Dual-Frequency Radar Retrievals of Snowfall Using Random Forest

Abstract

The microphysical parameters of snowfall directly impact hydrological and atmospheric models. During the International Collaborative Experiment hosted at the Pyeongchang 2018 Olympic and Paralympic Winter Games (ICE-POP 2018), dual-frequency radar retrievals of particle size distribution (PSD) parameters were produced and assessed over complex terrain. The NASA Dual-frequency Dual-polarized Doppler Radar (D3R) and a collection of second-generation Particle Size and Velocity (PARSIVEL²) disdrometer observations were used to develop retrievals. The conventional look-up table method (LUT) and random forest method (RF) were applied to the disdrometer data to develop retrievals for the volume-weighted mean diameter (D_m), the shape factor (mu), the normalized intercept parameter (N_w), the ice water content (IWC), and the snowfall rate (S). Evaluations were performed between the D3R radar and disdrometer observations using these two methods. The mean errors of the retrievals based on the RF method were small compared with those of the LUT method. The results indicate that the RF method is a promising way of retrieving microphysical parameters, because this method does not require any assumptions about the PSD of snowfall.

1. Introduction

In middle to high latitudes, the most common precipitation originates from snowfall [1]. Snowfall plays an important role in global precipitation, radiative balance, vegetation, and climate [1,2,3,4,5,6]. Additionally, snowstorms can cause significant injury and financial loss at higher latitudes [7]. Furthermore, the thermal, dynamic, and microphysical mechanisms of snowfall generation and evolution are linked to the microphysical properties of snowfall. At the same time, the microphysical parameterization process of snowfall in the current numerical weather prediction (NWP) models is not accurate [1,8,9,10,11,12,13,14,15,16]. Therefore, the microphysical parameters of snowfall need to be retrieved as accurately as possible to improve the accuracy of snowfall forecasts.

Retrieving the microphysical parameters of snowfall is challenging. This can be explained by the much greater natural variabilities of snowflakes, such as their density, shape orientation, terminal fall velocity (as a function of snowflake size), and structure, and also the inabilities of the modeled PSD to represent actual snow spectra compared to those of raindrops. In addition, the uncertainties related to simulating the scattering characteristics of snowfall are large because of the diverse habits of snowflakes [17,18,19,20,21,22,23,24,25]. All of these can lead to errors in the retrieval of snowfall parameters.

Traditional estimates of snowfall derived from single-frequency radar observations adopt empirical formulas, which are inherently uncertain [26,27,28,29,30,31] because the relationship is suitable for a specific area and the results may vary greatly for different cases. Additionally, single-frequency radars provide only one reflectivity observation, which is an average parameter per volume. All of these uncertainties result in large errors when using single-frequency radars to retrieve snowfall parameters. The Global Precipitation Measurement (GPM) core satellite was launched on 27 February 2014, which was a joint project between NASA and JAXA [32,33,34]. The GPM dual-frequency Precipitation Radar (DPR) was proposed to detect and retrieve clouds and precipitation, which operates with frequencies of 13.6 GHz (Ku-band) and 35.5 GHz (Ka-band). One of the DPR’s goals is to produce more accurate S and IWC estimations for higher latitude regions. Dual-frequency radar observations provide two reflectivities in an observation volume as a function of their size, which can be used to determine the snowfall distribution’s characteristic size. The general principle of dual-frequency radar is that snowfall backscattering at one wavelength operates in the Rayleigh regime or close to it, while another frequency operates in the non-Rayleigh (Mie) regime for a typical snowflake size, resulting in a measurable difference in reflectivities that can be directly related to size. When compared to a single-frequency radar, this allows for a more precise calculation of the microphysical parameters. Dual-wavelength radar is a potential method for properly retrieving microphysical snowfall information.

Several studies have been conducted to retrieve snowfall parameters from ground and airborne radar measurements using dual-frequency radar [35,36,37,38,39,40,41,42]. For computing radar backscattering cross sections, traditional DPR algorithms use a fixed-snow-density model and the assumption of a PSD function, such as exponential, gamma, or lognormal distribution.

The conventional DPR algorithms for retrieval set the density of snowfall as a constant for computing radar backscattering cross sections and assume the PSD function as the gamma distribution. However, some assumptions are introduced in this way. The assumptions cannot represent and characterize the actual parameters of snowfall, so the retrieval results remain uncertain. The development of deep learning techniques provides new methods for atmospheric science [43,44,45,46,47,48,49,50,51]. A few studies have explored the possibility of retrieval using machine learning [52,53]. However, there have been no machine learning applications for PSD retrieval utilizing Ku- and Ka-band radars. The random forest method will be used in this paper to obtain microphysical snowfall properties. The method uses information from observed PSDs while retrieving and does not need any assumptions.

The goal of this research is to investigate if the random forest technique can be used to obtain microphysical snowfall parameters, such as the mass-weighted diameter, S, IWC, and PSD parameters (shape factor µ and normalized intercept parameter N_w). As for the density of snowfall, we adopted the method proposed before [54,55]. In Section 2, the data and method used to produce and evaluate the algorithm are described. The retrievals using the conventional method and random forest are conducted based on dual-frequency radar (D3R) in Section 3, and the frequency bands of it are at Ku and Ka. Evaluations of the results using the second-generation Particle Size and Velocity (PARSIVEL²) disdrometer observations are analyzed in Section 4. Section 5 presents the main results of this study.

2. Data and Instruments

2.1. Experimental Design

Pyeongchang, South Korea, hosted the 23rd Olympic Winter Games and the 13th Paralympic Winter Games from 9 to 25 February and 9 to 18 March 2018. The Korea Meteorological Administration (KMA), with support from the World Meteorological Organization (WMO), conducted the International Collaborative Experiment for the Pyeongchang 2018 Olympics and Paralympic Winter Games (ICEPOP 2018) campaign to enhance our understanding of winter precipitation and the accuracy of snowfall forecasting over complicated terrain. Between December 2017 and March 2018, supersites were deployed along the coast and throughout the mountain range, and intense remote sensing and in situ cloud and precipitation studies were conducted, such as X-band doppler dual-polarization radar, pluvio² weighting precipitation gauges, precipitation imaging probes (PIP), micro rain radar (MRR), particle size and velocity precipitation disdrometer (Parsivel), dual-frequency dual-polarimetric doppler radar (D3R), etc. Radiosondes were launched at the same time. More detailed information about the campaign and observations can be found in a few papers [56,57,58,59]. Such comprehensive datasets enable a deeper understanding of snowfall. In this study, we will focus on the data collected by a D3R and three disdrometers located at three different supersites, the details of which are provided in the following subsections.

The location of Pyeongchang and the observation sites are depicted in Figure 1. The western part of the Pyeongchang Olympic region is characterized by a continental climate due to its location in the eastern alpine region. The eastern part of the Pyeongchang Olympic region is located on the east coast of the South Korean peninsula. This location results in an oceanic climate at the same time, which means that it has a relatively narrow annual temperature range. The D3R radar is stationed at DGW (DaeGwanryung Regional Weather Office; 37°40′38.39″ N, 128°43′07.7″ E, 773 m a.m.s.l.), and the red circle in the Figure 1 depicts the D3R radar’s coverage. DGW, CPO (Cloud Physics Observatory; 37°41′13.03″ N, 128°45′31.09″ E, 855 m a.m.s.l.), and YPO (YongPyoeng cloud physics Observatory; 37°38′36.03 N, 128°40′13.78 E, 772 m a.m.s.l.) are the locations of the three different disdrometers (the red font in Figure 1). In relation to the DGW location, the YPO site is placed at 226° azimuth and 6.5 km range. With respect to the DGW site, the CPO site is placed at 75° azimuth and a range of 2 km. The data obtained at the three sites (YPO, DGW, and CPO) were chosen for analysis because the heights between the radar beam and ground observation at YPO, CPO, and DGW were 0.55, 0.17, and 0.15 km, respectively, resulting in minor height discrepancies between the radar beam and surface observation. As a result, the data measured with height difference were ignored.

During the field campaign, 21 snowfall events were selected to be analyzed in this study, as shown in

Table 1. Snow events used to for analysis in this study. Meteorological conditions are listed, including the accumulation of snowfall, temperature (T), relative humidity (here abbreviated as RH), wind speed (WS), and wind direction (WD). The date is in UTC.

NO.	Date and Time (UTC)	Accumulation (mm)	T (°C)	RH (%)	WS (m/s)	WD (°)
1	3 December 2017 00:00–23:00	3.18	−1.1	86.0	5.0	261.0
2	6 December 2017 10:00–19:00	1.99	−3.3	81.0	11.0	294.0
3	10 December 2017 00:00–16:00	4.16	−3.7	72.0	16.0	284.0
4	17 December 2017 17:00–24:00	1.38	−11.0	50.0	11.0	247.0
5	18 December 2017 00:00–13:00	2.39	−2.5	73.0	18.0	274.0
6	24 December 2017 00:00–16:00	6.29	−2.2	95.0	15.0	281.0
7	30 December 2017 11:00–23:00	1.80	−0.2	77.0	2.0	302.0
8	8 January 2018 00:00–20:00	4.74	−3.2	73.0	10.0	279.0
9	9 January 2018 13:00–21:00	2.24	−9.6	64.0	16.0	274.0
10	16 January 2018 10:00–24:00	1.52	−0.2	82.0	2.0	43.0
11	22 January 2018 03:00–22:00	4.93	−2.9	91.0	6.0	277.0
12	30 January 2018 07:00–24:00	3.78	−8.6	77.0	10.0	276.0
13	22 February 2018 11:00–22:00	1.06	−2.8	65.0	12.0	261.0
14	28 February 2018 00:00–24:00	50.17	−0.4	97.0	12.0	80.0
15	4 March 2018 15:00–24:00	21.30	−3.0	96.0	7.0	85.0
16	4 March 2018 00:00–09:00	4.72	−5.5	91.0	1.0	87.0
17	7 March 2018 05:00–24:00	12.59	−0.9	90.0	4.0	78.0
18	8 March 2018 00:00–24:00	4.46	−2.0	94.0	2.0	34.0
19	16 March 2018 00:30–06:00	1.58	−5.6	90.0	2.0	286.0
20	20 March 2018 18:00–24:00	4.45	−5.8	88.0	14.0	88.0
21	21 March 2018 00:00–14:00	8.59	−3.7	95.0	8.0	54.0

. The meteorological conditions are listed in Table 1, including the temperature, humidity, wind speed, and wind direction. Because the temperatures during these periods were much lower than 0 °C, the particles were dry snowflakes and were not wet snowflakes or mixed with raindrops. This is important because the scattering properties are related to the types of the particles, which are important parameters when retrieving microphysical parameters, and the detailed approach to retrieval will be presented in the following section. Another reason that these cases were selected is that the accumulations of snowfall were large enough (>1 mm).

2.2. Instruments

OTT developed the disdrometer, which is a second-generation laser-based optical system [33,60,61]. It has a horizontal strip of light that is 30 mm wide, 180 mm long, and 54 cm² in the sample area. When particles travel through the laser beam, the particle velocity is determined by the duration of the output voltage, and the particle size is determined by the signal reduction. Every 60 s, the particle size and velocity are separated into 32 bins, with sizes ranging from 0.062 to 24.5 mm and velocity from 0.05 to 20.8 m s⁻¹, respectively. Because the signal-to-noise ratio (SNR) is poor in these classes, the smallest two size classes (less than 0.312 mm) were excluded from this investigation to reduce measurement uncertainty. As a result, the minimum particle size and velocity were 0.25 m s⁻¹ and 0.312 mm, respectively. Every 60 s, total particle numbers that were less than 10 were deleted to eliminate noise. The requirements for data quality control were the same as those in the previous investigation [54,55].

The NASA D3R was developed in cooperation between Colorado State University, Remote Sensing Solutions, and NASA the Goddard Space Flight Center for ground validation from a GPM dual-frequency radar. The NASA Global Hydrology Resource Center DAAC [62] provided the dataset used in the study. At 35.5 GHz (Ka-band) and 13.9 GHz (Ku-band), the D3R radar delivers polarimetric and doppler measurements.

Table 2. Operating parameters of D3R radar.

	Parameters
Frequency	Ku: 13.91 GHz ± 25 MHz Ka: 35.56 GHz ± 25 MHz
Minimum operational range	450 m
Maximum range	40 km
Operational range resolution	150 m
Minimum detectable signal	−10 dBZ at 15 km for a single pulse at 150 m range resolution
Angular coverage	Az: 0–360°, El: −0.5–90°

lists the D3R radar’s particular parameters. D3R has a range resolution of 150 m, a feasible minimum operable range of 450 m, and a maximum detectable range of 40 km. D3R is more sensitive to light rain and snowfall than S- and C-band radars since its minimum detectable signal is −10 dBZ at a distance of 15 km. During ICE-POP 2018, the radar acquired data that helped us to better understand winter precipitation over complicated regions. The differential frequency ratio (DFR), which is defined as the difference in radar reflectivity between two frequencies, is provided by the D3R radar. Z at the Ku-band and DFR were used to estimate the microphysical snow properties and associated bulk parameters in this paper, and then comparisons with the disdrometer observations were made.

3. Retrieval Methods

3.1. Conventional Method

After measuring the particle size distribution, the microphysical parameters, such as the volume-weighted mean diameter D_m, normalized intercept parameter N_w, snowfall rate S, and ice water content IWC, could be obtained when coupled with a density–size (ρ-D) relationship. Radar parameters, such as the radar reflectivity factors at the Ku- and Ka-bands, DFR, could be obtained when coupled with a scattering property dataset. The parameters computed made up the look-up tables. The microphysical features of snowfall were thus directly related to the radar observations. This algorithm is called the LUT method. This method introduces some assumptions: the scattering properties dataset, density–size relationship, and PSD distribution. The retrieval of the scattering properties of snowflakes is basic, but it is the most challenging procedure at the same time, because the true structure, shape, orientation, and density are too complex to be represented as a unified model. In this study, we simplified the snowflake as a spheroid. By analyzing images acquired by a MASC, Garrett et al. (2015) discovered that the axis ratio of a snowflake particle is between 0.6–0.7. The density of snowfall varies greatly during an event and was usually considered as a fixed constant or described using a density–size relationship when retrieved in early studies. However, the relationships have huge differences between different locations. As for the PSD model, the three-parameter gamma distribution was adopted in this study. The shape factor µ was assumed as a constant. There are a few studies that have conducted assessments of the factor for snowfall retrieval. The gamma distribution is expressed as:

$$\mathrm{N}\left(\mathrm{D}\right)={\mathrm{N}}_{\mathrm{w}}\mathrm{f}\left(\mathsf{\mu }\right){\left(\frac{\mathrm{D}}{{\mathrm{D}}_{\mathrm{m}}}\right)}^{\mathsf{\mu }}\exp \left(-\mathsf{\Lambda }\mathrm{D}\right)$$

(1)

$$\mathrm{f}\left(\mathsf{\mu }\right)=\frac{6}{4^4}\frac{{\left(4+\mathsf{\mu }\right)}^{\mathsf{\mu }+4}}{\mathsf{\Gamma }\left(\mathsf{\mu }+4\right)}$$

(2)

$$\mathsf{\Lambda }=\frac{4+\mathsf{\mu }}{{\mathrm{D}}_{\mathrm{m}}}$$

(3)

where µ is the shape factor; D_m is the volume-weighted diameter; and N_w is the normalized intercept parameter. In this study, we adopted a power law ρ-D_m relationship [54], which is suitable for the Pyeongchang region of South Korea:

$$\left\{\begin{array}{c}\rho =0.3358{\mathrm{D}}_{\mathrm{m}}^{-1.243} {\mathrm{D}}_{\mathrm{m}}>1.7 \mathrm{m}\mathrm{m}\\ \rho =0.3774{\mathrm{D}}_{\mathrm{m}}^{-1.386} 1.7 \mathrm{m}\mathrm{m}<{\mathrm{D}}_{\mathrm{m}}<2.7 \mathrm{m}\mathrm{m}\\ \rho =0.462{\mathrm{D}}_{\mathrm{m}}^{-1.879} {\mathrm{D}}_{\mathrm{m}}<1.7 \mathrm{m}\mathrm{m}\end{array}\right.$$

(4)

The radar reflectivity factor at a wavelength of λ is given by:

$${\mathrm{Z}}_{\mathsf{\lambda }}=\frac{{\mathsf{\lambda }}_{\mathrm{i}}^4}{{\mathsf{\pi }}^5{\left|{\mathrm{K}}_{\mathrm{w}}\right|}^2}{{\displaystyle \int }}_{{\mathrm{D}}_{\min }}^{{\mathrm{D}}_{\max }}{\mathsf{\sigma }}_{\mathrm{i}}\left(\mathrm{D}\right)\mathrm{N}\left(\mathrm{D}\right)\mathrm{dD}$$

(5)

where ${\mathsf{\sigma }}_{\mathrm{i}}\left(\mathrm{D}\right)$ is the backscattering cross section, which can be calculated by the T-matrix method. We used a 0.7 axis ratio and a Gaussian canting angle distribution with a mean of zero and a standard deviation of 45°. ${\left|{\mathrm{K}}_{\mathrm{w}}\right|}^2$ is the dielectric factor, and it was set to 0.93.

According to Equations (1) and (5), the radar reflectivity factor at λ can be expressed as:

$${\mathrm{Z}}_{\mathsf{\lambda }}=\frac{{\mathsf{\lambda }}_{\mathrm{i}}^4}{{\mathsf{\pi }}^5{\left|{\mathrm{K}}_{\mathrm{w}}\right|}^2}{{\displaystyle \int }}_{{\mathrm{D}}_{\min }}^{{\mathrm{D}}_{\max }}{\mathsf{\sigma }}_{\mathrm{i}}\left(\mathrm{D}\right){\mathrm{N}}_{\mathrm{w}}\mathrm{f}\left(\mathsf{\mu }\right){\left(\frac{\mathrm{D}}{{\mathrm{D}}_{\mathrm{m}}}\right)}^{\mathsf{\mu }}\exp \left(-\left(4+\mathsf{\mu }\right)\frac{\mathrm{D}}{{\mathrm{D}}_{\mathrm{m}}}\right)\mathrm{dD}$$

(6)

The difference in the radar reflectivity factors (DFR) at two frequencies (λ₁ and λ₂) is:

$$\mathrm{DFR}=10\log 10\left[{\mathrm{Z}}_{{\mathsf{\lambda }}_1}/{\mathrm{Z}}_{{\mathsf{\lambda }}_2}\right]$$

(7)

According to Equations (6) and (7), DFR is dependent on D_m for a given µ. From Equation (6), after retrieving D_m and measuring the radar reflectivity factor, N_w will be retrieved by looking up tables. Then, associated bulk parameters, such as the snowfall rate S and ice water content IWC, will be obtained:

$$\mathrm{IWC}=\frac{\mathsf{\pi }}{6}\times {10}^{-3}{{\displaystyle \int }}_0^{{\mathrm{D}}_{\max }}{\mathsf{\rho }}_{\mathrm{s}}{\mathrm{D}}^3\mathrm{N}\left(\mathrm{D}\right)\mathrm{dD}$$

(8)

$$\mathrm{S}=6\mathsf{\pi }\times {10}^{-4}{{\displaystyle \int }}_0^{{\mathrm{D}}_{\max }}{\mathsf{\rho }}_{\mathrm{s}}{\mathrm{D}}^3\mathrm{v}\left(\mathrm{D}\right)\mathrm{N}\left(\mathrm{D}\right)\mathrm{dD}$$

(9)

Using the equations above and the results of scattering simulation based on the T-matrix, it is possible to obtain relationships between the microphysical snowfall properties and radar measurements. Figure 2 shows the results under the assumptions with µ = 0. The top-left (a), top-right (b), bottom-left (c), and bottom-right (d) panels show the plots of D_m, N_w/Z_Ku, IWC/Z_Ku, and S/Z_Ku versus DFR with the assumptions that the densities are 0.06 g cm⁻³ (red), 0.10 g cm⁻³ (blue), 0.20 g cm⁻³ (green), and 0.30 g cm⁻³ (black), respectively. Figure 3 shows the results of these parameters versus DFR with the assumptions of ρ = 0.1 g cm⁻³ and µ varying from −1 to 2. The analysis of these results indicated that different assumptions had effects on the results of retrievals.

To assess the LUT method, measurements from the Ku- and Ka-band radars were used for retrieval, as shown in Figure 4. D_m had the smallest errors at µ = 2, and the errors of IWC, S, and N_w did not have large differences when the µ values were altered. Liao et al. [42] evaluated the performance of snow retrieval considering PSD models and scattering tables from the perspective of PSD measurements, and the relative errors in the estimates of IWC, S, D_m, and N_w were in the ranges of −40% to 70%, −50% to 40%, −30% to 50%, and −100% to 1000%, respectively. Although the errors of the results are still high in Figure 4, this is the first attempt to use a dual-frequency radar to retrieve microphysical snowfall parameters. The previous studies about retrieving microphysical parameters did not use measurements from a dual-frequency radar for retrieval [39,42].

3.2. Random Forest (RF) Method

Before developing retrievals from RF, the microphysical parameters should be calculated from the PSD measurements according to (1)–(9). Random forest is a supervised learning algorithm. RF is made up of a series of decision trees, usually trained with the “bagging” method. The general idea of the bagging method is that a combination of learning models increases the overall result. One big advantage of random forest is that it can be used for both classification and regression problems, and this paper is a regression problem. Estimators are just the number of trees the algorithm builds before taking the maximum voting. Max features are the maximum number of features that random forest considers to split a node. In this study, decision trees were trained using the regression tree algorithm to discover the appropriate split for the subset data. The information gain and mean absolute error are two metrics that can be used to assess the split’s quality. The RF model combines the predictions of the estimators to produce a more accurate prediction. We used Scikit-Learn in Python to train the model, which is a free machine learning library. It supports both supervised and unsupervised machine learning. A number of parameters, such as the number of trees, max data per tree, max depth, min data required to create a new branch, and min data per leaf, in the RF model should be tuned. The most ideal parameters in this study were selected using a grid searching approach, which is an iterative process, as shown in

Table 3. The most optimal parameters used to generate the RF model to predict D_m, N_w, µ, S, and IWC.

	Dm	Nw	µ	S	IWC
NO. of trees (n_estimators)	2910	910	1110	1010	710
max data per tree (max_features)	(N)1/2	(N)1/2	(N)1/2	(N)1/2	(N)1/2
max_depth	4	5	3	8	5
min data required to create new branch (min_samples_split)	21	21	21	4	21
min data per leaf (min_samples_leaf)	10	10	10	2	8

.

In this study, the most optimal parameters were determined through a grid searching method, which is an iterative method, and are listed in Table 3. The RF method develops retrievals from the calculated reflectivity factor Z and DFR as inputs to retrieve D_m, N_w, µ, S, and IWC. The training data consisted of 75% of the PSD data, and testing data were the remaining 25%, which were randomly selected.

Figure 5 shows scatterplots of the PSD-observed and retrieved D_m, N_w, µ, S, and IWC from training and testing. Their bias and correlation coefficient are also presented in the figures.

Table 4. Mean absolute error, accuracy, importance of DFR, importance of Z, correlation coefficient of the training model, and correlation coefficient of the testing model.

	Dm	Nw	µ	S	IWC
Mean Absolute Error	0.32	0.32	1.33	0.27	0.07
Accuracy	85.77%	91.62%	72.96%	72.93%	55.75%
importance of DFR	0.98	0.79	0.86	0.95	0.97
importance of Z	0.02	0.21	0.14	0.05	0.03
training CORR	0.89	0.71	0.8	0.99	0.93
testing CORR	0.88	0.66	0.75	0.97	0.92

lists some other statistical parameters, such as the mean absolute error, accuracy, training, and testing correlation coefficient. It is obvious that the RF model developed in this study to retrieve the microphysical parameters performed well, as shown in Figure 5 and Table 4. The DFR made a great contribution because the importances of DFR for D_m, N_w, µ, S, and IWC retrievals were 0.98, 0.79, 0.86, 0.95, and 0.97, respectively.

4. Evaluation of Retrievals

To evaluate the performance of the RF models, observations from the D3R radar during ICE-POP 2018 were used to retrieve the microphysical parameters using the models we developed above. The probability density of DFR and Z calculated from the PSD measurements and D3R observations are shown in Figure 6. Although there were some differences in certain regions, they matched well, generally speaking. We think that the differences are due to the fact that we assumed the snowflake as spheroid.

Figure 7 presents the distributions of the absolute error between the RF and the LUT retrievals and PSD measurements. The RF retrievals offered considerable advantages compared with the LUT method. The mean absolute error of D_m was about 0.7 mm using the RF method and about 0.75 mm using the LUT method. The mean absolute errors of log₁₀N_w, S, and IWC using RF were 0.45 (N_w in mm⁻¹m⁻³), 0.4 mm/h, and 0.10 g m⁻³, respectively. As for using the LUT method, the mean absolute errors of log₁₀N_w, S, and IWC using RF were 0.9 (N_w in mm⁻¹m⁻³), 1 mm/h, and 0.20 g m⁻³, respectively. The errors of all quantities from RF were small. The 25th and 75th absolute errors of the microphysical parameters based on RF were far less than those of the results using the LUT method.

Figure 8 shows the probability density of the microphysical parameters retrieved using RF methods. The volume-weighted diameter Dm around 2 mm (1.4 mm~2.4 mm) had the highest frequency, more than 50%. The highest frequency of ${\log }_{10}{\mathrm{N}}_{\mathrm{w}}$ was about 3.8 (which means that the value of N_w was 10^3.8 = 6310 mm⁻¹m⁻³). The results with the shape factor µ smaller than 2, IWC less than 0.5 g m⁻³, and S less than 2 mm/h accounted for 90% of the total snowfall. To some extent, the results above have guiding significance for the microphysical parameterization of snowfall in the current numerical weather prediction models.

5. Conclusions

In this study, a conventional look-up table method and random forest method were developed to obtain dual-frequency radar retrievals of snowfall using a D3R radar during ICE-POP 2018. The DFR data, which are the differences in reflectivities at two bands, are one advantage of dual-frequency radars because they may be directly attributed to size. When compared with a single-frequency radar, this allows for more precise retrievals of microphysical parameters. The traditional dual-frequency algorithm is called the look-up table method (LUT). It adopts a fixed-snow-density model and assumes a parameter in the PSD function as a constant. This paper is the first attempt to use a dual-frequency radar to retrieve the microphysical parameters of snowfall and assess the performance of this method. The assumptions that this method adopted have effects on the accuracy of retrievals, and the absolute errors of D_m, N_w, IWC, and S are high (exceeding 50%).

The development of machine learning provides a new method for snowfall retrieval. This paper is the first to use random forest to retrieve the microphysical parameters of snowfall. In this method, no assumptions are introduced. The radar retrieval method for D_m, N_w, µ, IWC, and S is directly constructed using observations for disdrometer observations. The training and testing results show that the model developed in this paper matches the PSD observations well because of the low bias and high correlation coefficient between them. After development, evaluations showed that the retrieval results of random forest were more accurate than those of the traditional LUT method. The applications of random forest to dual-frequency radar for microphysical snowfall parameter retrieval provides a novel method, and this method is better for capturing the retrievals.