Evaluation of the WDM6 scheme in the simulation of number concentrations and drop size distributions of warm-rain hydrometeors: comparisons with the observations and other schemes

ABSTRACT

The number concentrations and drop size distributions (DSDs) of warm-rain hydrometeors play an important role in the simulation of microphysical processes. To evaluate the performance of the WDM6 scheme, which predicts the cloud number concentration (N_c) explicitly in aspects of warm-rain hydrometeors number concentrations and DSDs, the simulation of the WDM6 scheme is compared with airborne observations of a flight trial, as well as with the simulations of the Thompson scheme and Morrison scheme. Results show that the WDM6 scheme produces smaller (larger) cloud (rain) number concentrations and wider cloud DSDs compared to the observations, with the largest biases at upper levels of stratiform cloud (SC). The Thompson scheme and the Morrison scheme, both of which set the Nc as a constant, compare better to the observations than the WDM6 scheme in aspects of N_c and DSD. Sensitivity tests of the initial cloud condensation nuclei (CCN) number concentration (CCN₀) of the WDM6 scheme show that a better choice of the initial CCN₀ may improve the simulation of convective cloud but helps little in terms of SC. The simulation of rain number concentration and DSD is not sensitive to the CCN₀ in the WDM6 scheme.

GRAPHICAL ABSTRACT

摘要

暖云粒子数浓度及粒子谱对微物理过程的模拟有着重要影响，不同于许多微物理方案，WDM6方案显示预报云滴数浓度。为评估其模拟效果，本文对比了WDM6方案与Thompson方案、Morrison方案在一次飞机观测试验中的模拟结果。结果表明：相比于观测结果，WDM6方案模拟云（雨）滴数浓度偏小（大），云滴谱较宽，特别是对于层状云中上部的模拟偏差较大。尽管Thompson方案和Morrison方案将云滴数浓度设置为常数，但这两种方案的云滴数浓度及云滴谱却更接近于观测。对于WDM6方案初始云凝结核数目（CCN₀）的敏感性试验表明，改变CCN₀能够改进WDM6方案对于对流云的模拟，但对于层状云的模拟结果影响较小。

KEYWORDS:

• Warm-rain hydrometeor number concentration
• drop size distribution
• airborne observation

关键词:

• WDM6 scheme暖云粒子数浓度；粒子谱；飞机观测；WDM6方案

1. Introduction

Instead of only predicting mixing ratios of cloud hydrometeors in single-moment bulk microphysics schemes (Kessler 1969; Tao, Simpson, and McCumber 1989; Chen and Sun 2002), double-moment schemes (Reisner, Rasmussen, and Bruintjes 1998; Cohard and Pinty 2000; Seifert and Beheng 2001) also predict number concentrations of hydrometeors. The prediction of mixing ratios and number concentrations at the same time in double-moment schemes provides flexibility in the description of drop size distribution (DSD) and the ability to reproduce size-sorting (Milbrandt and Yau 2005a). The number concentrations and DSDs of warm-rain particles play an important role in the simulation of microphysical processes and the macrophysical properties of weather systems. Ferrier, Tao, and Simpson (1995) and Li et al. (2009) claimed that the evaporation rate affected by the rain number concentration (N_r) is decisive in the difference in downdraft and storm structure simulation. Lim and Hong (2010) and Morrison, Thompson, and Tatarskii (2009) also found that the simulation of trailing stratiform precipitation was mainly influenced by N_r and the corresponding evaporation rate in an idealized 2D squall line case. The cloud number concentration (N_c) affects both warm-rain and cold-rain microphysical processes. Typically, an increase in N_c leads to a narrower cloud DSD and smaller mean diameter of cloud droplets. This inhibits the autoconversion and delays the onset of precipitation, and meanwhile, more cloud droplets can be transferred to upper levels to intensify cold-rain processes (Rosenfeld et al. 2008; Fan et al. 2016).

Lim and Hong (2010) developed the WDM6 scheme, which was claimed to outperform its single-moment counterpart (Hong and Lim 2006) in both idealized and real case simulations (Hong et al. 2010; Lim and Hong 2010). Some double-moment schemes, such as the Thompson scheme (Thompson et al. 2008) and the Morrison scheme (Morrison, Thompson, and Tatarskii 2009), set N_c as a constant. Different from these schemes, WDM6 predicts the N_c and has been used to study the effects of aerosol on the simulation of weather systems (Lim and Hong 2010; Lim et al. 2011; Dong, Xu, and Luo 2012). Meanwhile, the WDM5 scheme and the newly released WDM7 scheme in the Weather Forecasting and Research (WRF) model are similar to the WDM6 scheme in the calculation of warm-rain hydrometeors. However, little attention has been devoted to the accuracy of N_c simulation in these schemes.

In this study, the warm-rain hydrometeor number concentrations and DSDs simulated by the WDM6 scheme are compared with airborne observations of a flight trial, as well as the simulations of the widely tested Thompson and Morrison schemes, to evaluate the performance of the WDM6 scheme. The paper is organized as follows: Section 2 describes the flight trial and model configuration. Comparisons of warm-rain hydrometeor number concentrations and DSDs, along with the results of sensitivity tests of initial cloud condensation nuclei (CCN) number concentration (CCN₀) of the WDM6 scheme, are presented in section 3. A summary of the present findings and suggestions for future work is given in the final section.

2. Description of the flight trial and model configuration

2.1 Flight trial description

A flight trial was conducted on 22 May 2017 in Hebei Province, China, with five periods of observation mainly concentrated in the area of 2–7 km in height and −20°C to 10°C in temperature. Three airborne DSD probes (a cloud droplet probe (CDP), cloud imaging probe (CIP) and high-volume precipitation spectrometer (HVPS)), along with an aircraft-integrated meteorological measurement system (AIMMS-20) recording environmental information such as geolocation, height, temperature, etc., were used during the flight trial. Details of the instruments are shown in Table 1. The locations of the second and fourth periods of observation are presented in Figure 1(a and b), marked by the red boxes along with the radar composite reflectivity. The second period of observation was regarded as the observation of a convective cloud (CC), since the radar composite reflectivity was over 30 dBZ in most parts, with the maximum exceeding 35 dBZ, which could be taken as the threshold of a convective echo. The fourth period of observation, with a uniform reflectivity of 20 dBZ, was regarded as the observation of a stratiform cloud (SC).

Table 1. Description of instruments used in the flight trial.

Instrument	Range	Bin width	Bin number	Manufacturer
Cloud droplet probe	2–50 μm	1–2 μm	30	DMT, USA
Cloud imaging probe	25–1550 μm	25 μm	62	DMT, USA
High-volume precipitation spectrometer	150–8700 μm	150–750 μm	37	SPEC, USA
Aircraft integrated meteorological measurement system	Height, temperature, geolocation etc.			DMT, USA

Figure 1. Observed radar composite reflectivity and simulated rain rate: (a, b) composite reflectivity, with the red box marking the location of the observation; (c, d) time series of maximum and standard deviation of observed composite reflectivity, in which the dashed red lines represent the start time and end time of the observation; (e, f) time series of the simulated rain rate, in which the dashed blue lines represent the start time and end time of the model output used for comparison. The first and second rows represent the results of the convective cloud and stratiform cloud, respectively.

2.2 Model configuration

The model used in this study was the WRF model, version 3.6, the model configuration of which is presented in Table 2. The microphysics schemes used in this study included the WDM6 scheme, the Thompson scheme and the Morrison scheme. Detailed description of these schemes can be found in Lim and Hong (2010), Thompson et al. (2008), and Morrison, Thompson, and Tatarskii (2009), respectively. The activation of CCN in the WDM6 scheme follows Twomey (1959):

(1) $n_a=C{S}^k$(1)

Table 2. Model configuration.

	D01	D02	D03
Grids	106 × 106, 9 km	151 × 151, 3 km	190 × 250, 1 km
Center	38.0°N, 114.0°E	37.72°N, 113.48°E	37.08°N, 113.69°E
Model top	50 hPa
Vertical layers	40 layers
Cumulus	Kain-Fritsch	None	None
Radiation	RRTM longwave, Dudhia shortwave
PBL	Yonsei University Scheme
Surface layer	Revised MM5 Scheme
Land surface	Noah–MP Land Surface Model
Microphysics	WDM6, Thompson, Morrison

Here, n_a is activated CCN₀ (N_CCN) and S is supersaturation; C is the total CCN; k is a parameter that can be devised from observations and is set to 0.6 in this case (Khairoutdinov and Kogan 2000). The CCN₀ of the WDM6 scheme was set to 10³ cm⁻³ at a supersaturation of 0.48% (S_max), and thus Equation (1) could be written as

(2) $n_a=\mathrm{C}\mathrm{C}{\mathrm{N}}_0{\left(\frac{S}{S_{max}}\right)}^k$(2)

at the beginning of the simulation. The N_c was set to 300 cm⁻³ in both the Thompson scheme and the Morrison scheme, as recommended for continental systems. The time series of simulated rain rate was compared with that of the reflectivity and model output of 48 min before the convective observation was used for the comparison, since the reflectivity indicated that the CC was in the developing stage.

3. Results and discussion

3.1 Comparisons with observations and other schemes

The observed and simulated cloud DSDs are presented in Figure 2. The plane’s movement during the observation period would have mainly been a spiral pattern while ascending or descending. As a result, the plane could have been outside of the clouds some of the time, leading to discontinuity in the observations, as shown in Figure 2(a and b). Generally, an aerosol-aware scheme should be more sophisticated and do a better job than microphysics schemes with a constant droplet number concentration. However, the results of the WDM6 scheme are distinct from the observations and the other two schemes, especially in the SC. The cloud DSDs of the WDM6 scheme are wider than observed. Most cloud droplets have a diameter of 10–30 μm in the WDM6 scheme simulation, while most are concentrated within 5–20 μm in the observation. The cloud DSDs of the WDM6 scheme noticeably broaden above 7°C, which is not observed or simulated by the other two schemes in the SC. The relatively poor performance of the WDM6 scheme might be because of the use of the somewhat simplistic Twomey’s CCN activation formula, in which the activated N_CCN is only determined by the supersaturation. In fact, the supersaturation in contact with CCN, which relies on the vertical velocity, temperature, pressure, etc., is usually not well predicted at grid scale in 3D mesoscale models (Cohard and Pinty 2000). Clearer illustrations are shown in Figure 3(a–d). Generally, the Thompson scheme and the Morrison scheme are consistent with each other in both the CC and SC, though the cloud DSDs of the Morrison scheme are slightly narrower. The Thompson (Morrison) scheme compares well with the observation in the CC and is larger in magnitude at upper levels and narrower at lower levels, as shown in Figure 3(b and d), in the SC. Note that this study is mainly focused on the warm parts of clouds, since the DSD probes used on the flight could not distinguish between liquid particles and ice particles.

Figure 2. Contours of cloud DSD. The first and second rows represent the results of the convective cloud (CC) and stratiform cloud (SC), respectively. Columns 1–4 respresent the results based on observation (cloud droplet probe), the WDM6 simulation, the Thompson simulation, and the Morrison simulation, respectively.

Figure 3. Observed and simulated cloud DSDs and number concentrations: (a, b) cloud DSD of the convective cloud (CC) and stratiform cloud (SC) at 3°C, respectively; (c, d) cloud DSD of the CC and SC at 7°C, respectively; (e, f) cloud number concentration (Nc) of the CC and SC, respectively.

The N_c results shown in Figure 3(e and f) provide a similar conclusion as from the cloud DSD results. The WDM6 scheme underestimates N_c, especially in the SC. The extremely low N_c of the WDM6 scheme in the SC above 7°C corresponds to the extremely wide cloud DSD. The constant N_c set in the Thompson scheme and the Morrison scheme is reasonable in the CC and approximately five times larger in the SC compared to the observations.

The observed and simulated N_r and rain DSDs at 7°C are presented in Figure 4. The 7°C level was chosen since the rain DSD observation near the melting layer may be affected by unmelted ice particles, thus becoming less accurate. The WDM6 scheme overestimates, while the other two schemes underestimate, the N_r compared to the observations. The observations of rain DSDs are composed of the CIP observations of 100–750 μm and the HVPS observations of 750–3000 μm, considering their best measuring ranges. The N_r of the Thompson (Morrison) scheme is smaller in the SC than the CC, which is consistent with many observations and model simulations (Ferrier, Tao, and Simpson 1995; Tokay and Short 1996; Gong, Liu, and Li 1997; Morrison, Thompson, and Tatarskii 2009), though the difference between different clouds for this flight trial is small. The Thompson scheme and Morrison scheme underestimate the quantity of small raindrops in both the SC and CC compared to the WDM6 scheme, possibly because of the underestimation of autoconversion processes (shown in Figure 4(e)) owing to the overestimation of N_c. On the contrary, the WDM6 scheme produces notably fewer large raindrops in the SC.

Figure 4. Observed and simulated rain number concentration (N_r) and rain DSD, together with the average autoconversion rate: (a, b) N_r of the convective cloud (CC) and stratiform cloud (SC), respectively; (c, d) rain DSD at 7°C of the CC and SC, respectively; (e) autoconversion rate of N_r averaged during the total simulation period in domain 3.

3.2 Sensitivity tests of the initial CCN₀ of the WDM6 scheme

As mentioned by several researchers (Khain, Rosenfeld, and Pokrovsky 2005; Cheng, Wang, and Chen 2010; Fan et al. 2012), an increase in the N_CCN will lead to a larger N_c and a narrower cloud DSD. The N_CCN observed in North China lies mostly between 10³ and 10⁴ cm⁻³, with a maximum value exceeding 4 × 10⁴ cm⁻³ at a supersaturation of 0.4%–0.6% (Shi and Duan 2007; Wang et al. 2013). Here, four experiments with different CCN₀ values of 10³, 5 × 10³, 10⁴, and 10⁵ cm⁻³ were conducted to examine if the smaller N_c and narrower cloud DSD produced by the WDM6 scheme is caused by an inappropriate selection of CCN₀.

The average profiles of simulated N_c and N_r in the CC, SC, and whole of domain 3 (D03), using the WDM6 scheme with different CCN₀, are shown in Figure 5. The results show that an increase in CCN₀ leads to an increase in the domain-average N_c, while the responses of the N_c vary with cloud type. At SC upper levels, N_c is still substantially underestimated, even if the CCN₀ is increased 100-fold, which could also be limited by the prediction of supersaturation. As a result, an increase in the CCN₀ is unable to improve the cloud DSD in the SC. In the CC, both the N_c and cloud DSDs agree better with the observations when the CCN₀ is set to 10⁴ cm⁻³ as shown in Figure 6 and, although this value is within the range of N_CCN observation, more case studies are needed for a more comprehensive evaluation of the best CCN₀ to select. N_r varies little when the CCN₀ is increased from 10³ to 10⁵ cm⁻³, which is consistent with the findings of Lim and Hong (2010).

Figure 5. Average cloud number concentration (N_c) and rain number concentration (N_r) under a differing initial CCN number concentration (CCN₀) in different areas. The first and second rows represent N_c and N_r, respectively. Columns 1–3 show the average for the convective cloud (CC), stratiform cloud (SC), and domain 3, respectively.

Figure 6. Cloud and rain DSDs of different cloud types and levels: (a, b) cloud DSDs of the convective cloud (CC) and stratiform cloud (SC) at 3°C, respectively; (c, d) cloud DSDs of the CC and SC at 7°C, respectively; (e, f) rain DSDs of the CC and SC at 7°C, respectively.

4. Summary and future work

In this study, the performance of the WDM6 scheme in the simulation of warm-rain hydrometeor N_c and DSD is compared with airborne observations from a flight trial and other two double-moment bulk schemes.

The results show that the WDM6 scheme underestimates (overestimates) the cloud (rain) number concentration. The N_c is predicted in the WDM6 scheme, while it is set as a constant in the Thompson scheme and Morrison scheme. The WDM6 scheme performs worse than the Thompson scheme and Morrison scheme in aspects of N_c and DSD compared to the airborne observations. Sensitivity tests of the initial CCN₀ in the WDM6 scheme indicate that changing the initial CCN₀ provides a possible way to improve the simulation of N_c and DSD in CC, whereas it does not help much in SC simulation.

Unfortunately, the observations of this flight trial, covering only a small part of the clouds in both time and space, were discontinuous in height. As a result, our comparisons were restricted to certain specific levels. In future work, more observations from other sources, such as conventional surface observations, surface distrometers, and dual-polarization radar, should be used to obtain a more comprehensive conclusion. The N_c simulated by the WDM6 scheme is expected to be more accurate because it is predicted explicitly, but the present results indicate that more efforts are needed to improve its performance. In future work, other aerosol-aware microphysics schemes (i.e. Milbrandt and Yau 2005b; Thompson and Eidhammer 2014) using different CCN activation formula will also be evaluated.

Acknowledgments

The authors thank the anonymous reviewers for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was sponsored by the National Natural Science Foundation of China [grant number 41530427 and 41875172]. It was also supported by the demonstration project of artificial precipitation enhancement and hail suppression operation technology at the eastern side of Taihang Mountains [Grant No. hbrywcsy-2017-2].