Cloud optical depth and other cloud radiative properties vary substantially with particle size distribution (PSD) and ice water content (IWC). In fact, many cloud observations (mostly remote sensing techniques) rely on knowledge of PSD to retrieve total cloud IWC from the part of particle size spectrum that the particular instruments are sensitive to. Uncertainties in the PSD can generate large differences among IWC retrievals with remote sensing techniques. IWC has become the key variable used in models and observations to characterize cloud radiative, dynamical, and hydrological properties.

For a given PSD, or particle number density n(r), IWC is determined by

where r is particle radius and riceis ice density. Cloud volume extinction coefficient bc_e , which is measured with remote sensing techniques, is also related to PSD (hence indirectly related to IWC) as follows

where xe is the Mie efficiency as a function of size parameter c=2pr/l for particle radius r and wavelength l . The PSD is the key cloud property relating bc_e measurements to IWC. As we will discuss next, there are large complexities and uncertainties associated with cloud ice PSDs and we seek means to reduce these uncertainties with future space and ground-based observations.

Shown in Figure 1 is the bimodal size distribution of ice crystals often seen in cloud observations [e.g., Mitchell et al., 1996; Platt, 1997]. The bimodal distribution of ice particle spectra is not fully understood although it has been speculated as a result of balancing between the nucleation of ice particles and the removal of ice particles by aggregation and enhanced diffusion growth via ventilation [Mitchell, 1994]. In addition, PSD can also vary largely with cloud type, height, latitude and IWC.
 
 

Fig 1. Cloud ice particle number density n(D) vs. the long dimension of particles as observed at the temperature range of -25° C and -30° C [from Platt, 1997]. It shows a bimodal structure in the ice crystal distribution with the second peak at ~500 mm.

Numerical climate/weather models and cloud remote sensing require good knowledge of PSDs to evaluate cloud radiative and hydrological properties. It has been found that the concept of effective particle size is not sufficient for characterizing cloud PSDs and their variabilities. There has been plenty of evidence now against the single-parameter or simple-function characterization. Heymsfield and Platt (1984) concluded that the size distributions observed by airborne probes were fitted quite well to a simple power law at sizes less than 100 mm, which enables a simple PSD parameterization for such sizes. To parameterize the bimodal size distribution, Platt [1997] presents a model for particle sizes at temperatures of -5° C to -50° C with two functions, one for sizes greater than100 mm and one for sizes less than 100 mm.

Recently, PSD parameterization has become more sophisticated in order to fit more observational data. McFarquhar and Heymsfield [1997] have developed a PSD parameterization based on IWC and cloud height. It is derived from observations of cirrus anvils flowing out from tropical deep convection during the Central Equatorial Pacific Experiment (CEPEX). The size distribution function is composed of a first-order gamma distribution function for small particles (D<100mm) and log-normal distribution function for large particles (D>100mm). The MH parameterization is able to produce the bimodal PSD for either low altitude or large IWC clouds.

The parameterization used in Liu and Curry [1998] is based on the same dataset but depends only on cloud altitude. No bimodal PSD can be obtained from the Liu-Curry parameterization.

Knollenberg et al. [1993] reported some in-situ measurements of ice PSD at 0.1-1000 mm, which were made from the anvils in tropical and extratropical cumulonimbus complexes. They found that IWC could be as high as 0.07 g/m3 at 15-17.5 km altitudes in tropical anvils, which has not been observed by other groups. With rare exceptions, particles large than 100 mm were not observed near the cloud tops, and therefore, the bimodal feature is not as prominent in Knollenberg et al [1993] as in McFarquhar and Heymsfield [1997] for these high clouds. In his thesis, Bond [1996] came up with an empirical formula to represent the ice PSDs from the Knollenberg observations but the dependence of the fit parameters on cloud height and IWC is not specified.

Donovan and Lammeren [2002] developed a parameterization using combined lidar and radar backscattering at ARM's Southern Great Plains site. Bimodal size distributions are used to fit the lidar/radar data, showing a much wider spread of the large particle mode than the above two parameterizations.

Finally, simple gamma size distributions are also commonly used in the literature [Evans and Stephens, 1998] but this type of parameterizations cannot produce the bimodal feature.

Figure 2 shows very different curves produced by the various parameterizations for the same IWC. At sizes less than 10mm, the differences mainly result from lack of reliable observations, where the parameterizations are mostly speculative. At sizes of hundreds of mm, large differences occur between the in-situ and remote sensing techniques, partly because of poor understanding of cloud radiative properties, and partly because of limitations in observing techniques.
 

Fig.2 For the MH, LC, and DL distributions, line thickness represents temperature of -15° C, -30° C, -45° C, -60° C, and -75° C (from thin to thick). Two Gamma distributions represent for Dm =30 mm at -75° C and Dm = 300 mm at -15° C. For all distributions, IWC=0.1g/m3.

 
 
 
 

The MLS experiment on the Aura satellite plans to produce cloud volume extinction coefficients with a multi-frequency scattering-based technique [Wu and Jiang, 2002]. MLS cloud measurements are able to provide additional constraints on ice PSD at sizes greater than ~100 mm. As shown in Figure 3, MLS 200 and 640GHz measurements are sensitive mostly to particles of sizes greater than 100mm because the scattering Mie efficiency is negligible for small particles at the MLS frequencies and diminishes for large sizes due to the sharp decrease in particle number density. The bimodal feature is especially important for microwave remote sensing because the second mode (near 300-500mm) is just where the sensitivity peaks.

Fig.3 Mie scattering efficiency normalized by total scattering coefficient under two MH size distributions where the input IWC and T are in g/m3° C respectively. For low thick ice clouds (top), most scattering contributions come from 100-400mm and 200-600mm for 203 and 640GHz, respectively. For high thin clouds, most scattering contributions come from 100-300mm for the two frequencies.

From MLS cloud-induced radiances, we can deduce profiles of cloud volume extinction coefficient, b _{c_e}, which represents the integrated effects of particles greater than 100mm. However, we need to assume an ice PSD to retrieve total IWC from MLS cloud extinction. As shown in Figure 4, various PSD parameterizations yield very different b _{c_e}-IWC relationships for 200GHz. Depending on what parameterization is used, the inferred IWC may differ by an order of magnitude for the same cloud extinction.
 

Fig. 4 The bc_e-IWC relationships from different PSDs for 200GHz.

Statistical and climatological studies would be effective ways to improve our understanding of global cloud PSD and IWC because of the large spatial-temporal variability and undersampling ca with both space and ground-based instruments. This goal can be achieved through understanding climatological differences between MLS IWC/extinction measurements and other existing datasets such as airborne in-situ IWC, ground-based backscattering/IWC observations from cloud radar networks, and airborne radar backscattering/IWC measurements. Other global passive measurements from space, such as 150-220GHz cloud radiances from SSM/T2, AMSU, and Aqua AIRS, also require better knowledge of PSD to deduce Ice Water Path (vertical column IWC). The Cloudsat 95GHz cloud profiling radar, to be launched in 2004, will measure cloud backscattering/IWC with good vertical and horizontal resolution. By flying in formation with Aura, Cloudsat will generate the closest coincident (in space and time) cloud observations to those made by MLS, allowing studies of the same clouds with both back- (Cloudsat) and forward-scattering (MLS) properties.

In summary, better knowledge of cloud PSD and IWC needs to be gained for such comparison studies to be successful. More reliable statistics and associated uncertainties of cloud PSD and IWC need to be developed. This can be obtained from existing and future in-situ aircraft measurements as well as observations from ground-based radar networks. Better coordination of analyses among these communities is also desired.