1. Introduction
Clouds, with their compensating greenhouse and albedo effects as well as complex microphysical processes, impose a large and uncertain effect on the radiation balance of the climate system and precipitation growth. To improve the simulation of clouds, prognostic bulk microphysical schemes have been used in general circulation models (GCMs) (e.g., Tiedtke 1993; Fowler et al. 1996) and numerical weather prediction models, such as the Weather Research and Forecasting (WRF) model (Skamarock et al. 2005). For ice sedimentation in GCMs, empirical relationships relating ice fall speed with ice water content (IWC; Heymsfield and Donner 1990, hereafter HD) are widely used. Recent retrievals of ice mass and fall speeds in cirrus clouds using Atmospheric Radiation Measurement (ARM) program (Stokes and Schwartz 1994) datasets provide another ice fall speed parameterization useful for GCMs (Deng and Mace 2008). Ice fall speed, which significantly controls the ice water content aloft, is a parameter to which climate simulations are very sensitive (Sanderson et al. 2008).
Mixed-phase clouds occur when supercooled water coexists with ice particles. They occur worldwide, including Arctic stratus, midlatitude frontal systems and orographic clouds, and tropical deep convection (Shupe et al. 2008). Riming occurs when ice particles accrete cloud droplets, which changes the shape, mass, fall speed, and radiative characteristics of ice crystals (Locatelli and Hobbs 1974; Heymsfield and Kajikawa 1987; Mitchell et al. 1990). Riming also impacts the precipitation efficiency and cloud lifetime (Rauber 1987; Zhang and Lohmann 2003), which impacts cloud radiation and hydrological cycle. However, riming impact on ice particle properties has not been considered in most GCM prognostic cloud schemes. Many weather models (e.g., WRF) consider heavily rimed snow through the addition of the graupel category to the bulk scheme (Thompson et al. 2004; Hong and Lim 2006; among others).
The amount of riming of an ice particle is generally described by two distinct definitions. One is the riming degree, which is a rather subjective classification of the percent coverage of the crystal surface covered with rime (e.g., Locatelli and Hobbs 1974; Mosimann et al. 1994). Another is the rimed mass fraction (RMF), defined as the ratio of the rime mass to the total mass of a particle. RMF is more physically meaningful and is used widely in the model and theoretical calculations (e.g., Mitchell et al. 1990; Mosimann et al. 1994; Stoelinga et al. 2007; Morrison and Grabowski 2008). Direct subjective observation and categorization of the in situ (either at surface or in cloud by aircraft) collected ice particles is the most used method to obtain riming degree (Locatelli and Hobbs 1974; Woods et al. 2005). Using a vertically pointing Doppler radar and surface collected snow crystals on Mt. Rigi in the Swiss Alps, a relationship between riming degree and Doppler velocity in stratiform precipitation has been derived (Mosimann 1995, hereafter M95). With the mass of accreted cloud droplets derived as a function of riming degree and the mass of the unrimed snow crystals computed using empirical mass diameter relationships, an empirical relationship between riming degree and RMF has been derived [Mosimann et al. 1994, their Eq. (16)]. There have been a few observational studies relating riming degree to ice particle properties. The increase of ice fall velocity with riming degree has been noted (Zikmunda and Vali 1972; Locatelli and Hobbs 1974). Using an optical instrument on Mt. Rigi, Barthazy and Schefold (2006) also found that the fall velocity of snowflakes depends both on riming degree and crystal type. However, attempts to relate the riming degree or RMF to cloud environmental conditions such as temperature, vertical motion, cloud liquid water content, ice water content, and so on have not been quantified much. For example, observations indicate that riming increases with vertical motion and temperature in orographic clouds (Woods et al. 2005; Houze and Medina 2005), but the quantitative dependence of riming on these variables has not been fully explored.
Intensive cloud measurements are collected in the Atmospheric Radiation Measurement Program (Stokes and Schwartz 1994). This study utilizes ARM data at the U.S. Southern Great Plains (SGP) site to develop
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a rimed mass fraction parameterization and comparison with observational estimates, and
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a new ice fall speed parameterization that considers riming impact and evaluation using available observations.
The riming parameterization discussed below has been implemented and evaluated in the WRF model for two orographic precipitation events (Lin and Colle 2011). In this paper the parameterization will be implemented and tested within a GCM.
Section 2 describes the observational data and rimed mass fraction estimates. The proposed rimed mass fraction parameterization and its impact on ice fall speed is presented in section 3. Section 4 provides a brief comparison of GCM simulations using the new parameterization and the conventional parameterization, and section 5 summarizes the results.
2. Data and observed rimed mass fraction estimates
ARM Active Remotely Sensed Clouds Locations (ARSCL) combines the Millimeter Cloud Radar (MMCR), micropulse lidar (MPL), and microwave radiometer measurements and provides high spatial (45 m in vertical) and temporal (10 s) cloud measurements (Clothiaux et al. 1999). Cloud properties at SGP have been retrieved combining the ARSCL data with conventional radiosonde measurements of the temperature and moisture profiles (Mace et al. 2006, hereafter M06). Liquid water content (LWC), IWC, temperature, and vertical Doppler velocities every 5 min and 90-m vertical resolution up to 15 km above the ground are used in this study. Detailed description of LWC and IWC retrievals can be found in M06.
Figure 1 shows the evolution of Doppler velocity for clouds extending to 12 km AGL on 4 February 2004 at the SGP site. During this event, there was a weak (∼1003 hPa) cyclone developing over southeastern Colorado (not shown), with 2–5 m s−1 surface easterlies over Oklahoma and the freezing level dropping to near the surface by 1400 UTC 4 February. The Doppler velocity after 0600 UTC rapidly increases downward from ∼0.5 m s−1 at 4.5 km AGL to ∼1.2 m s−1 at ∼3.5 km AGL (approximately −10°C), with localized high-velocity streaks of ∼2.0 m s−1 around 0800 and 2000 UTC. These high-velocity streaks correspond well with periods of abundant (∼0.5 and 1.0 mm) liquid water content as measured in the vertical by a microwave radiometer (Fig. 1). The rapid variation of fall velocity with temperature and LWC is also seen in other events and indicates the large impact of riming on ice particle fall speed.
We estimate the riming degree using the ARSCL data at the SGP site for the year of 2004 as follows. Doppler velocity measured by a vertically pointing Doppler radar is the sum of reflectivity-weighted particle fall speed and vertical air motion; thus, to minimize the vertical motion contamination, only stratiform clouds are included, which are determined using the convective index method introduced in M95 [his Eq. (4)]. As suggested by Orr and Kropfli (1999), particle fall velocity can be estimated by averaging the Doppler velocity from a vertically pointing Doppler radar over a relatively long (30 min) time period, assuming small-scale vertical air motions within the cloud average to be near zero or much smaller than particle fall speed. They found that the average vertical motion over 30 min in stratiform clouds is <0.08 m s−1, which is smaller than most ice particle fall speeds in mixed-phase clouds. Considering this, and to be consistent with M06 data, ARSCL Doppler velocity at three consecutive vertical levels every 30 min (a total of 540 values) is treated as one average value. After discarding cloudy points below melting level and applying the stratiform screening, there are still 45 523 average values for the year of 2004.
3. Rimed mass fraction parameterization and fall speed impact
Cloud schemes in most GCMs generally have fewer prognostic variables (total water content or cloud liquid and ice) than in mesoscale models [see Lopez (2007) for a review]. Because of the large time step (10–60 min) used in GCMs, a diagnostic treatment is sufficient for rain. However, ice fall speed is needed to represent its sedimentation since ice might not fall to the ground in one time step. An ice fall speed parameterization, which relates the ice fall speed to ice water mass (HD), is widely used. Since the ice category in GCM cloud schemes generally represents ice, snow, and graupel, a more general parameterization explicitly considering riming impact is helpful to represent the full spectrum of ice particles.
Figure 3 compares the parameterized RMF-dependent fall velocity [Eq. (4)] and HD fall velocities with the observed Doppler velocities obtained from ARSCL for the stratiform clouds during the year of 2004. The HD formula underestimates the observed fall velocity with a mean error (ME) of −0.17 m s−1, especially for those velocities larger than 1 m s−1. In contrast, the RMF-dependent fall velocity compares better with the observed velocity, with a ME of −0.05 m s−1. The root-mean-square error (RMSE) is also slightly reduced from 0.35 for HD to 0.31 m s−1 for the new formula. In addition, the RMF-dependent formula has a higher correlation coefficient (0.46) with the observed Doppler velocity than HD (0.34). Most of the underestimate of HD occurs when RMF_para is larger than 0.2 (not shown), which indicates the importance of riming on the ice fall velocity. The scatter in Fig. 3 can be from several sources, such as the uncertainty in the retrieved IWC and LWC, ice particle shape effect on the fall velocity, uncertainty associated with the riming parameterization, and so on. Further observational and theoretical studies are needed to refine and improve the proposed RMF parameterization and its effect on the ice particle fall velocity.
4. Preliminary test in GFDL AM3
It is relatively straightforward to implement the proposed parameterization in a GCM as long as the IWC and LWC are predicted. The new RMF approach was implemented and tested in the recently developed Geophysical Fluid Dynamics Laboratory (GFDL) atmospheric model (AM3; Donner et al. 2011). The main differences between AM3 and AM2 (Anderson et al. 2004) are briefly summarized here. AM3 uses a finite-volume dynamic core and a 48 × 48 × 6 cube-sphere grid, which corresponds to a horizontal resolution of about 220 km × 220 km (Putman and Lin 2007). AM3 also increases the number of vertical levels from 24 to 48. The relaxed Arakawa–Schubert scheme (RAS; Moorthi and Suarez 1992) in AM2 has been replaced with the deep convection of Donner (Donner 1993; Donner et al. 2001), which is a mass flux scheme that includes a parameterization of mesoscale anvils, and the University of Washington shallow convection (Bretherton et al. 2004). The stratiform cloud scheme, which is based on Tiedtke (1993), Rotstayn (1997), and Jakob and Klein (2000), is basically the same as in AM2 except that a prognostic equation for cloud droplet number is now implemented (Ming et al. 2007). The stratiform cloud scheme predicts cloud water and cloud droplet number, cloud ice, and cloud fraction. In the scheme, cloud ice represents cloud ice, snow, and graupel (Rotstayn 1997), and the HD or the new fall speed parameterization is applied to cloud ice. Ice fallout is treated as a sink term to represent the autoconversion from ice to snow in the scheme.
Two 28-yr (1980–2007) simulations using prescribed sea ice and SST from the Hadley Center (Rayner et al. 2003) were conducted. Note that the control simulation (hereafter called CTL) uses ice fall speed based on HD, but it was increased by a factor of 1.5 to adjust the top-of-atmosphere (TOA) radiation balance (Donner et al. 2011). The new simulation (hereafter called NEW) uses the RMF-dependent ice fall speed proposed in section 3. Other than that, the setup and configurations for the two simulations are identical. More details about the simulation and a full evaluation of the CTL simulation are in Donner et al. (2011). The following comparisons use the 20-yr (1981–2000) model climatology. Here, only model quantities directly related with the change of ice fall speed are compared between the two simulations with available observations as references.
Budget calculations indicate the ice sedimentation is a significant sink term for the ice budget in AM3 (Salzmann et al. 2010), with two main source terms from Bergeron process and ice accreting cloud water. As a result, IWC will likely change depending on the ice fall speed used. For the same ice mass, Eq. (4) indicates that the new ice fall speed is larger than HD when RMF is larger than zero and it is larger than 1.5 times the HD value when RMF is larger than ∼0.45 (Fig. 4a). Figure 4b compares the ice fall speeds between the CTL and NEW simulations. CTL has larger ice fall speeds than NEW, with a mean of ∼69 cm s−1 compared to ∼49 cm s−1 for NEW. This is mainly due to the use of a large ice fall speed (1.5 times that of HD) in CTL as described above. The RMF in NEW is generally less than 0.3, which results in smaller ice fall speeds than in CTL (Fig. 4b), although stratiform ice water content increases by ∼20%–30% in NEW as compared with CTL (Fig. 5). Overall, compared with CTL, NEW reduces the mean ice fall speed by ∼30%; this will impact the model IWC and ice water path (IWP).
Global retrieved ice water content is becoming available as new satellites are launched, such as CloudSat (Austin et al. 2009; Waliser et al. 2009). Despite the rather large uncertainty (∼40%) in the CloudSat retrieved IWC (Austin et al. 2009), it still serves as a useful constraint for GCM simulated IWC (Waliser et al. 2009). IWP varies by two orders of magnitude among GCMs compared in Waliser et al. (2009). A fair comparison between GCM IWC and satellite retrievals is difficult because of different resolutions between GCM and satellite observations. In addition, the separation between resolved cloud (stratiform cloud) and parameterized cloud (deep and shallow convection) and the partial cloudiness due to the subgrid variability in GCM also make the comparison difficult. The following comparison emphasizes the IWC difference between the two simulations with CloudSat retrievals as a reference. Figure 5 shows the zonal mean IWC from CloudSat (August 2006–July 2007; Waliser et al. 2009), CTL, and NEW. Note the IWC are all-sky values for CloudSat and the gridbox mean for model. CloudSat IWC (Fig. 5a) is large (∼20 mg m−3) over the tropical upper troposphere (450–200 hPa) and the Northern and Southern Hemisphere storm tracks. Both CTL and NEW (stratiform cloud ice only; Figs. 5b,d) capture the spatial variation of the observed IWC; NEW has ∼20%–30% more IWC than CTL over the tropical upper troposphere and NH and SH storm tracks. However, IWC in NEW is still only ∼30% of CloudSat retrievals over the tropical upper troposphere. IWC over the tropics increases significantly in both CTL and NEW once convective IWC is included (Figs. 5c,e). Model total IWC is comparable with CloudSat retrievals over the tropical upper troposphere now, but it is still ∼30% smaller than CloudSat in the midlatitudes. Overall, AM3 IWC is within the uncertainty of CloudSat retrievals and the importance of ice fall speed parameterization for model IWC is evident.
Figure 6 shows the model zonal mean of IWP, surface precipitation, liquid water path (LWP), and total cloud fraction with available observations. Consistent with Fig. 5, IWP in NEW is 0.01–0.02 mm larger than in CTL over the tropics and midlatitudes (Fig. 6a). Total IWP in NEW and CTL is ∼20% larger than CloudSat over the tropics and ∼30% less over the midlatitudes. Compared with version 2 of the Global Precipitation Climatology Project (GPCPv2; Adler et al. 2003), both runs overpredict precipitation slightly over the tropics, with a reduced overprediction (∼5%) for NEW (Fig. 6b). Stratiform precipitation (dashed lines in Fig. 6b) is similar between the two simulations, with NEW having ∼5% less than CTL in the NH midlatitudes. Stratiform LWP difference between the two simulations is within 2% (Fig. 6c). Model LWP is comparable with Special Sensor Microwave Imager (SSM/I) retrievals (Weng and Grody 1994) over the midlatitudes, while it is ∼50% smaller over the tropics than observed (Fig. 6c). Total cloud cover is within 20% of the International Satellite Cloud Climatology Project (ISCCP) climatology (Rossow and Schiffer 1999) over the midlatitudes (Fig. 6d). Over the tropics, model total cloud cover is ∼20% larger than the ISCCP (Fig. 6d). NEW increases the total cloud cover slightly by ∼1% (Fig. 6d) and this increase is mainly from high clouds (not shown).
With increased IWC and slightly increased high cloud cover (not shown), the TOA radiation fluxes also change slightly (Figs. 7 and 8). Compared with Clouds and the Earth’s Radiant Energy System–Energy Balanced and Filled (CERES-EBAF; Loeb et al. 2009), global mean OLR of CTL is ∼4 W m−2 smaller, with a large negative bias over the tropical convective regions (Fig. 7b). With more ice aloft, more longwave radiation is trapped. As a result, OLR is slightly reduced globally in NEW compared to CTL, with a reduction of up to ∼20 W m−2 over the Maritime Continent and a global mean reduction of ∼2.8 W m−2 compared with CTL (Fig. 7c). TOA shortwave radiation absorbed is also smaller in NEW, with a global mean reduction of ∼1.5 W m−2 compared with CTL (Fig. 8). As a result, global mean TOA net radiation has only ∼1.3 W m−2 change. This relatively small TOA radiation imbalance induced by using the new ice fall speed parameterization can be adjusted relatively easily in the future.
AM3 has a realistic precipitation climatology compared with GPCPv2 (Fig. 9). The global mean precipitation bias is 0.42 mm day−1 for CTL, with most of the overestimates over tropical convective regions, such as the Maritime Continent and ITCZ (Fig. 9b). NEW reduces the precipitation overestimates in CTL by up to 1 mm day−1 over tropical convection areas, with the global mean precipitation bias reduced from 0.42 to 0.27 mm day−1 (Fig. 9c). Interestingly, precipitation reduction over the tropics in the NEW is mainly from the convective (Donner) scheme (not shown). Determining why and how the ice fall speed impacts the convective precipitation needs future investigation. Precipitation over the NH storm track is also slightly reduced in NEW (Fig. 9c).
Other variables, such as 850- and 200-hPa winds, sea level pressure, surface temperatures, etc., are also compared, and there are no obvious differences between the two simulations. Overall, AM3 using the new parameterization produces comparable climatology to the CTL simulation. This suggests that the new parameterization can be used in AM3 without introducing large unforeseeable results.
5. Conclusions
Ice fall speed in current GCMs exerts a large impact on the TOA radiation balance via control of ice water content aloft. In mixed-phase clouds, riming increases ice particle fall velocity, and this effect should be considered in large-scale cloud parameterizations. Using ARM ARSCL and the comprehensive data prepared by M06, we propose a diagnosed rimed mass fraction parameterization depending on LWC and IWC. This parameterization compares well with the rimed mass fraction estimated from ARSCL observations of stratiform clouds in 2004 at the ARM SGP site. Using the proposed rimed mass fraction parameterization, a widely used ice fall speed formula suitable for ice clouds is extended to include the riming impact for mixed-phase clouds. The new ice fall velocity parameterization is shown to compare better with observations than the conventional parameterization for mixed-phase clouds.
The new parameterization is tested in the recently developed GFDL AM3 and compared with the standard (CTL) simulation and available observations. Compared with the standard simulation, the new simulation increases the stratiform IWC by 20%–30% in the midlatitudes and tropical upper troposphere and reduces the global mean OLR and TOA shortwave absorbed by ∼2.8 and ∼1.3 W m−2, respectively. The new simulation slightly reduces the global mean precipitation, especially over the tropics. Total cloud cover and LWP are similar between the CTL and NEW simulations. Overall, simulation using the new parameterization gives a reasonable climatology without inducing any unforeseeable detrimental results. Above all, it improves the physical basis for using an ice fall velocity larger than HD in current AM3.
Acknowledgments
This research was supported by the Office of Science (BER), U.S. Department of Energy, and the National Science Foundation ATM-0908288 (Colle). Data were obtained from the Atmospheric Radiation Measurement Program sponsored by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Environmental Science Division. We thank Yi Ming and Song-Miao Fan for helpful discussions and comments on the manuscript. We appreciate the constructive comments by the three reviewers to help improve the manuscript.
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APPENDIX A
Riming Parameterization Derivation
APPENDIX B
Derivation of Graupel Fall Speed Mass Relationship
Time–height plot of the Doppler velocity (color shaded every 0.2 m s−1) and the temperatures (solid lines) for 4 Feb 2004. Dashed line denotes the LWP from the microwave radiometer.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
Normalized probability density distribution (in %) of the proposed RMF parameterization (RMF_para) with the observational estimates (RMF_obs) using ARSCL and M06 data for the year 2004.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
(a) Scatterplot of the observed Doppler velocities from the MMCR against the ice fall velocities derived using the HD formula. (b) As in (a), but for the ice fall velocities derived using Eq. (4) with RMF_para.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
(a) Comparison of the new ice fall speed [Eq. (4)] with the HD formula. The two black solid lines are the values of HD and 1.5 times the values of HD, and gray lines are the new ice fall speed with varying RMF (from 0 to 1 at 0.1 intervals). Note the new ice fall speed is the same as HD when RMF is zero. (b) Scatterplot of the ice fall speeds from the NEW and CTL simulations. The two black lines denote the 1:1 and 1:1.5 ratios, respectively. Color indicates the RMF of the NEW simulation computed from the annual mean IWC and LWC using Eq. (3).
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
(a) Zonal mean ice water content (IWC) from CloudSat retrievals (Waliser et al. 2009); (b) zonal mean stratiform IWC from CTL; and (c) zonal mean total IWC from CTL. (d),(e) As in (b) and (c), respectively, but for NEW.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
(a) Zonal mean model IWP (solid lines for total and dashed lines for stratiform) and CloudSat IWP. (b) Zonal mean surface precipitation from model and GPCPv2 (Adler et al. 2003). Dashed lines are model stratiform precipitation. (c) Zonal mean LWP from model and SSM/I (Weng and Grody 1994). (d) Zonal mean total cloud cover from model and ISCCP (Rossow and Schiffer 1999).
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
Annual long-term mean OLR in W m−2 for (a) CERES-EBAF observations, (b) CTL minus CERES-EBAF, and (c) NEW minus CTL.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
Annual long-term mean TOA shortwave absorbed in W m−2 for (a) CERES-EBAF observations, (b) CTL minus CERES-EBAF, and (c) NEW minus CTL.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1
Annual long-term mean precipitation in mm day−1 for (a) GPCPv2, (b) CTL minus GPCPv2, and (c) NEW minus CTL.
Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3299.1