Cloud and precipitation processes are important components of the climate system of Earth and have been gaining increased attention in recent years. The importance of clouds and precipitation to climate and the uncertainties clouds introduce into future climate projections have emerged as such important topics that a new chapter in the most recent assessment of the Intergovernmental Panel on Climate Change (IPCC) is now dedicated to clouds and aerosols (IPCC, 2013; Chapter 7). As this chapter makes clear, amongst the many outstanding issues related to clouds and precipitation are those that result from ice-particle properties and processes, issues that must be solved to reduce uncertainties related to clouds and precipitation in future climate assessments.

Passive and active microwave-based observations of cloud- and precipitating-ice processes have an important role to play in improving our understanding of them and their impacts. This includes, for example, observational characterization of cloud and precipitation properties via the core Global Precipitation Measurement (GPM) mission (e.g., Hou et al., 2014), assimilation of cloud- and precipitation-affected microwave radiances in operational numerical weather prediction schemes (e.g., Geer and Baordo, 2014), and assessment of cloud-ice microphysics parameterization performance (e.g., Galligani et al., 2015). As studies on these topics have advanced, so has awareness of the importance of developing models of ice particles with realistic shapes (e.g., Westbrook et al., 2004; Maruyama and Fujiyoshi 2005) and radiative scattering properties (e.g., Kim, 2006; Liu, 2008; Petty and Huang, 2010; Kulie et al., 2010; Johnson et al., 2012). As ice-particle research has gained momentum, so has the importance of ice-particle identification via remote sensing, leading to many studies on the value of multiple frequencies  (e.g., Matrosov, 1998; Kneifel et al., 2011, 2015; Leinonen et al., 2012, 2015; Battaglia et al., 2014; Kulie et al., 2014; Stein et al., 2015; Leinonen and Moisseev, 2015), polarization (e.g., Straka et al., 2000; Aydin and Singh, 2004; Chandrasekar et al., 2013; Kumjian, 2013), and the two combined (e.g., Tyynelä and Chandrasekhar, 2014) in their identification. Polarimetric, multi-frequency measurements also provide one path forward for quantitative estimation of ice water content (IWC). For example, Aydin and Tang (1997), using 94 and 220 GHz radar frequencies; Ryzhkov et al. (1998), using a 3 GHz radar frequency; and Lu et al. (2015), using multiple radar frequencies, derived relationships between IWC and polarimetric observables such as KDP and ZDR.

To develop ice-particle retrieval algorithms and forward radiative operators, one must know the single-scattering properties (e.g., backscattering cross section) of the ice particles in clouds and precipitation, which are quite challenging to calculate because of their complex morphologies. Examples of numerical methods capable of calculating single-scattering properties of ice particles with arbitrary shapes are the discrete dipole approximation (DDA; Purcell and Pennypacker, 1973; Draine and Flatau, 1994; Yurkin and Hoekstra, 2011), the finite-difference time domain method (FDTD; Yee, 1966; Tavlove and Hagness, 2005), the pseudo-spectral time domain method (Liu et al., 2012), the generalized multi-particle Mie method (GMM; Xu, 1995), and the recently developed invariant embedding (Bi and Yang, 2014) and superposition (Mackowski and Mishchenko, 1996; Mackowski, 2014) T-matrix methods. Though accurate, these methods are often computationally expensive and are not yet practical in running online calculations. Instead, pre-calculated databases of ice-particle scattering properties at microwave wavelengths are created and made publicly available, such as those published by Kim (2006), Liu (2008), Nowell et al. (2013), Tyynelä and Chandrasekar (2014), and Kuo et al. (2016) at microwave wavelengths. However, these existing databases use randomly oriented ice particles, for which some polarimetric information is lost, such as differential reflectivity (ZDR) and specific differential phase (KDP), and they are thus not suitable for all types of polarimetric studies.

In this work scattering calculations for ice aggregates (Botta et al., 2010, 2011), branched planar ice crystals (Botta et al., 2013; referred to as “dendrites” in their paper), ice plates and columns (Lu et al., 2015), and conical graupel (Oue et al., 2015) are assembled and synthesized into one self-consistent set of scattering properties. The results are arranged into a database containing single-scattering properties of ice particles at frequencies of 9.4 GHz (X-band), 13.4 GHz (Ku-band), 35.6 GHz (Ka-band), and 94.0 GHz (W-band) and for different orientations of the ice particles relative to the incident radiation, which permits their use in all polarimetric studies. The database is now publically available for interested investigators. The remaining parts of this paper describe the particle morphologies and the numerical methods used in calculating the ice-particle single-scattering properties (Sect. 2), the scattering geometry  (Sect. 3), the scattering properties calculated (Sect. 4), the structure of the database (Sect. 5), and some illuminative results from the database (Sect. 6), followed by a brief summary and description of future refinements to the database (Sect. 7).

The numerical methods we used to create the database are the GMM method implemented by Xu (1995) and the DDA method implemented by Yurkin and Hoekstra (2011). Both of these numerical methods have the flexibility to model ice particles with arbitrary shapes. When using the GMM method, which calculates scattering properties of clusters of non-overlapping spheres, the ice particles are modeled using clusters of closely packed tiny (orders of magnitude smaller than the wavelength) spheres that collectively resemble the shape of the ice particles. Modeling ice aggregates using this approach is convenient due to its flexibility in constructing arbitrary shapes using clusters of spheres (Botta et al., 2010, 2011).

The DDA method approximates an ice particle as a cluster of polarizable points. This method calculates scattering properties of the cluster by considering both the dipoles induced by the incident electric field at these polarizable points and the interactions between these dipoles. Although not required, the polarizable points are often arranged in cubic lattices to accelerate calculations using the fast Fourier transform (Goodman et al., 1991); thus the DDA method is suitable for calculating scattering properties of compact particles such as ice columns and plates. A cubic lattice arrangement for the polarizable points is less efficient computationally for sparse particles because of the many gaps within the lattice (Petty and Huang, 2010). As such, we do not use the DDA method to calculate scattering properties of ice aggregates.

Although the GMM and DDA methods provide scattering results with accuracies specified in the calculations, they do not provide identical results because they model ice particles in different ways (i.e., GMM as clusters of spheres and DDA as dipoles). However, the shape differences between the two representations of the same ice particle do not appear critical for ice-particle scattering studies because of the variability in ice-particle morphologies. Differences in the representation of a conical ice-particle shape are overwhelmed by the differences of any conical shape with respect to similarly shaped (but not identical) particles in nature. The morphologies of the ice particles in the database and the methods used to represent them in GMM and DDA calculations are now summarized.

Polarimetric radar observables are of value in ice-species classifications and ice water content retrievals. In order to retain polarimetric information for each ice-particle scattering calculation, we did not assume random orientations for the ice particles as doing so leads to the loss of some polarimetric information. Instead, the ice particles were fixed in orientation, and their single-scattering properties calculated for different directions of the incident radiation. For these calculations planar ice crystals were oriented with their basal faces parallel to the xy plane and their maximum dimensions along the x axis (Fig. 2). Ice columns had their lengths parallel to the x axis as well, with the diagonals (maximum dimensions) of the basal faces aligned parallel to the xy plane. For ice aggregates the axis of symmetry of the circumscribing reference spheroid was parallel to the z axis, as was the axis of symmetry for conical graupel. We used one right-handed xyz coordinate system, called the particle coordinate system, to describe the orientations of the ice particles. A second right-handed coordinate system was used to describe the direction of the incident radiation and the scattering plane. The orientation of this second coordinate system was obtained by first assuming it to be identical to the particle coordinate system. Then, the xy plane of this second coordinate system was rotated by ϕPinc about the z axis, with positive rotations representing a counterclockwise rotation when viewed in the negative z axis direction (Fig. 3a). The newly oriented coordinate system, labeled with primes, was subsequently rotated by θPinc about the y′ axis, to form the coordinate system labeled with double primes, so that the z′′ axis of this coordinate system pointed in the direction of the incident radiation. For any direction of the scattered radiation the plane containing the incident and scattered radiation formed the scattering plane (Fig. 3b). The angle between the directions of the incident and scattered radiation (i.e., the scattering angle) was θsca, and the angle between the projection of the scattered radiation onto the x′′y′′ plane and the x′′ axis was ϕsca (Fig. 3b).

Scattering properties associated with different incident angles were calculated. The choice of the ranges and intervals of θPinc and ϕPinc were based on the symmetry properties of the ice particles. The aggregates had no symmetry axis, so θPinc varied from 0 to 180∘, inclusive, in 10∘ increments, while ϕPinc varied from 0 to 340∘, inclusive, in 20∘ increments. The ice crystal plates and branched planar crystals had a six-fold symmetry about their symmetry axis perpendicular to their basal faces, so θPinc varied from 0 to 90∘, inclusive, in 10∘ increments, while ϕPinc was set to 0 and 30∘. The conical graupel particles had rotational symmetry about their symmetry axis, so θPinc varied from 0 to 180∘, inclusive, in 10∘ increments, while ϕPinc equaled 0∘. The ice columns had reflection symmetry, so θPinc varied from 0 to 90∘, inclusive, in 10∘ increments, while ϕPinc also varied from 0 to 90∘, inclusive, in 10∘ increments. The orientation of the diagonals of the basal faces of ice columns had only a small influence on the single-scattering properties at the wavelengths investigated, so rotations of the basal face diagonals outside of the xy plane were not considered.

For some of the ice-particle sizes and radiation wavelengths used to construct the database, lack of accurate interpolation from incident radiation directions in the database to new directions of incident radiation is by far its major limitation. This is true because some ice-particle single-scattering properties changed by significant amounts, and nonlinearly, over the angular intervals in θPinc and ϕPinc used to construct the database. Furthermore, this makes averaging over canting angle problematic for these particular ice particles. One possible means to accelerate the calculation of orientation-averaged single-scattering properties over a range of ice-particle orientations is use of the invariant embedding (Johnson, 1988; Bi and Yang, 2014) or superposition (Mackowski and Mishchenko, 1996; Mackowski, 2014) T-matrix methods. In these approaches the T-matrix for an ice particle can be computed once and then used to calculate efficiently the single-scattering properties averaged over a range of ice-particle orientations.

In the far field, the amplitude scattering matrix can be used to describe the relationship between the incident and scattered electric fields. Following the convention in Bohren and Huffman (1983, Sect. 3.2), E∥sE⟂s=exp(jkR)-jkRS2(θsca,ϕsca)S3(θsca,ϕsca)S4(θsca,ϕsca)S1(θsca,ϕsca)E∥iE⟂i, where E is the electric field; the subscripts ∥ and ⟂ indicate parallel and perpendicular to the scattering plane (Fig. 3b); the subscripts s and i represent the scattered and incident radiation; j is the square root of -1; and k=2π/λ is the wave number, where λ is the wavelength of the radiation, R is the distance between the ice particle and an observation point in the far field, and Sn (n=1,2,3, or 4) are the elements of the amplitude scattering matrix, which are dimensionless under this convention and a function of the scattering polar angle θsca and scattering azimuth angle ϕsca. For each triplet of a realization of an ice particle, radiation frequency, and incident radiation direction, the amplitude scattering matrices are computed and stored for every 1∘ in θsca from 0 to 180∘, inclusive, and every 5∘ in ϕsca from 0 to 355∘, inclusive.

Note that in the GMM output the amplitude scattering matrix is actually in terms of Sn′ given by E∥sE⟂s=exp(jkR)-jkRS2′S3′S4′S1′E∥i′E⟂i′, where E∥i′ and E⟂i′ are defined with respect to the x′′z′′ plane in Fig. 3b rather than the scattering plane, while E∥s and E⟂s are still defined with respect to the scattering plane. The amplitude scattering matrix elements Sn′ of the GMM output can be converted to the convention of Bohren and Huffman (1983) via the transformation S2S3S4S1=S2′S3′S4′S1′cos(ϕsca)sin(ϕsca)-sin(ϕsca)cos(ϕsca). The amplitude scattering matrix elements in the DDA output are of the same convention as Bohren and Huffman (1983). In construction of the database we adopted the convention of Bohren and Huffman (1983). The GMM output amplitude scattering matrices are first transformed to the convention of Bohren and Huffman (1983) before insertion into the database.

Once the amplitude scattering matrices are computed, all of the single-scattering properties follow. Because many of these single-scattering properties are frequently used in applications, they are reported in the database along with the amplitude scattering matrices. If a single-scattering property was not provided directly by the GMM or DDA codes, it was computed directly from the amplitude scattering matrices.

In radar meteorology the electric fields are usually broken down into components horizontal to the surface and perpendicular (vertical) to the horizontal component. With this geometry the amplitude scattering matrix in the forward-scatter alignment (FSA) convention of Bringi and Chandrasekar (2001) is defined as EhsEvs=exp(jkR)RShhShvSvhSvvEhiEvi, where the subscripts h and v indicate horizontal and vertical polarizations, and the superscripts s and i represent the scattered and incident radiation. For the backward and forward scattering directions the scattering plane is not uniquely defined. For these two directions we adopt the convention of Bohren and Huffman (1983) in which the scattering plane rotates with ϕsca. The scattering plane set by ϕsca=90∘ is the y′′z′′ plane in Fig. 3b. In this case e^∥ is always parallel to the horizontal polarization direction, and e^⟂ is always parallel to the vertical polarization direction no matter what the direction of the incident radiation. Therefore, if h^ and v^ represent horizontal and vertical polarization directions, then the wave propagation direction is v^×h^, the same as e^⟂×e^∥.

The Shh and Svv amplitude scattering matrix elements for backward and forward scattering can be obtained from the dimensionless amplitude scattering matrix elements Sn as Shhb=1-jkS2(180∘,90∘),Svvb=1-jkS1(180∘,90∘)(backwardscattering);Shhf=1-jkS2(0∘,90∘),Svvf=1-jkS1(0∘,90∘)(forwardscattering). So the backscattering cross sections were computed as σhh=4πShhb2,σvv=4πSvvb2. And KDP produced by some concentration n of a specific ice crystal can be computed as KDP=103180π2πknRe(Shhf-Svvf)[∘km-1].

The database is stored in multiple NetCDF-formatted files for ease of use. The name of each file contains an identifier indicating whether the GMM or DDA method was used to produce the scattering properties that it contains. Each file contains the scattering properties associated with one individual ice particle at one frequency but for all directions of the incident and scattered radiation. Because there are 181 scattering (polar) angles (0 to 180∘, inclusive, in 1∘ increments) and 72 scattering azimuth angles (0 to 355∘, inclusive, in 5∘ increments) associated with the scattered radiation for each direction of the incident radiation, there are 181 × 72, i.e., 13 032, sets of amplitude scattering matrices associated with each direction of incident radiation. Because aggregates have the greatest number of directions of the incident radiation at 342, they lead to the largest files, containing 342 × 13 032 amplitude scattering matrices. Single-scattering properties that have only one value for each calculation (e.g., extinction cross section, absorption cross section, scattering cross section and backscattering cross section) or are of particular interest (e.g., forward-scattered differential phase) are extracted from each file and concatenated in a separate, much smaller, file. This smaller file is indexed via the following parameters: particle index indicating which particle is used in the calculation (e.g., 1 through 405 for branched planar crystals); frequency or wavelength indicators of the incident radiation (i.e., W-, Ka-, Ku-, and X-bands for the calculations currently in the database); polar angle θPinc of the incident radiation (e.g., 0 to 90∘, inclusive, in 10∘ increments for branched planar crystals); and azimuth angle ϕPinc of the incident radiation (e.g., 0 and 30∘ for branched planar crystals).

Physical properties related to each ice-particle realization are stored in this smaller file as variables with the particle index as the only dimension. These properties include ice-particle maximum dimension, thickness, mass, and projected area onto the xy (horizontal) plane of the particle coordinate system. Detailed information of the ice particles in the database, including the location and radius of each tiny sphere used in the GMM representation of an ice particle or the locations of the polarizable points in the DDA representation of an ice particle, is provided in separate files for interested users. Finally, images of the ice particles in the database are also available.

The NetCDF files that compose the database are available through 10.5439/1258029 (Aydin et al., 2016). The dimensions, coordinate variables, geophysical variables, and file naming conventions for the NetCDF files are summarized in Tables S1–S5.

The backscattering cross sections of the ice particles in the database are presented a number of different ways in Fig. 4. Focusing on the aggregates in the database (all of whose scattering properties were computed with the GMM), they range in mass from approximately 1×10-3 to 20 mg with backscattering cross sections at W-band from approximately 10-6 to 101 mm2 (Fig. 4b3). The aggregates in Leinonen and Moisseev (2015) range in mass from approximately 5 ×10-3 mg to just over 10 mg with W-band backscattering cross sections from just below 1 ×10-4 mm2 to just above 2 ×100 mm2 (their Fig. 2). While these ranges are comparable to each other, there are differences within them. For example, the drop in backscattering cross section that takes place when particle dimensions along the direction of the radiation reach about one-third of the wavelength (Fig. 4b1,b2) occurs at smaller particle masses here than in Leinonen and Moisseev (2015). We attribute these differences between the two databases to the methods for building the aggregates and differences in the orientations of the aggregates for the backscattering calculations. The spacing in mass between ice particles is much smaller in Leinonen and Moisseev (2015) as they needed small steps in mass for their integrals of backscattering cross sections over aggregate size distributions.

Upon inspection of the X-band backscattering cross sections in the database, only the aggregates have maximum dimensions exceeding one-third the wavelength (Fig. 4a₂) and hence exhibit the drop in cross section with increasing size. For particles that are small compared to the wavelength, backscattering cross sections generally increase with mass (Fig. 4a₃) and its proxy re (Fig. 4a₁). The residual spread about the best-fit line to the backscattering cross sections at X-band wavelengths for ice-particle masses less than 1 mg, with the plates falling slightly above the line and columns slightly below the line, is explained by near-field interactions within the crystals (Lu et al., 2013). The ratio of plate to column backscattering cross sections at 0.5 mg is about 4, or 6 dB, which is quite close to the spread illustrated in Lu et al. (2013) for electric fields parallel and perpendicular to the basal faces of dendritic crystals.

Finally, the spread in the backscattering cross sections of ice particles at X-band wavelengths and at W-band wavelengths for side incident radiation of each ice-particle type for a given mass (Fig. 4a₃, b₃) is due to variations in morphologies for aggregate and branched planar particles, in thickness and maximum dimension for plate and column particles, and in cone angle and density for conical graupel. For branched planar, plate, and column particles, the different numerical methods also contribute to the spread.

The database developed by Liu (2008) and Nowell et al. (2013) is well documented and openly accessible. In Fig. 5 scattering cross sections, backscattering cross sections, and asymmetry parameters computed via both DDA and GMM for branched planar crystals in the current database are compared to those of snowflakes in Liu (2008). Because Liu (2008) provides values averaged over random orientations of each snowflake and has a single snowflake for each maximum dimension (or mass represented by a single value of re, where re is the radius of a solid (0.916 g cm-3) ice sphere with mass equal to that of the crystal), values for the two snowflake types in Liu (2008) vs. size parameter 2πre / λ, where λ is the wavelength of the incident radiation, can be represented as lines. For the current database the spread in values for fixed r_e results from changes in ice-particle orientation with respect to the incident radiation, changes in ice-particle morphology, and differences between the DDA and GMM scattering methods.

For branched planar crystals oriented such that the normal to their basal planes is parallel to the incident radiation (θPinc=0∘), incident radiation scattered across the crystal constructively interferes in both the forward and backward scattering directions, because the thickness of each crystal is much smaller than the wavelength, resulting in induced dipoles that are all in phase. This, together with symmetry in the phases of the waves scattered into the forward and backward hemispheres, leads to asymmetry parameters that remain 0 for all crystal sizes (Fig. 5a₃, b₃, dark blue circles). At oblique incident radiation, there are both constructive and destructive interferences for the scattered waves. As θPinc increases towards 90∘, scattered waves in the forward direction retain their constructive interference, whereas waves scattered in other directions, including the backward direction, lose it. This is especially true at the smaller W-band wavelength as the planar crystals increase in maximum dimension. As this happens, forward scattering dominates, with asymmetry parameters of the largest planar crystals at the W-band wavelength reaching values near 0.9 at side incidence (θPinc=90∘; Fig. 5b₃, red circles). Though these tendencies are also apparent at the X-band wavelength, they are much smaller because all branched planar crystals in the database are small compared to (less than one-third of) the wavelength. As a result, at the X-band wavelength the asymmetry parameters never exceed 0.08.

The loss in constructive interference in the backward scattering direction for increasing incident polar angle θPinc is also reflected in drops in the backscattering cross sections, once again with the drop increasing with branched planar crystal maximum dimension and with it being significantly greater at the W-band wavelength compared to the X-band wavelength (Fig.  5a₂,b₂).

Carefully inspecting the backscattering cross sections at the X-band wavelength near a size parameter of 0.13 (red oval in Fig. 5a₂), one finds eight different particles contributing to them. As expected, the backscattering cross sections for all eight particles decrease with increasing incident polar angle. However, four of the particles have significantly larger backscattering cross sections at θPinc=0∘ than the other four. These differences result from the method (i.e., DDA vs. GMM) used to compute the scattering properties. The four sets with the largest backscattering cross sections were computed with DDA, whereas the four sets with the smallest backscattering cross sections are for the same four branched planar crystals but computed via GMM. The backscattering cross sections in Fig. 5a₂ that fall below those for the sector and dendrite snowflakes in Liu (2008) all result from GMM calculations, though many GMM calculations also lie above them. That the Liu (2008) backscattering cross sections split the difference between the DDA and some GMM results in the current database was not by design. All of these same features are evident in the scattering cross sections in Fig. 5a₁, though the decrease with increasing incident polar angle θPinc is not as large because the scattering cross sections are an integral quantity that includes contributions from directions other than backward.

Differences in the scattering cross sections at the W-band wavelength between DDA and GMM are again evident (Fig. 5b₁). However, for size parameters larger than 0.75 the branched planar crystals are sufficiently large that complicated patterns of constructive and destructive interference vs. scattering angles (θsca, ϕsca) take place for all incident polar angles θPinc. As a result, variability is driven by the incident polar angle, and the scattering cross sections first increase and then decrease with incident polar angle, reaching maximum values near θPinc=50∘.

Richness in the directionality of the scattering for branched planar crystals that are large compared to the W-band wavelength is illustrated in Fig. 6. Figure 6a is a depiction of the branched planar crystal upon which the Fig. 6 results are based; it has a maximum dimension greater than 5.5 mm and is nearly twice the wavelength. For unpolarized radiation with an incident polar angle θPinc=60∘ and incident azimuth angle ϕPinc=0∘, the resulting scattering phase function lacks azimuthal symmetry except for scattering angles close to the forward and backward directions (Fig. 6b, grey dots; Fig. 6c, blue and red lines). This lack of azimuthal symmetry is one motivating factor for not reporting a scattering phase function in the database while retaining the amplitude scattering matrices at 1∘ intervals in scattering polar angle and 5∘ intervals in scattering azimuth angle. The scattering phase function for a specific direction can be calculated from the amplitude scattering matrices following Bohren and Huffman (1983, pp. 71–72). Averaging the scattering phase function over all azimuth angles for fixed scattering polar angle leads to smooth dependence on scattering polar angle (Fig. 6b, solid red line) with similar values in the forward scattering direction to the scattering phase functions for randomly oriented snowflakes (Fig. 6b, dashed red and blue lines; Liu, 2008).

As Liu (2008) points out, when computing the scattering properties of a randomly oriented ice particle, one must average over small changes in the orientation of an ice particle, especially in order to compute accurate backscattering cross sections. This being the case is evident in Fig. 6d, where the scattering phase function does not depend strongly on the orientation of the branched planar crystal for forward directions, where constructive interference always occurs. In the backward direction the scattering phase function is highly dependent on the ice-particle orientation, dropping by 4 orders of magnitude as the incident polar angle changes from θPinc=0∘, for which the asymmetry parameter is 0, to θPinc=90∘, for which the asymmetry parameter is much closer to 1.

The imaginary part of the refractive index of ice is about 4 orders of magnitude smaller than its real part at radar wavelengths (Table 1) and is sensitive to the dielectric constant adjustment that we used to compensate for the tiny sphere and air-gap mixture representation of ice particles in the GMM scattering calculations. Moreover, the imaginary part can have large relative changes over temperatures ranging from -40 to 0 ∘C (Mätzler, 2006). Because the current database incorporated dielectric constants from Ray (1972), the imaginary parts of which are significantly smaller than those of Mätzler (2006), and because we made adjustments to them for the GMM calculations that may have substantially altered their imaginary parts, the absorption cross sections in this database should be used with caution.

A database of single-scattering properties of ice particles at millimeter to centimeter wavelengths is presented to facilitate ground-based, airborne, and satellite-based retrievals of ice cloud and ice precipitation properties. Branched planar crystals, plates, columns, aggregates, and conical graupel are generated, and their single-scattering properties calculated, using the GMM and/or DDA methods for different directions of the incident radiation. In addition to the scattering properties of each ice particle, including their amplitude scattering matrices as a function of incident and scattered directions, which provide full polarization information, the database also contains the physical properties of each ice particle, including the location of each ice-particle component (a tiny sphere in the GMM calculations and a polarizable point in the DDA calculations), together with imagery of it. The addition of new ice-particle realizations or new ice-particle species, such as rimed or melting particles, will be incorporated into the database as they become available and then subsequently documented.

There are several limitations to the current database. First, the ice particles in the database are just a small representation of the ice particles that exist in nature. Direct observations of exact morphologies of real ice particles, especially those in clouds, are limited. Improvements in the observation of detailed ice-particle structures would serve as valuable guidance in the future development of the database. Second, calculations at high frequencies for more directions of the incident radiation will be necessary to ensure accurate interpolation of ice-particle single-scattering properties to other directions of the incident radiation. And finally, the absorption cross sections in the database should be used with caution as they are based on older dielectric constants (Ray, 1972), and in the case of the GMM calculations may have errors in them as a result of adjustments made to compensate for the air gaps in the tiny sphere representations of the ice particles.

The database is available through 10.5439/1258029 (Aydin et al., 2016).