Atmospheric particles absorb, emit and scatter electromagnetic radiation. The optical properties governing these processes are not easily determined for an arbitrarily shaped particle e.g.. Accordingly, these properties can not be calculated “on-the-fly” and radiative transfer simulations must frequently make use of tabulated values. At microwave wavelengths, the targets of a database of particle optical properties are hydrometeors, i.e. cloud and precipitating particles that consist of condensed water. The need to consider particle shape in detail increases with frequency and is the highest for hydrometeors containing ice. Aerosols can in general be neglected for microwave radiative transfer, but measurements of volcanic ash are another potential application of sub-millimetre radiometry .

Microwave particle optical properties, also often denoted as scattering data, are most obviously needed for measurements of precipitation and cloud properties. Active instruments, i.e. radars, perform such measurements by detecting backscattering of hydrometeors, but extinction of the signal must also be considered. Radars targeting rain operate at relatively low frequencies and are well established . For example, ground-based networks of precipitation radars are today found in many countries. The sensitivity to cloud particles and snow increases with frequency. The highest standard radar frequency today is 94 GHz , used from both ground e.g and aircraft e.g. and by the first space-based cloud radar onboard CloudSat launched in 2006 as well as the CPR instrument onboard ESA's EarthCARE mission .

Rain and ice particles affect passive microwave radiances by scattering as well as by contributing to absorption and emission e.g.. The relative importance of absorption and emission is the highest for particles that are small compared to the wavelength, and also higher for liquid particles, compared to ice ones, due to differences in refractive index. The present set of operational microwave sensors covers frequencies of up to about 190 GHz e.g.. The main hydrometeor products of these measurements today are cloud liquid water and rain . Ice hydrometeor retrievals exist e.g., but are less established and are often purely empirical using satellite radar data for “training” .

At present, the sub-millimetre part of the microwave region is primarily used for limb sounding. These instruments target mainly the stratosphere and mesosphere, but can provide data on humidity and cloud ice down to about 10 km . Sub-millimetre measurements dedicated to the troposphere are so far only available for some aircraft instruments . Operational sensors, such as used for weather forecasting, making use of sub-millimetre wavelengths will be available from about 2022 . The addition of this wavelength region will improve the general sensitivity of passive microwave measurements, particularly regarding ice hydrometeors. Adding this wavelength region should provide a better constraint on particle size of frozen hydrometeors and, not only the sensitivity, but also the accuracy of ice hydrometeor mass retrievals should be improved .

Scattering data are not only important for the direct measurement of hydrometeors, but also essential to characterise the interference of clouds and precipitation on measurements targeting other quantities. One such example is the “cloud screening”, applied in humidity retrievals, based on channels around the 183 GHz water vapour spectral line . The addition of sub-millimetre channels should facilitate this cloud screening. Passive microwave data, particular using channels on the low-frequency end, are also used to estimate ocean surface variables, and even these retrievals are affected by hydrometeors. The characterisation of this interference can even involve polarisation effects .

In summary, microwave sensors offer information on cloud and precipitation, as well as surface variables, humidity and other gases with relatively low cloud interference . These advantageous aspects are today heavily used for both climate studies and weather prediction. However, the full potential of existing data is far from fully exploited e.g., and preparations for future measurements are needed e.g.. In both cases, progress is today strongly limited by a lack of hydrometeor scattering data . Liquid particles can to a large extent be assumed to be spherical, and their scattering properties can be calculated efficiently by Mie theory. On the other hand, both cloud and snow ice hydrometeors exhibit a huge variability in shape e.g., and to derive their scattering properties is a demanding calculation task. These complications have resulted in patchy coverage of ice hydrometeor microwave scattering properties.

To be of a general character, scattering data must cover a number of attributes, as discussed in later sections. For a given particle, the scattering properties vary with frequency, polarisation, temperature and orientation. Furthermore, particle size and shape play a significant role where the comprehensive description of particle shape is less clear. Several measures on particle size are being used, but those represent a small complication in comparison to morphology classification. Traditional schemes, such as , offer a good starting point regarding the classification of pristine crystals. Ice hydrometeors above about 200 µm in maximum dimension tend to be aggregates of crystals ; hence, aggregates should in general dominate the scattering signatures in microwave data, which is mainly determined by particles larger than 100 µm . However, there is no established manner to categorise particle classes. So far aggregates are described in relatively crude terms, by, for example, effective density and degree of riming. A further complication is that both liquid and ice water can be found in a particle simultaneously. The so-called radar bright band is normally taken as a manifestation of the presence of melting ice hydrometeors .

A review of existing microwave scattering data was done by . At that point, the most general collection was provided by despite it having been limited to totally random particle orientation, frequencies below 340 GHz and low complexity in particle morphology. The only source of data covering sub-millimetre wavelengths was , but it was found to be based on an outdated ice refractive index parameterisation. More complex ice particles, i.e. particles of aggregate type, had been considered , but then providing data with limited frequency coverage and mainly targeting radar applications. More recently, presented data for a large number of habits, including many aggregate realisations, but the publicly available data lack detailed information and provided only parameters applicable in simplified radiative transfer. The data of have interesting features regarding particle shapes and orientation, but are not well suited for passive microwave applications since they are based on an obsolete, and inaccurate, refractive index parameterisation (see Sect.  for details). The data of , which are an updated and extended version of the database by , cover 1 to 874 GHz, at multiple temperatures, and can thus be considered to be the first to provide full coverage of the microwave region, but are still limited to totally random orientation and relatively simple habits.

Besides the production of databases, there are a number of investigations of relationships between particle properties and optical properties. For example, the data of were compared to the scattering properties of more complex, snow-like, particles by . The impact of riming on scattering properties was studied by , using a triple-frequency approach. A clear shift in radar signature was observed as riming was gradually applied to pristine aggregates. Also, data for melting particles have been reported , showing an increase in extinction and backscattering at increasing melting fractions.

In summary, important progress has been made, but there are still important gaps in available data. Based on the findings in , a decision was taken to gradually build up a database of microwave scattering properties, with the long-term goal of providing a comprehensive source of such data. The ambition is to provide data of a general character supporting both passive and active observations involving polarimetric information in a consistent manner. A secondary objective is to ensure that advanced scattering solvers (e.g. RT4 by and MC by ) as included in the ARTS-2 forward model can be fully utilised. In the following, we will hence refer to this data compilation as the “ARTS scattering database”.

The first version of the database is presented below. The database is not complete. This versions lacks at least features found in some databases targeting radar applications, but this version is already more extensive than comparable efforts with a broad scope. The frequency coverage is high, very similar to the one of , and multiple temperatures are covered. Full polarimetric data are given. A special emphasis has been given to improvements in the representation of aggregates; 34 ice hydrometeor habits of totally random orientation are included, with 16 of these being of aggregate type. Pure liquid particles are also covered, in the form of liquid spheres. Data for more specific orientations (such as particles with a preference for the horizontal plane) are left for the next database version. Non-spherical liquid particles and melting particles are other planned database extensions.

An overview of the database content is found in Sect. . A number of software tools have been used to generate the database, and those are presented in Sect. . The various microphysical assumptions are summarised in Sect. . Example results are found in Sect. . Data format, interfaces and availability are discussed in Sects.  and . Finally, conclusions are found in Sect. .

The optical properties of a particle can be reported in several ways. The ARTS database assumes that electromagnetic radiation is described using the Stokes formalism and provides the extinction matrix, the absorption vector and the phase matrix. These quantities are most easily introduced by considering the basic radiative transfer equation: dI(ν,r,n)ds=-K(ν,r,n)I(ν,r,n)+a(ν,r,n)B(ν,r)+∫4πZ(ν,r,n′,n)I(ν,r,n′)dn′, where I is the Stokes vector of the radiance, ν is the frequency, r is the position, n is the propagation direction, s is the distance along n, K is the extinction matrix, a is the absorption vector, B is the Planck function, Z is the phase matrix and n′ represents the propagation direction of radiation scattered towards n. See for an exact definition of the Stokes vector assumed, as well as for details regarding assumptions and relationships implied by the equation. Note that a can be derived from K and Z, but is included in the database anyways in order to avoid numerical issues and ensure good accuracy of all three main quantities.

To be clear, K, a and Z in Eq. () represent bulk properties, while the database provides these quantities on a particle basis, which are dependent on particle size and dielectric properties. Furthermore, the scattering is assumed to be incoherent between particles, and the bulk properties are simply obtained by summing up K, a and Z of all particles inside the considered atmospheric volume. Information allowing radiative transfer with the full Stokes vector (length 4) is provided. However, transformations are used in order to save storage space, and some processing of the data is needed (Sect. ) before they can be applied in Eq. ().

The radiative transfer equation is not always expressed as in Eq. (), but it should be possible to derive the quantities found in other versions of the equation from the optical properties provided. For example, some “scattering solvers” operate with the single scattering albedo and the asymmetry parameter. These scalar quantities can be calculated from the elements in K, a and Z matching the first Stokes component. The main quantity for simulations of radar measurements is backscattering, which essentially is the value of Z representing the backward direction. For further details around these derived properties, see the database technical report .

The database considers orientation-averaged quantities only. In general, using the scattering matrix Z as an example, orientation-averaged quantities are calculated as Zon′,n=∫02π∫0π∫02πpααpββpγγZn′,n,α,β,γsin⁡βdαdβdγ, where Zo is the orientation-averaged scattering matrix, α, β and γ are the three Euler angles describing the orientation of particles, and pj are probability density functions describing the distribution of particle orientations.

The database currently only covers particles in one orientation mode: totally random, defined as the distribution where all particle orientations are equally probable. That is, pα, pβ and pγ are all uniform distributions. The database is designed and intended to also include what can be denoted as azimuthally random orientation. In this orientation case, the angles α and γ are fully random as for the totally random case, while the data are evaluated at some discrete tilt angle β (i.e. pβ is a Dirac delta function). By integrating over β, arbitrary fluttering distributions can then be determined. It turns out that azimuthally random orientation is much more costly with respect to both calculation burden and data storage, and this orientation mode is left for the next database version.

Also, a reference particle alignment must be defined, as it affects both our definition of aspect ratio (Sect. ) and data for azimuthally random orientation. The reference alignment should be linked to how ice particles on average are oriented in the atmosphere. Accordingly, we align the particle with its maximum principal moment of inertia axis parallel to the z-axis. Furthermore, the minimum principal axis is aligned along the x-axis. This approximates the mean alignment of falling particles without performing extensive aerodynamics simulations. The definition is also stable in the sense that particular features, such as a narrow arm of a particle, will have less impact than the overall mass distribution of the particle.

Quantitatively characterising size and shape of irregularly shaped particles is a non-trivial task. We provide several descriptive values on particle size. First of all, particle mass m is reported. Secondly, the volume equivalent diameter is given, which is related to mass by Dveq=6mπρ1/3, where ρ is the actual density of the material found in the particle, in the case of ice set to 916.7 kg m-3. Note that Dveq relates to the diameter of the volume-equivalent ice sphere, not of a mass equivalent melted sphere. The size parameter applied, x, is defined with respect to Dveq: x=πDveq/λ, where λ is the wavelength.

Another common parameter is the maximum dimension Dmax (sometimes used interchangeably with the maximum diameter), for which no standard convention exists. For instance, photography-based in situ measurements often derive the maximum dimension by the largest distance between two pixels in a 2-D image. Such a definition is highly dependent on the particle orientation with respect to the camera. In the ARTS database Dmax is defined as the diameter of the minimum circumscribing sphere, which takes the whole 3-D structure into account. However, ice particles are often highly irregular, and since Dmax is a measure of a particle's extreme points, it is an inherently ambiguous and ill-defined parameter.

Similarly, the aspect ratio (AR) is defined differently by different authors. In general it provides a measure of the non-sphericity of the particle of concern, thus affecting the particle's preferred orientation and its scattering properties (polarimetric quantities in particular). The definition of AR is ambiguous and ill defined, similar to Dmax. Our definition of AR is linked to how the particle is oriented with respect to the horizontal plane. Based on the particles' reference orientation outlined in Sect. , we define AR as the ratio of the maximum particle span found in the XY-plane to the span along the z-axis.

Axial ratio is sometimes used interchangeably with aspect ratio. We restrict the use of this term to describe the shape of hexagonal prism columns and plates, with axial ratio defined as L/(2a) where L is the height of the prism and 2a its diameter. With this definition, columns/plates have an axial ratio above/below unity.

The database also contains a simplistic measure of the aerodynamic cross-sectional area for each particle. The variable stored is the diameter of a circle with an area equal to the cross-sectional area when viewing along the zenith angle. For this calculation the particle orientation is assumed fixed in its reference position.

The term “habit” is frequently used in the context of particle shape. We define habit as a set of particles with a common basic morphology and following a rule on how the morphology varies with size. As an example, a common habit assumption is hexagonal columns having an aspect ratio that depends on size according to an analytic expression. Furthermore, the relationship between maximum diameter and mass of a habit is commonly parameterised by two constants, a and b, as m=aDmaxb. The a and b values reported below assume SI units. As a reference, a habit consisting solely of ice spheres has a=480 and b=3. The goal is that the database habits will follow Eq. () as far as possible, but an exact fit is normally not possible, for example, when using third-party generated shape data. For b<3, Eq. () can only be considered valid above some threshold size, normally of the order of 100 µm, because Eq. () otherwise requires unphysically high densities (“superdensity”) for Dmax below the threshold size.

In total, 34 habits divided into several subgroups are provided (Table ). Each habit is assigned a unique Id number. Visualisations of the single crystal and aggregate habits are displayed in Figs.  and , respectively. The a and b parameters given in Table  were calculated by a least squares fit between log⁡(m) and log⁡(Dmax), including only particles having a Dmax≥200 µm.

As mentioned, no totally general classification of particle shape exists, but for user friendliness the database is structured according to a rough categorisation of the habit type. The top category is “phase”: liquid, ice or melting. Melting is not covered by the current database version, but such habits are intended to be included in the future and the database structure is set up accordingly. The ice and melting habits are further divided between single crystals and aggregates. This classification level is not applied for liquid particles. Both single crystals and aggregates are classified as either pristine or rimed. Table  gives an overview of this categorisation. Further information on how the particles were generated is provided in Sect. .

The number and range of sizes are not identical between the habits for a number of reasons. For some habits, mainly aggregates, it is not possible to generate shape data on a predefined size grid. Certain habits have been provided by third-party sources, where control of the size grid is limited. Furthermore, the methodologies of designing habits have evolved over the time of the database creation. Lastly, it makes sense to target different size ranges with single crystal and aggregate habits. However, the general strategies to set the size grids are similar.

The minimum number of sizes was set to 30, but single crystal data are still provided for 35 to 45 sizes. Aggregates have mainly 35 sizes. The size ranges of the habits (see Table ) are not consistent, due to the diversity in methods to generate the shape data. However, target ranges were set to give a reasonable coverage of particle sizes reported in the literature. The single crystals' habits have sizes reaching either 2 mm in Dveq or 10 mm in Dmax. The aggregates go up to 5 mm in Dveq or 20 mm in Dmax. Exceptions are the aggregates consisting of relatively small crystals, where it was computationally too costly to reach the upper limit of any of the target ranges. The smallest single crystal particles are mostly Dveq=10 µm. The smallest aggregates mainly have Dveq<100 µm, but this criterion is not met when the constituting crystals are larger than this limit. Habits consisting of solid spheres (handled by Mie code) were allowed both to have more sizes (200) and cover larger size ranges, in order to allow detailed reference calculations using these habits. The final size range of all habits is found in Table . The general strategy to select intermediate sizes is to aim for an approximately equidistant linear spacing of up to Dveq=100 µm and equidistant spacing in the logarithm of Dveq above.

Additionally, an upper limit with respect to size parameter (x) was introduced for practical reasons since the computational burden to calculate the scattering properties increases strongly with x. That it is possible to apply a limit on x is due to the fact that the size range that contributes the most to bulk scattering properties is shifted towards smaller sizes when going up in frequency. That is, for a given (large) particle, x itself increases with frequency, but the particle becomes less influential for the scattering properties of the overall local particle mix. This effect is illustrated in Fig.  for extinction. An analysis of backscattering would give a similar result as extinction and backscattering are highly correlated (both increase with D6 in the Rayleigh regime, etc.).

Figure  demonstrates that x=10 is a reasonable limit. It shows the estimated relative error in the calculation of bulk extinction considering data to a given limit in x. Figure  presents a worst case scenario as a relatively high ice water content (1 g m-3) and a frequency in the upper end of the database's coverage (671 GHz) are considered. Particles with x<1 contribute marginally to the bulk extinction here indicated by the tail distribution staying close to 1 up to about x=1. There are three cases in Fig.  where the tail distribution is well above 10 % even at x=10. These cases are all combinations with the PSD of and habits having b=3. This PSD is intended for snow-type hydrometeors, where b around 2 is expected . That is, these three cases of concern represent fairly unrealistic, or extreme, assumptions.

It is not unlikely that further problematic situations with respect to the PSD exist apart from those three cases presented above, and occasional errors above 10 % can not be ruled out. On the other hand, it should be remembered that the water vapour absorption at 671 GHz is high, giving a decreased sensitivity to lower altitudes, where most large particles are found most frequently, when observed by satellite instruments. In summary, our interpretation of Fig.  is that the error by applying a limit at x=10 should in general be well below 10 %.

The size limit with respect to x is evaluated separately for each frequency. This means that, for example, at typical radar frequencies data are at hand for all sizes, while data can be lacking for large particles at higher frequencies. The limit was applied in such a way that, if possible, coverage up to x=10 is maintained. That is, assuming that particles matching x≥10 are available, the smallest one exceeding the limit still got included.

The overall frequency coverage was set to be 1–886.4 GHz. Inside this range, optical properties are given for 34 frequencies (Table ). A majority of the frequencies were selected to bracket channel sets found on both existing and planned operational microwave sensors. These are in the following termed “channels” with arbitrary channel numbers assigned (see Table ). For example, data are provided for 50.1 and 57.6 GHz, forming channel 3, which provides coverage of the standard set of microwave temperature sounding channels. Additional frequencies were picked to cover standard radar wavelengths, as well as to obtain a general coverage between 1 and 15 GHz. Above 200 GHz, the frequencies are mainly governed by the channels of the planned Ice Cloud Imager (ICI) mission . The upper end at 886.4 GHz was set in order to support the ISMAR and IceCube instruments.

We stress that the database should be used with great care for frequencies outside the defined channel ranges. Whether interpolation between the channels can be applied must be judged from case to case. For example, interpolation to 170 GHz should not be problematic as the distance between channels 6 and 7 is small (in fact smaller than the width of channel 7 itself), while frequencies around, for example, 550 and 770 GHz can not be claimed to be properly covered by the database. The relevant measure to judge whether an interpolation can be performed should be the ratio between spacing and frequency, not the absolute size of the frequency spacing. As a general rule, only the closest database frequencies should be used when performing interpolation.

Optical properties are given for multiple temperatures, rather than a set of real and imaginary refractive index values. The reason for this is that the used parameterisations, and for ice and water, respectively, should predict the refractive index with sufficiently high accuracy (Sect. ). The selected set of temperatures contains 190, 230 and 270 K for hydrometeors consisting solely of ice. For pure liquid droplets, the temperatures are 230, 250, 270, 290 and 310 K. See Sect.  for further details regarding issues related to refractive index and to temperature interpolation.

Beside sizes and shapes of particles, single scattering properties are determined by the dielectric properties of the particle material. These are commonly described by the complex refractive index, where the real part mainly affects the scattering properties while the imaginary part primarily determines the absorption. The refractive index of liquid and frozen water at microwave frequencies varies significantly with frequency as well as with temperature.

A review of (water) ice refractive index models is shown in , and a comparison between some models is also found in Fig. . The refractive index model by is included in Fig.  as it strongly deviates from more recent parameterisations, based on a wider set of laboratory measurements, but it has still been applied in some recent studies . The most significant deviations are found for the imaginary part. This causes concern for at least passive measurements, as ice absorption has been shown to play a non-negligible role for such observations. e.g..

In , the ice refractive index model by was suggested as a good choice for the full microwave region (up to about 1 THz) and Earth atmospheric temperatures. Newer models e.g. refer or are essentially identical to . Hence, for our database, we set the refractive index of ice according to .

For liquid water, the model of is applied, which provides refractive indices for frequencies of up to 25 THz and temperatures between 0 and 100 ∘C based on empirical fits to an extensive collection of water refractive index data . Deviations to the model by , which focuses on super-cooled liquid water but does not cover sub-millimetre frequencies, remain smaller than 30 % even at the lowest temperatures of concern (-40 ∘C). Hence, although is, in the strict sense, not recommended for super-cooled liquid water, it is applied here at all temperatures.

Finally, a smaller study on the required temperature grid for ice habits was performed. Assuming optical properties of solid Mie spheres, a number of forward calculations with varying temperature grid resolution were compared. Forward calculations using a 2.5 K spaced temperature grid covering 150 to 270 K were used as a reference. A number of coarser grids, all equally spaced between 190 and 270 K and applying linear interpolation and extrapolation in temperature, were compared to the reference set. Simulations were performed for all channels employed by the ISMAR airborne radiometer and 5000 atmospheric scenarios contained in , in order to maximise the temperature profile diversity. Deviation statistics over these 5000 cases and the 13 channels were derived. Figure  summarises the results, showing that for a setup with three temperature grid points, maximum deviations to the reference simulations over all scenarios and channels are <2 K, and the 99.7 percentiles of differences are <0.2 K. For five grid points, maximum deviations fall below 0.3 K and the 99.7 percentile below 0.05 K. The accuracy can be improved further by applying higher-order polynomial temperature interpolation. A three-point grid was judged as a good compromise between attainable simulation accuracy and the calculation burden required to generate the database.

The single crystal habits provided by the database are summarised in the upper part of Table . Example visualisations are found in Fig. . The crystal shapes are mainly based on parameterisations taken from the literature , but some new crystal habits have also been defined. For completeness and as a reference, the ice sphere habit was also included.

For crystal habits, external data are restricted to numerical parameterisations of shape properties, while the actual shape data matching those parameterisations were generated by the Snowflake Toolkit. The long column, short column, block column, thick plate and thin plate, taken from , are all hexagonal and have axial ratios of 4, 2, 1, 0.2 and 0.05, respectively. These axial ratios were defined by to be constant over all sizes. As a consequence, they all obtain b=3. In contrast, plate and column type 1, with dimensions taken from , are defined to have a b of 2.48 and 2.05, respectively, implying an axial ratio that grows with mass. These definitions were based on measurements of ice crystal dimensions . The sector snowflake, defined in , is an idealised representation of a snowflake, consisting of three intersecting ellipsoids with their mass centres positioned at the origin. This parameterisation was based on surface measurements of aggregates .

The different bullet rosette habits all consist of hexagonal bullets connected at the tips. The crystal dimensions are taken from , based on measurements listed in that paper. All bullets grow in a similar fashion, in the sense that all bullets with equal mass will have the same dimensions regardless of the considered habit. Furthermore, in all versions, the bullets are aligned perpendicularly to each other. The flat 3- and 4-bullet rosettes have all their arms lying in a common plane. The perpendicular versions have one arm rotated 90∘, resulting in more compact particles.

Two crystal habits were generated specifically to match the a and b assumed for cloud ice in two atmospheric models: GEM (Global Environmental Multiscale Model) and ICON (Icosahedral non-hydrostatic general circulation model). The GEM model was prepared for the EarthCARE mission and the ICON model is a part of the German HD(CP)2 project

http://hdcp2.eu (last access: 11 July 2018)

The ARTS database includes habits developed specifically both for this database and from third-party sources. For calculations at higher frequencies, aggregates are arguably lacking in the current scattering databases and the aim has been to include a relatively diverse set of aggregate habits.

Three different habits designed to represent graupel are included in the database. All three can be considered heavily rimed particles, i.e. only composed of rime. The spherical graupel was generated using the Snowflake Toolkit module treating aggregation of spheres. The angle distribution of the incoming spheres was set to be isotropic, resulting in an overall spherical shape of these graupel particles. Furthermore, the constituting spheres have randomly distributed diameters, selected from a gamma distribution with a mean radius of 300 µm and a standard deviation of 75 µm. Furthermore, the habit was designed to have an effective density of approximately 140 kg m-3 in order to roughly match observations .

The ICON and GEM graupel habits were generated in the same general way as the ICON and GEM hail habits, but the settings were tuned to create a granular pattern when examining slices through the resulting graupels. Particles that can be classified as lightly or moderately rimed can be generated by RimeCraft, and are intended to be included in a next database version.

The liquid phase is so far limited to spherical drops, with scattering properties calculated by Mie theory (Sect. ). The number of sizes was set to 200, and, as mentioned, data are provided for five temperatures between 230 and 310 K. Spherical drops should be an acceptable approximation for liquid cloud and drizzle particles, but not for larger raindrops, and liquid drops of non-spherical shape will be part of the next database version.

A number of comparisons have been made in order to obtain a rough assessment of the accuracy of the data. At an early stage, dedicated tests were made to ensure that there is an acceptable agreement between our usage of ADDA and equivalent results obtained by the T-matrix implementation of . Some deviations were unavoidable as T-matrix is a fully analytic method, while DDA is numerical and operates with discretised shape data. This is of special concern for particles where the properties vary quickly as a function of size (due to “Mie resonance features”). However, this should not be critical as these details are largely removed when averaging over size to obtain bulk properties.

Further, Fig.  compares the extinction of some hexagonally shaped particles with T-matrix calculations for cylinders. The T-matrix cylinders were given the same length or height and the same cross-sectional area; i.e. volume (and hence also mass) is maintained. The ADDA results for backscattering mainly agree with the T-matrix, but also show indications of some instability. A closer examination of the poorer cases revealed that high deviation in backscattering is associated with low number of orientations used by ADDA, indicating that its iteration criterion is not optimal with respect to this quantity. That is, the Romberg scheme has stopped prematurely with respect to backscattering. On the other hand, an acceptable accuracy appears to have been reached for extinction. As expected, the extinction deviates between ADDA and T-matrix, but not strongly: the difference is throughout below 4 %. These results give additional indications on the accuracy of the database, but also indicate that the microwave extinction of ice particles primarily follows overall particle properties, such as mass and maximum size, while surface features, such as roughness, have a relatively low impact. That is, if plates and columns are treated to be hexagonal or cylindric has only a marginal impact on microwave optical properties.

For habits, where external shape definitions have been used, comparison with their source databases is possible. However, these comparisons involve interpolation in temperature, frequency and size, and again a perfect agreement can not be expected. In order to minimise the impact of these interpolations, close matches in frequency and temperature between the databases have been selected. Discrepancies will also depend on differences in DDA convergence criteria selected as well as on the exact sampling methodology used when discretising the particle shapes. Of concern is also that set dipole sizes following our Eq. (), while used a stricter criterion resulting in a factor of 2 smaller dipole size. Both performed DDA calculations for a set of specific particle orientations and based the orientation averaging on these data, but the number of orientation angles differ. Tests to estimate the impact of these later factors are reported by both and .

As we do not have access to the discretised shape data used in other databases, it is not possible to assess applied particle shapes on that level, but reported masses can be compared. The masses obtained by us show insignificant deviations to the corresponding values reported by and , with the exception of the sector snowflakes. For this habit, discrepancies in mass of up to 9 % are found (Fig. ). A simple discretisation of the particle shape normally results in a change in the particle mass. Our strategy has been to apply a rescaling of the discrete data to ensure that the final data correspond to the target mass. Already, noted that the sector snowflake habit in shows an non-smooth variation in mass, and it seems that no similar rescaling was applied by . The discretisation is a particularly critical issue for the sector snowflake habit, as these particles have the highest aspect ratios and can be only a few dipoles thick. Just the decision to place dipole centres at …,-l,0,l,… or …,-l2,l2,… (where l is the dipole size) has here a significant impact, both for the effective mass after discretisation and the final optical properties.

The differences in the mass of sector snowflakes give a direct imprint in the extinction reported for this habit by the two databases (Fig. ), but it is also noticeable that the difference in extinction is for some sizes considerably larger than the mass difference. However, the most striking feature is the high deviation in backscattering. Again, the sector snowflake stands out, and, as a much more representative example, a comparison for the block column habit is shown in Fig. . The agreement is better for the block columns in overall terms, but the backscattering still frequently deviates by 10 % or more.

A comparison with data of is found in Fig. . Clear systematic differences originating from the different refractive index models applied can be recognised. The scattering data of are based on the refractive index of . This parameterisation deviates significantly from more recent ones (Sect. ), particularly regarding the imaginary part. The deviations in the refractive index are such that the data of exhibit a higher/lower absorption below/above about 400 GHz. The difference in the real part of the refractive index is much less pronounced and there is a fairly good agreement on the extinction due to scattering. The same is true for the backscattering at 90 GHz, while the backscattering at, for example, 664 GHz deviates significantly for millimetre-sized particles. Putting aside deviations that should be caused by the older refractive index data used by , the remaining data indicate a good underlying agreement between the two sets of DDA calculations.

The difference in refractive index with respect to is relatively small at 448 GHz. With this in mind, the combined interpretation of Figs. , and is that the calculation of extinction disagrees by 10 % at most, but is generally inside 5 %. Larger differences are found for backscattering, particularly at higher frequencies. If only the radar frequencies of today (i.e. <100 GHz) are considered, then the general agreement for backscattering is also of the order of 10 %, with a strong exception in the sector snowflake habit and some data points with early stop of the Romberg scheme.

The results found for backscattering give a direct indication on the accuracy of the phase matrix for the direct backward direction. This is likely the direction with the highest calculation errors. However, the finer details of the phase matrix should not be critical for passive measurements as the radiation field is relatively smooth (except around the limb direction), and the overall accuracy of the phase matrix should be similar to the one of the extinction. To study the effective accuracy of the phase matrix data provided would require full radiative transfer simulations, which are beyond the scope of this article.

Figure  displays effective densities for a selection of habits. The effective density is defined as ρe=6mπDmax3, i.e. the mass divided by the volume of the minimum circumsphere. It is linked to the a and b coefficients of a habit as ρe=6aDmaxb-3π, where the m has been replaced by Eq. (). Accordingly, the data in Fig.  should ideally end up along straight lines. This is also the case for habits having an analytic description of the shape, while deviations are observed for habits having stochastically generated shape data.

The effective density is governed by two main factors, the particle's “fluffiness” and aspect ratio. Habits having throughout a high ρe are generally dense particles with a spherical appearance. Particles with low values either have a high aspect ratio (such as the sector snowflake) or are very porous. Habits with b<3 have negative slopes in Fig.  and tend to grow differently in the spatial dimensions, e.g. the plate type 1 habit has an increasing aspect ratio with size. However, b<3 can also correspond to particles that increase in fluffiness with increasing distance to the particles' centre, e.g. the GEM snow habit.

The legend of Fig.  is divided into groups of habits, with single crystals having solid lines, aggregate and snow particles dashed lines, and dense graupel or hail-type particles dot–dashed lines. The ice sphere habit serves as an upper bound, while the long column, the flat 3-bullet rosette and the sector snowflake exhibit the lowest density, depending on the Dmax range. More generally, the graupel and hail habits occupy the upper part of the plot, being the densest habit group. The aggregates and crystals tend to share the same area in the middle to lower parts of the graph. It will be seen later on that the effective density has a noticeable impact on the observed optical properties.

Example data of extinction and backscattering efficiencies are displayed in Fig.  for some selected frequencies and habits. The habits and legends are the same as in Fig. , i.e. single crystals have solid lines, aggregate or snow particles dashed lines, and dense graupel or hail-type particles dot–dashed lines. The extinction and backscattering efficiencies are calculated as Q=4σπDveq2, where σ is the given cross section. That is, both x and Q are defined with respect to Dveq. A related remark is that efficiencies are thus compared in Fig.  between particles with the same mass (as a given x implies a specific mass).

A few characteristics can be observed in Fig. . Firstly, the groups tend to cluster. For example, the aggregate habits tend to have low extinction at 175 GHz and high extinction at 670 GHz. An opposite tendency can be observed for the dense particles given dot–dashed lines, which have relatively high and low extinction at 175 and 670 GHz, respectively. The crystal habits (solid lines) have efficiencies similar to heavy/dense particles at 175 GHz, but varying, intermediate, extinction values at 670 GHz. Similar observations can be made for backscattering; dense particles tend to have high backscattering, and aggregates low backscattering. Interestingly, the features observed for effective density in Fig.  are to a large degree transferred to the scattering properties in Fig. , but exceptions are also noted. For example, the spheres and ICON hail have comparatively low extinction at x>3 at 175 GHz, and several crystal habits have higher backscattering at 94.1 GHz than the dense particles. Overall, the effective density can be considered an important parameter, but other aspects, such as exact particle shape, can exert influence as well. This discussion refers to how extinction and backscattering are related to particle mass. Other relationships can be found if the comparison is made with respect to Dmax.

A common manner to evaluate scattering properties in the radar community is the triple-frequency signature . This is a multi-frequency bulk backscattering analysis involving three frequencies with data reported as two dual-wavelength ratios (DWR). The approach involves the effective reflectivity factor Ze: Ze=1018λ4π5⋅|K|2∫0∞σbDmaxNDmaxdDmax, where σb(Dmax) is the backscattering cross section, N(Dmax) the number of particles of size Dmax, and K is calculated as K=(m2-1)/(m2+1), with m being the complex refractive index of liquid water. The DWR for two wavelengths λ is then obtained as DWRλ1,λ2=10⋅log⁡Ze(λ1)Ze(λ2). Example triple-frequency results are shown in Fig. , using three standard radar frequency bands. Refractive index of water (m) was taken from , assuming a reference temperature of 270 K. Further, an exponential PSD, defined over Dmax, dNdDmax=N0exp⁡-ΔDmax, was selected. This PSD is identical to the one applied by and . N0 is set to a constant value of 1, which is of no consequence since this constant is cancelled out in Eq. (). In order to not let truncation issues influence strongly, Δ was varied for each habit separately, in such a way that the mean size of the PSD ranges from 1.5 times the smallest available Dmax to 1/3 times the largest available Dmax.

Effective reflectivity is defined in such a way that if all particles scatter according to Rayleigh theory, Ze is independent of frequency. This has the consequence that most high slope parameters (Δ), which correspond to low ice water contents, give rise to zero or low DWR. The other end of each triple-frequency curve corresponds to the highest Δ that could be accommodated with the size range available for the habit.

The triple-frequency signatures have been shown to act as an indication of effective density, frequently linked to the degree of riming . Figure  shows that the backscattering of the database habits matches the general expectations. First of all, the data span the same general ranges of DWR as reported by and . Further, the single crystal habits (solid lines), which are of comparatively low effective density (see Fig. ), tend to occupy the left part of the graph. On the other hand, the dense graupel and hail habits (dot–dashed lines) are found in the rightmost part of the graph. The aggregate-type habits generally occupy the space in between the crystals and denser habits.

The database is structured in a folder hierarchy, following the habit classification displayed in Table . At the bottom of the folder structure, there is one folder for each habit. These folders contain auto-generated pdf documents and text files that summarise the scattering data as well as a “habit logo” figure (Figs.  and ). The actual data are also found in these folders, with one netCDF4 file for each particle size of the habit. Inside each netCDF4 file, there is an internal folder structure to organise the data according to frequency and temperature. These folders contain the scattering data, as well as particle shape and processing information. The stored variables and their attributes are summarised in Table . The variable names should hopefully all be self-explanatory, but for clarity they are accompanied by a description tag.

The SingleScatteringData group contains not only the core scattering properties (Z, K, and a), but also information on frequency, temperature, and angular grids. The ShapeData group provides information on the particle behind the scattering properties, such as mass, Dmax, Dveq, aspect ratio, aerodynamic area equivalent diameter, and refractive index. The CalculationData group contains ADDA settings and log data (DDA residual error used, date of completion, etc.). In particular, an identifier of the used shape file is given, and these files are part of the database. Thus, each scattering calculation is fully reproducible.

For orientation-averaged scattering properties, the optical properties exhibit features that can be used to reduce the overall data volume. For example, the scattering matrix has only six unique, non-zero, elements: Z11, Z12, Z22, Z33, Z34 and Z44. The extinction matrix has only one such element, K11. Similarly, only one element of the absorption vector, a11, is non-zero. Only these unique elements are stored, together with information on how full matrices and vectors will be populated. For example, the scattering matrix is stored in the database as a tensor (phaMat_data) with dimensions (aa_scat, za_scat, aa_inc, za_inc and phaMatElem), where phaMatElem corresponds to the six stored values (Z11,Z12, …). Information on how to reconstruct the full matrix is provided separately, in phaMat_index that contains the position matrix 12002300004500-56. The numbers correspond to the indices of phaMatElem in phaMat_data, i.e. where to place those values in the matrix. The indexing is 1-based, where zero flags mean that the matrix is zero at that position. A negative number means the database value will be multiplied by -1 before it is inserted into the matrix. Corresponding systems are used for the extinction matrix and the absorption vector.

The scattering data described above can easily be extracted using any netCDF or HDF5 interface. However, for enhancing the user friendliness, two data interfaces are distributed with the database. The interfaces are implemented in MATLAB and Python. The aim has been to keep the functionality as similar as possible between the two interfaces (but details of the programming languages used make some differences unavoidable). The MATLAB interface should function with any relatively new MATLAB version. The Python interface should function with both Python 2 and Python 3, but Python 3 (≥3.5) is recommended for full functionality. There are no extensive requirements on the interfaces. The Python interface requires the netCDF4, numpy and os packages, and the MATLAB interface the netcdf package.

The functionalities provided by the two interfaces are exploration of the database content, extraction of selected parts of the data (with respect to habit, size, frequencies and temperature), interpolation of data in temperature, frequency, size and angles, preparation of habit mixes and calculation of bulk properties.

The interfaces also provide support for converting data to the format used by the ARTS and RTTOV-SCATT forward models. Both interfaces can deal with the ARTS scattering format, on the condition that the Atmlab (MATLAB) and Typhon (Python) packages

Both available at http://www.radiativetransfer.org/tools/ (last access: 11 July 2018).

To allow a quick introduction to the database, a set of “standard habits” has been generated and provided in both the ARTS and RTTOV-SCATT formats. These habits should cover a range of conditions, such as cloud ice, snow, graupel, and hail. Most of these habits are a direct compilation of the database content, but some can be denoted as habit mixes. These combinations were created to simplify the usage of some of the aggregate and rimed habits that do not give full coverage in size. In order to also cover the lower size range, those habits were complemented with data from some crystal habit. Further details about the standard habits are provided in the accompanying ReadMe file.