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 (Nc) 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 Nc 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


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 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 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 (CCN 0 ) 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

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).

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): Here, n a is activated CCN 0 (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 CCN 0 of the WDM6 scheme was set to 10 3 cm −3 at a supersaturation of 0.48% (S max ), and thus Equation (1) could be written as 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.

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 aerosolaware 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.
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 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. 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.

Sensitivity tests of the initial CCN 0 of the WDM6 scheme
As mentioned by several researchers (Khain, Rosenfeld, and Pokrovsky 2005;Cheng, Wang, and Chen 2010;Fan Figure 5. Average cloud number concentration (N c ) and rain number concentration (N r ) under a differing initial CCN number concentration (CCN 0 ) 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. 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 10 3 and 10 4 cm −3 , with a maximum value exceeding 4 × 10 4 cm −3 at a supersaturation of 0.4%-0.6% (Shi and Duan 2007;Wang et al. 2013). Here, four experiments with different CCN 0 values of 10 3 , 5 × 10 3 , 10 4 , and 10 5 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 CCN 0 .
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 CCN 0 , are shown in Figure 5. The results show that an increase in CCN 0 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 CCN 0 is increased 100-fold, which could also be limited by the prediction of supersaturation. As a result, an increase in the CCN 0 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 CCN 0 is set to 10 4 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 CCN 0 to select. N r varies little when the CCN 0 is increased from 10 3 to 10 5 cm −3 , which is consistent with the findings of Lim and Hong (2010).

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 CCN 0 in the WDM6 scheme indicate that changing the initial CCN 0 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, 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. 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.