More detailed observational capabilities in the microwave (MW) range and advancements in the details of microphysical schemes for ice and snow demand increasing complexity to be included in scattering databases. The majority of existing databases rely on the discrete dipole approximation (DDA) whose high computational costs limit either the variety of particle types or the range of parameters included, such as frequency, temperature, and particle size.

The snowScatt tool is innovative in that it provides consistent microphysical and scattering properties of an ensemble of 50 000 snowflake aggregates generated with different physical particle models. Many diverse snowflake types, including rimed particles and aggregates of different monomer composition, are accounted for. The scattering formulation adopted by snowScatt is based on the self-similar Rayleigh–Gans approximation (SSRGA), which is capable of modeling the scattering properties of large ensembles of particles. Previous comparisons of SSRGA and DDA are extended in this study by including unrimed and rimed aggregates up to centimeter sizes and frequencies up to the sub-millimeter spectrum. The results generally reveal the wide applicability of the SSRGA method for active and passive MW applications. Unlike DDA databases, the set of SSRGA parameters can be used to infer scattering properties at any frequency and refractive index; snowScatt also provides tools to derive the SSRGA parameters for new sets of particle structures, which can be easily included in the library.

The flexibility of the snowScatt tool with respect to applications that require continuously changing definitions of snow properties is demonstrated in a forward simulation example based on the output of the predicted particle properties (P3) scheme. The snowScatt tool provides the same level of flexibility as commonly used T-matrix solutions, while the computed scattering properties reach the level of accuracy of detailed discrete dipole approximation calculations.

Accurate characterization of scattering and absorption properties of hydrometeors in the microwave (MW) range is an essential prerequisite for retrievals of cloud and precipitation properties

As pointed out by

During recent years, the number of scattering databases and the complexity of included particles have strongly increased

The signals in active and passive MW observations are generally related to higher moments of the particle size distribution (e.g., radar reflectivity factor

Considering that any remote sensor is always measuring bulk scattering properties of an ensemble of particles, a better characterization of ensemble scattering properties is desirable. The self-similar Rayleigh–Gans approximation

The SSRGA does not require an effective medium approximation as the distribution of mass within the particle is explicitly parameterized. Principally, the mass–size relation is not fixed for SSRGA and it can be varied for a set of SSRGA parameters. The SSRGA parameters can be derived with relatively low computational costs for a large variety of aggregate structures

Previously published SSRGA parameters have been derived for slightly different formulations of the SSRGA, and not all of them provide the physical particle properties of the ensemble. In this study, we present a new software tool, snowScatt, which aims to simplify the application of the SSRGA method for the scientific community. It provides a database of previously derived SSRGA parameters and new parameters based on a large aggregate database generated at the University of Cologne

In Sect.

The basis of the SSRGA methodology is the Rayleigh–Gans approximation (RGA), which applies to “optically soft” particles. This condition states that the various parts of an arbitrarily shaped particle only interact with the incident wave, and the coupling among its scattering elements can be neglected. As a result, the scattered wave is the simple superposition of the individual contribution of each scattering element that behaves as a simple Rayleigh scatterer

The conditions for the applicability of RGA in the atmosphere of Earth are met when the refractive index of the scattering particle is not too different from the one of air (assumed to be 1). Also, the size of the scatterer along the propagation direction of the incident wave should not be much larger than the wavelength. These two conditions are expressed mathematically as

Using RGA, the differential scattering cross section

By exploiting the concept of snowflake self-similarity

The remaining three parameters

Figure

Example of the evolution of the fitted SSRGA parameters

As a consequence of the fact that RGA considers the scattering from a particle to be the linear superposition of Rayleigh scattering events, the resulting phase function (Eq.

The porous structure of snowflake particles is assumed to ensure the validity of the first RGA criterion (Eq.

The snowScatt tool has been designed to provide a similar interface structure as commonly used scattering databases, such as

The structure of the snowScatt package is illustrated in Fig.

Schematics of the modules included in the snowScatt package and basic workflow. The various components are color-coded according to their primary use. The reddish and green blocks respectively identify the data and algorithmic components of the package. The auxiliary “table generator” package, which can be used to extend the snowLibrary database, is colored in violet. Even though the output is not technically a module of the snowScatt package it is highlighted here in blue. The text along the connection lines describes the variables that are passed to the connecting module. The only independent variable for single-particle computations is

Although the number of scattering databases of realistically shaped snow particles is constantly increasing, the variability of available particle properties, especially for rimed particles, is still limited

In general, the particle types included in the snow library can be roughly divided into four classes of snowflakes: rimed aggregates from

The rimed aggregates included in snowScatt are based on

As a second class, snowScatt provides the physical and scattering properties of the particles generated in

The third class of aggregates consists of approximately 30 000 aggregates comprised of needle, column, dendrite, and plate monomers (hereafter named the Cologne aggregate Ensemble, CaE). The aggregates were generated using the aggregation code described in detail in

The fourth aggregate class in the snow library contains aggregates that are made up of a mixture of column and dendrite monomers (CaE mixture). The mixture aggregates used here are equivalent to the “Mix2” aggregates described in

Description of aggregates available in the snowScatt tool. For mD, AD, and vD relations see Fig.

Example of the different aggregates available in snowScatt. The first row shows aggregates described in

The basis for the calculations performed by the snowScatt core is made up of text files (snowTables in Fig.

The SSRGA parameters are derived for the snow shapes listed in Table

For the computation of the scattering and terminal fall velocity, the code assumes the snow particles to follow the mass–size and area–size fits as derived from the snowTable. Those mass and area fits are capped at small sizes by the maximum theoretical mass and cross section of a solid sphere of the same size. The default assumption can be overridden by specifying the sets of masses and areas to be used in the internal computations. This possibility is particularly useful because it allows for the use of snowScatt to forward-simulate the outputs of numerical weather prediction models by ensuring internal consistency with the snow microphysical properties assumed in the model

The snowScatt package also offers the tools required to fit the microphysical and SSRGA parameters from an ensemble of snowflake shapes. The tool produces a table formatted according to the snowScatt internal conventions that can be imported at runtime and immediately used along with the sets of snow particles already included in the snowScatt library. This would provide an easy way to extend the snowScatt library to an even larger ensemble of snow properties.

A comparison of the microphysical properties of a selection of the snowflake models included in snowScatt to relations derived from in situ observations

Mass

Both the mass (Fig.

In snowScatt, different hydrodynamic fall-speed models are implemented

The terminal fall velocities of the snowScatt aggregates computed with the

The snow-scattering properties are calculated by snowScatt using the SSRGA method. The calculated quantities include the absorption cross section

In Fig.

For sufficiently small size parameters (

Comparison of commonly used scattering methods for snowflakes in terms of backscattering

DDA calculations show that the uncertainty for properties of individual particles is much larger for backscattering than for scattering efficiency. This is more true for DDA calculations that assume fixed particle orientations

The SSRGA results for rimed particles provide a reasonable mean of the DDA-derived single-scattering properties. Interestingly, the sector snowflakes of the

The SSRGA form factor is, in fact, independent of the refractive index of ice. This makes SSRGA an interesting method to test the sensitivity of snowflake-scattering properties with respect to the ice refractive index model or the ice temperature.

The ice refractive index

An important correction to the computed scattering properties is made through the dielectric factor

Exact formulations for the polarizability prescription are available only for a limited set of simplified shapes such as ellipsoids

The snowScatt package also provides a simple built-in radar simulator to compute the radar Doppler spectrum

As mentioned in Sect.

The sets of particles included in our comparison comprise 48 different aggregate shapes including two types of unrimed and two rimed aggregates. The rimed aggregates of dendrites are taken from the

As the SSRGA scattering properties represent the scattering properties of an ensemble of particles, a direct evaluation with DDA would require DDA calculation for each ensemble member or at least a representative number. Considering the large frequency and size range for which we aim to test the SSRGA, this approach is unfeasible due to the extremely high computational resources necessary. In order to approach the single-particle scattering properties best, we applied the individual mass and size of the particle used for DDA to the SSRGA instead of the ensemble-averaged mass and size. This means that for each snowflake shape

The reference scattering method used in the present study is the DDA

Comparison of microwave absorption and scattering properties of single snowflakes calculated with SSRGA and DDA methods. The compared quantities are the total scattering cross section

The comparison of scattering, absorption, and backscattering cross sections (Fig.

The overall best match for DDA and SSRGA is found for the absorption cross section (Fig.

The asymmetry factor

As mentioned before, due to the high computational cost of scattering calculations, DDA databases comprise only a limited number of particles. Each single particle included in the database is thus considered to be representative of all the snowflakes of similar size or mass

In order to evaluate this effect, we used the

We have divided the database into size bins that are 1.5

The uncertainty introduced by sampling the natural variability of snow properties using only a few particles to represent the whole population of snowflakes. Panel

In order to evaluate the effect of this uncertainty on radar applications we integrated the resulting backscattering cross sections over various inverse exponential PSDs of the form

The limited number of particles included in the reference database is the major limitation to a proper evaluation of the potential bias caused by the insufficient representation of the variability of snowflake properties in scattering databases. This would require a much larger database that could comprise thousands of particles per size bin. This idealized experiment is meant to provide an indication of the importance of snowflake subsampling to use-case scenarios, such as the forward modeling of radar reflectivity based on a database with a low number of specific particle shapes.

Another potential source of uncertainty given by limited DDA databases is the size of the largest snow particle. SSRGA gives a physical way to extrapolate the scattering properties of aggregates to particles of any size, while DDA can only extrapolate from a best-fit curve. Given the high nonlinearity of the scattering processes this could cause large uncertainty in the modeling of scattering properties of very large snowflakes. This effect was not evaluated in the presented experiment since the integration over the PSD was always truncated at the size of the largest available DDA snowflake.

New model developments, such as the P3 scheme

Usually, bulk microphysical schemes represent ice variability using multiple categories

A paper describing the implementation of the P3 cloud microphysical scheme in the ICON model is under preparation

We used the mass–size relations derived from the model output to define the scattering properties of the snowflakes used in the forward simulations. The range of rimed particles included in snowScatt is characterized by the ELWP used to simulate the riming process

The results obtained from snowScatt are compared to those calculated using state-of-the-art T-matrix and DDA solutions. Regarding the T-matrix methodology

The DDA solution has been calculated by assuming the

Simulated W-band (94 GHz) radar reflectivity for the 24 November 2015 precipitation event over JOYCE based on the output of the ICON model implementing the P3 cloud microphysical scheme. Panels

The scattering properties of the liquid hydrometeors (cloud water and rain) have been computed using the T-matrix method with identical settings for all forward simulation experiments. Panels (a), (c), and (e) in Fig.

The differences among the reflectivities computed with the three methods become more significant for higher reflectivity values. The pattern of the differences correlates well with the bulk mean mass of the snowflakes (Fig.

The presented application experiment is not meant to prove the better accuracy of one scattering method over another. Although radar observations for JOYCE are available for this day

This application example clearly reveals that SSRGA can be used effectively to compute the synthetic unpolarized reflectivities of the hydrometeors produced by the P3 scheme. SSRGA combines the realism of scattering properties similar to DDA with flexibility in the computation of snowflakes that have different microphysical properties, which is characteristic of the T-matrix method. The applicability of SSRGA is not limited to P3, but it is also useful for the forward simulation of other shape-adaptive ice schemes

2D histogram of DWR X–Ka and Ka–W measured during the TRIPEx campaign

With this contribution we aimed to serve the snow scientific community with snowScatt, an innovative tool to access the microphysical and scattering properties of an ensemble of 50 000 snowflake aggregates. The snowScatt tool makes use of snow particle shape models in order to calculate the microphysical and scattering properties of snow. The combined derivation of snow microphysical and scattering properties ensures the physical consistency of the modeled quantities. This consistency is a necessary feature in order to properly connect the microphysical properties assumed in weather prediction models with the scattering quantities measured by remote sensing instruments. Moreover, snowScatt enables the study of the snow particle response to changes in growth processes (e.g., the aggregation and riming simulated by the shape models) from both a microphysical and scattering perspective.

The current version of the tool provides the properties of different snowflake types, including rimed particles and aggregates of different monomer composition. The tool can be easily interfaced with existing forward-modeling software and can be extended to include even more particle properties derived from either in situ observations or other aggregation models.

The scattering properties derived with the SSRGA techniques compare well with DDA reference computations, with the notable exception of the asymmetry parameter

The set of SSRGA parameters does not depend on the electromagnetic frequency or the ice refractive index. This makes SSRGA a perfect tool to make sensitivity tests of snowflake-scattering properties with respect to different refractive index models, temperature regimes, or frequency. On the other hand, one must acknowledge that the polarimetric pattern of the SSRGA scattering properties can only follow the Rayleigh form, which prevents any application to, e.g., radar polarimetry.

One of the main advantages of SSRGA and the large snowScatt library is its flexibility with respect to applications that require continuously changing definitions of snow properties. This feature is tested by forward-modeling the radar reflectivity of a P3 test scene. In order to be consistent with the P3 model output, the scattering method needs to be flexible regarding the definition of the snowflake density. The snowScatt tool provides the same level of flexibility as the T-matrix method, while the computed scattering properties reach the level of accuracy of DDA calculations.

The flexibility of the snowScatt methodology is not limited to the forward simulation of the P3 scheme. Provided that there is a reasonable basis of snowflake shapes, it is possible to parameterize the SSRGA parameters with respect to any structural property of snowflakes (e.g., rimed fraction, aspect ratio, monomer types). Therefore, snowScatt can be used for the forward simulation of complex microphysical schemes that explicitly predict the evolution of snow characteristics.

This paper presents the snowScatt software toolkit publicly available at

DO is the main developer and maintainer of the snowScatt package. DO additionally performed the DDA single-scattering computations, the forward modeling of the ICON P3 scene, and the various analyses presented in the study. LvT developed the Cologne aggregate Ensemble with significant contributions from MK. LvT also computed SSRGA parameters and produced the tables included in the snowScatt library. MK modeled and analyzed the microphysical properties of the snow aggregates and significantly contributed to the forward modeling of the P3 test scene. SK initiated the project of deriving SSRGA parameters from various aggregate models, provided early implementations of the SSRGA algorithm, and was heavily involved in the interpretation and testing of the snowScatt results. DO prepared the paper with contributions from all co-authors.

The authors declare that they have no conflict of interest.

Contributions by Davide Ori, Markus Karrer, and Stefan Kneifel were funded by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) under grant KN 1112/2-1 as part of the Emmy-Noether Group OPTIMIce. Work provided by Leonie von Terzi has been supported by the DFG Priority Program SPP2115 “Fusion of Radar Polarimetry and Numerical Atmospheric Modelling Towards an Improved Understanding of Cloud and Precipitation Processes” (PROM) under grant PROM-IMPRINT (project number 408011764). We thank the computing center of the University of Cologne (RRZK) for providing the CPU time on the DFG-funded high-performance computational cluster CHEOPS.
The authors acknowledge the original work of Robin Hogan and Chris Westbrook that developed the SSRGA methodology. We thank Jussi Leinonen for making the snowflake aggregation and riming model publicly available, which allowed for the construction of the Cologne aggregate Ensemble. We are grateful to Corinna Hoose and Juha Tontilla for providing the ICON-P3 output that enabled the analysis included in Sect.

We would like to take this opportunity to acknowledge the time and effort devoted by Grant Petty and a second anonymous reviewer to improving the quality of this paper. We really appreciate the detailed and useful comments provided during the review process.

This research has been supported by the Deutsche Forschungsgemeinschaft (grant nos. KN 1112/2-1 and 408011764).

This paper was edited by Simon Unterstrasser and reviewed by Grant Petty and one anonymous referee.