainfall Regions (Mean) and Regions of Seven Rainfall Types RMPE P RMPE M CMPE P CMPE M LSPE Mean TFM TFm tfm tfm TfM Tfm tfm RMPE P. The time mean estimates of CMPE M are similar to those of RMPE P in tfm and TfM, but they are significantly lower than those of RMPE P in TFm, tfm, Tfm, and tfm. 4. Summary [15] The spatial scale and rainfall type dependence of precipitation efficiency is investigated in this paper. A partitioning scheme based on the surface rainfall budget is used to categorize the grid scale rainfall simulation data into eight rainfall types. The precipitation efficiencies are calculated using hourly data from a 21 day two dimensional cloud resolving model simulation with imposed large scale vertical velocity, zonal wind, and horizontal advection obtained from TOGA COARE data. The precipitation efficiency is defined as RMPE in the rain microphysical budget, CMPE in the cloud microphysical budget, and LSPE in the surface rainfall budget. RMPE, calculated with accumulations of rainfall sources from each model grid, serves as the reference precipitation efficiency because the rainfall rate is a diagnostic term in the rain microphysical budget, and the cloud microphysical and surface rainfall budgets are derived from the rain microphysical budget. The major results include the following: [16] 1. The RMS differences between spatial scaleindependent LSPE and the reference precipitation efficiency are larger than the standard deviations of the reference precipitation efficiency in rainfall (TFM) associated with local atmospheric drying, water vapor convergence and hydrometeor loss or convergence, local atmospheric moistening and water vapor convergence, and local atmospheric drying and water vapor divergence. The time mean LSPE overestimates precipitation efficiency in TFM, whereas it underestimates precipitation efficiency in the other rainfall types. [17] 2. CMPE calculated using mean data versus the reference precipitation efficiency shows much less scatter in TFM than in the other rainfall types. Their RMS differences are smaller or marginally smaller than the standard deviations of the reference precipitation efficiency for all rainfall types. Time mean calculations reveal that CMPE can be used to estimate precipitation efficiency in TFM, the rainfall associated with local atmospheric moistening, water vapor convergence, and hydrometeor loss/convergence, and the rainfall associated with local atmospheric drying, water vapor divergence, and hydrometeor loss/convergence, but it underestimates precipitation efficiency for the other rainfall types. [18] 3. 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