1. Introduction
Microphysical parameterizations are crucial to high-resolution numerical weather prediction (NWP) models since microphysical processes exert large influences on atmospheric thermodynamics and cloud hydrometeor properties. Several studies have found that model forecasts of surface precipitation, storm structure, cloud residence time, cold pool strength, and response to aerosols are highly sensitive to microphysical schemes (Lin and Colle 2009; Morrison and Milbrandt 2011; Molthan and Colle 2012; Khain et al. 2015; Morrison et al. 2015).
In most bulk microphysics schemes, the particle size distribution (PSD) is described with a fixed distribution form, such as the Marshall–Palmer (M–P) distribution, gamma distribution or a combination of these two distribution forms (e.g., the Thompson scheme; Thompson et al. 2008). According to the number of free variables in the PSD, bulk microphysics schemes can be classified as one-, two-, or three-moment schemes. The ice categories in the Morrison scheme are all two-moment, and the Thompson scheme is a partial two-moment scheme since its snow and graupel categories are described with a single moment.
In most bulk schemes, including the aforementioned Morrison and Thompson schemes, ice particles are artificially partitioned into multiple categories (e.g., ice, snow and graupel) with prescribed properties. For example, ice hydrometeors are typically assumed to be spherical with the exponent b in the mass–diameter relationship [m–D; m(D) = aDb] set to 3, and each ice category has its own fixed particle density and terminal fall velocity–diameter (V–D) relationship. In this paper, these schemes that have predetermined ice-phase category-based particle properties are referred to as traditional bulk schemes. Recently, several schemes that allow additional properties of ice particles to evolve freely in time and space have been proposed, such as the Stony Brook University (SBU) scheme (Lin and Colle 2011), the Predicted Particle Properties (P3) scheme (Morrison and Milbrandt 2015), and the Ice-Spheroids Habit Model with Aspect-Ratio Evolution (ISHMAEL) scheme (Jensen et al. 2017). Morrison and Milbrandt (2015) suggested that these new microphysics schemes can avoid some of the intrinsic limitations of traditional bulk schemes, e.g., the abrupt transition in particle properties during the interaction between different particle categories and the method that is used to partition particles into different categories (Morrison and Grabowski 2008; Lin and Colle 2009). These schemes proved to be capable of providing comparable simulations of surface precipitation, storm structure, and ice particle size distributions (Morrison et al. 2015; Jensen et al. 2018a,b). In this study, these schemes are referred to as particle property–evolving schemes.
Spectral bin schemes (SBM) are another approach used to describe PSDs. Unlike bulk schemes, PSDs and microphysical processes are explicitly calculated for finite mass or size bins (several tens to several thousand bins). Conceptually, SBM schemes are more sophisticated than bulk schemes in representing the microphysical evolution, including the aerosol–cloud interaction (Seifert et al. 2006; Fan et al. 2012; Wang et al. 2013), the evaporation process (Li et al. 2009; Shipway and Hill 2012; Wang et al. 2013), and collision–coalescence mechanism between particles (Seifert and Beheng 2006; Morrison and Grabowski 2007; Saleeby and Cotton 2008). Even though the bin schemes can simulate the PSD better than the bulk schemes for certain physical processes, there are many pieces of research that suggest that bin schemes do not improve simulations for real cases compared to observations. For example, vanZanten et al. (2011) found that the magnitude of the spread of simulation results provided by different liquid-only SBM schemes is even larger than that simulated by different bulk schemes. Xue et al. (2017) found that the microphysical and thermodynamic characteristics of a squall line simulated by the WRF Model configured with three different SBM schemes varied widely. They attributed these disparities to different assumptions, algorithms and numerical representations of microphysical processes, hydrometeor processes and properties. Meanwhile, the bin microphysics schemes within Eulerian dynamical models also suffer from unphysical broadening of cloud droplet size distributions (DSDs) caused by numerical vertical advection, which limits the investigation of natural broadening of DSDs in clouds using the Eulerian bin schemes (Morrison et al. 2018).
A new kind of microphysical scheme, the Lagrangian particle-based microphysics scheme, has been proposed and it has received increasing attention over the past decade (Andrejczuk et al. 2008; Shima et al. 2009, 2020; Riechelmann et al. 2012; Grabowski et al. 2018). This kind of scheme uses discrete samplings of aerosol, cloud, and precipitation particles, called superparticles or superdroplets, to represent particle populations. Each superparticle represents a group of multitude natural particles that have the same properties and move according to the flow field predicted by the Euler model. The Lagrangian particle-based microphysics approach has a fundamental conceptual advantage and is expected to be widely used and developed (Grabowski et al. 2019; Morrison et al. 2020).
Due to the lack of sufficient understanding of microphysics, uncertainties are inevitably introduced into the microphysics schemes when parameterizing PSDs and microphysical processes. The uncertainty also increases as the schemes become more complicated through including additional process complexity. Morrison et al. (2020) argues that the scheme complexity and uncertainty are “running ahead” of our knowledge of cloud physics. It is necessary to use observations to evaluate microphysics schemes and find out what the simulation biases are, how large they are, what the sources of the biases and uncertainties are, and how to constrain and improve the microphysics schemes.
Aircraft in situ observations, benefiting from direct measurement of particle PSDs in clouds, are viewed as the “gold standard” for evaluating, constraining and improving microphysics schemes. Garvert et al. (2005) compared the observed and simulated PSDs of aggregates for a heavy precipitation event during the Second Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-2) and found that the simulated PSDs deviated from the observations with an overestimated (underestimated) number of moderate-to-large (small) aggregates. Lin and Colle (2009) evaluated the simulation results of an orographic rainfall event of IMPROVE-2 using aircraft in situ measurements. They found that most bulk schemes overestimated the aggregates amount aloft, which led to the overprediction of precipitation over the lee side of a mountain. Molthan et al. (2010) and Molthan and Colle (2012) compared the ice particle properties observed in a snowfall event that occurred during the Canadian CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) Validation Project (C3VP) with those provided by several bulk schemes. They concluded that the two-moment scheme as well as the one-moment scheme with an intercept parameter dependent on temperature could provide a better representation of the vertical variability of observed aggregates compared to the one-moment scheme with a fixed intercept parameter. Naeger et al. (2020) suggested that only the model configured with the particle property–evolving P3 scheme well captured the evolution of rimed particles measured by aircraft in the Olympic Mountain Experiment (OLYMPEX). Moreover, the Thompson scheme is an example of using aircraft observations to constrain and develop microphysics scheme. Its m–D relationship, the PSD form combined from the M–P and gamma distributions, and the relationships between different moments with which to calculate several microphysical process rates for the snow category, are all fitted from aircraft observations. However, the microphysical particle properties, especially those of ice particles, were not evaluated in detail due to a lack of sufficient microphysical observations by aircraft equipped with particle detecting instruments.
In this study, we extend the evaluation of the microphysical parameterization schemes to a frontal stratiform cloud in North China on 22 May 2017. Microphysical modeling with two traditional bulk schemes (the Morrison and Thompson schemes), two particle property–evolving bulk schemes (the P3 scheme, including the P3_1ice and P3_2ice scheme, and the ISHMAEL scheme), and the Hebrew University of Jerusalem, Israel (HUJI) spectral bin fast version microphysics scheme (the SBM_fast scheme) in the WRF were conducted and analyzed. The focus of this work is on ice-phase particle properties in this stratiform cloud case. The motivational questions for this work are the following:
-
1) What are the simulation biases of the WRF Model configured with different microphysical schemes compared with the aircraft observations?
-
2) What are the potential sources for some of these simulation biases?
-
3) What should be considered to improve some relevant aspects of these microphysics schemes based on the aircraft in situ observations?
The paper is organized as follows. The selected precipitation event, the instruments equipped on the aircraft for the field study, the numerical experimental design, and the microphysical parameter retrieval methods are described in section 2. Section 3 presents the characteristics of the observed ice particles, compares the model simulations with observations, and shows the simulation biases quantitively. Section 4 discusses a finding of the P3_2ice scheme concerning the value of the collection efficiency between two ice-phase categories. A summary and a discussion of how to improve these microphysics schemes are given in section 5.
2. Data and methods
a. Case overview
The case studied in this paper is a frontal rainfall event that occurred in North China on 22 May 2017 reported in Hua et al. (2020). Heavy precipitation occurred over Taihang Mountain during this rainfall event, featuring moist convection triggered by multiscale orography. The system contained some weaker precipitation from frontal stratiform clouds and decaying convection over the North China Plain. These stratiform clouds, sometimes with embedded convection, were detected by an instrumented aircraft operated by the Chinese Hebei Weather Modification Office (Hebei King Air, hereafter referred to as the HKA) as shown in Fig. 1. The HKA flight track was composed of five vertical profiles with three ascending and two descending spirals. The first ascending spiral was located at the boundary of a decaying convective cloud (Fig. 1b), while the second and third spirals were near the core of a moderate-intensity convective cloud with the column-maximum reflectivity up to 35 dBZ (Figs. 1c,d). Stratiform clouds with a column-maximum reflectivity under 30 dBZ were detected in the fourth and fifth spirals (Figs. 1e,f).
(a) Elevation (unit: m) of North China and radar composite reflectivity (color shading; unit: dBZ) and flight tracks (black lines) at (b) 0742, (c) 0824, (d) 0906, (e) 0936, and (f) 1000 UTC 22 May 2017. Gray lines are the provincial borders. The black box in (a) represents the region shown in the other panels. The small red boxes in (e) and (f) represent the sampling region of the simulation results in the fourth and fifth spirals, respectively.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
b. Observed datasets
The five flight spirals provided rich measurements of the clouds by a group of particle spectrometers equipped on the HKA. A two-dimensional stereo probe (2D-S; 10–1280 μm) and a high-volume precipitation spectrometer (HVPS; 0.15–19.2 mm) were used to measure the shape, total cross-sectional areas, and PSDs of liquid and ice particles along the flight path. Both the King and Nevzorov hotwire probes detected the liquid water content (LWC), while the ice water content (IWC) was retrieved from the Nevzorov probe by subtracting the LWC from the total water content (TWC). The LWCs calculated from the cloud droplet probe (CDP) and fast cloud droplet probe (FCDP) were also used in this work. The basic information for these instruments is shown in Table 1, and more detailed information can be found in King et al. (1978), Korolev et al. (1998), and Lawson et al. (2015). The instrumental errors for the 2D-S and HVPS includes 1) particles where the focus is poor and the real size and shape could not be obtained; 2) large ice particles shattering on the inlets and tips of probes, which produces copious ice particles that could be mistakenly measured as naturally occurring ice particles; 3) variable depth of field (DOF), which affects the calculation of number concentration; and 4) the relatively slow time response of the probes, which causes counting and sizing errors. The method proposed by Korolev (2007) was adapted to reconstruct the particles that were out of focus. Shattered particles were removed following the method proposed by Lawson (2011). Moreover, all the aircraft data were postprocessed at 5-s intervals to ensure the representativeness of sampling, following Schmitt and Heymsfield (2010).
In situ cloud particle instruments.
The combined PSDs were obtained from direct splicing of the 2D-S data from 100 to 1000 μm and the HVPS data larger than 1000 μm. Moreover, if the LWCs detected by the Nevzorov hotwire probe and calculated from the FCDP and CDP were all higher than 0.05 g m−3, then the data at the corresponding times measured by the HVPS and 2D-S were removed to ensure that the remaining data were free of liquid-phase particles and make this research focus on ice-phase particles only.
With the aircraft measurements, the mass–diameter (m–D) relationships, area–diameter (A–D) relationship, and terminal velocity–diameter (V–D) relationship were computed. Since the number concentration of particles smaller than 1 mm detected by HVPS was always less than that measured by 2D-S in the cloud region with temperatures higher than −5°C (not shown) and considering that the present evaluation work is focused on the stratiform cloud, only the data at temperatures lower than −5°C in the fourth and fifth spirals were analyzed for deriving the m–D, A–D, and V–D relationships. The m–D relationship (m = aDb) was fitted by assuming the coefficient b = 2 and then minimizing the difference between the measured IWC and the integrated composite PSD mass. The assumption of b = 2 is based on many observational studies (e.g., Brown and Francis 1995; Heymsfield et al. 2004, 2010; Schmitt and Heymsfield 2010; Cotton et al. 2013; Fontaine et al. 2014) that recommend an exponent b ∼ 2 for the aggregated ice m–D relationship. Theoretical considerations (Westbrook et al. 2004) also show that the effective density is inversely proportional to the maximum squared dimension (M ∼ D2) for aggregates. The A–D relationship, A(D) = cDe, was fitted using the observed total cross-sectional areas as well as the combined PSDs. Following the method proposed by Mitchell and Heymsfield (2005), the V–D relationship for ice particles was derived by linking the above fitted m–D and A–D relationships through a revised relationship between the Best number and the Reynolds number, which was more suitable for aggregates. This retrieval method is introduced in appendix A. In addition, information about the Doppler radar observations as well as the associated quality control method are detailed in Hua et al. (2020).
c. Model setup and configuration
The Advanced Weather Research and Forecasting (WRF; Skamarock and Klemp 2008) Model version 4.2.1 is configured for the modeling experiments in the same ways as those used by Hua et al. (2020). The model is initialized at 1800 UTC 21 May 2017 and integrated for 24 h to 1800 UTC 22 May with three two-way nested domains centered on Taihang Mountain in North China (Fig. 2). The horizontal grid spacings are 9, 3, and 1 km, respectively. There are 51 levels in the vertical direction, and the layer interval varied from approximately 10 m near the surface to approximately 1000 m at the top of the model. The National Centers for Environmental Prediction 1° × 1° final (FNL) global analysis dataset is used as the initial and boundary conditions of the model experiments. All the domains adopt the Yonsei University planetary boundary layer (PBL) scheme (Hong et al. 2006), revised MM5 Monin–Obukhov scheme (Jiménez et al. 2012) for the surface layer, Rapid Radiative Transfer Model longwave radiation scheme (Mlawer et al. 1997), and Dudhia shortwave radiation scheme (Dudhia 1989). A modified Kain–Fritsch cumulus parameterization (Kain 2004) is adopted in the outermost domain while it is turned off in the inner two domains. The time step for the outermost domain is 15 s.
Geographic location of the three model domains. The grid spacings were 9, 3, and 1 km for D01, D02, and D03, respectively.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
Five microphysical schemes are evaluated on the basis of the model outputs of the inner domain with 1-km grid spacings. They are the two-moment Morrison scheme (Morrison et al. 2009), the Thompson scheme with constant cloud number concentration (Thompson et al. 2008), the 1-ice-category and 2-ice-category configurations of the P3 scheme (Morrison and Milbrandt 2015; Milbrandt and Morrison 2016), the ISHMAEL scheme (Jensen et al. 2017), and the HUJI SBM_fast microphysics scheme (Khain et al. 2009). The Morrison and Thompson schemes are deemed traditional schemes in this paper since ice particles are partitioned into different categories with predefined properties. Note that the “traditional scheme” defined here only refers to the ice phase. The P3 scheme and ISHMAEL scheme are regarded as the particle property–evolving microphysics schemes because several ice particle properties are predicted rather than fixed. More information about these microphysics schemes is detailed in appendix B. For convenience, the simulation produced by the WRF Model configured with one microphysics scheme is referred to as WRF_[scheme_name] (e.g., WRF_P3_1ice).
3. Results
a. Characteristics of observed ice particles
We first analyzed the ice particle properties observed in the fourth and fifth flight spirals of the stratiform cloud. Figure 3a compares the IWC measured by the Nevzorov hotwire probe and that derived from the integration of measured PSDs by the 2D-S and HVPS probes with the fitted m–D relationship. As shown in Fig. 2a, the IWCs derived with the fitted m–D relationship generally agree well with the directly measured IWCs. The mean absolute percentage error (MAPE) of the derived IWCs is 17.19%. Thus, the PSD measured by the 2D-S and HVPS and the IWC detected by the Nevzorov hotwire probe are compatible. Additionally, the corresponding coefficient a (0.0321 kg m−2) is confirmed to be close to that in previous studies (e.g., 0.0278 kg m−2 in Lin and Colle 2009).
(a) IWC (unit: g m−3) measured by the Nevzorov hotwire vs IWC derived from integration of the 5-s-averaged 2D-S and HVPS PSD measurements of ice particles with the fitted mass–diameter relationship. (b) Measured ice particle total cross-sectional areas (unit: m2 m−3) by 2D-S and HVPS vs the calculated areas with the fitted area–diameter relationship. (c) The terminal fall velocities (unit: m s−1) of ice and snow categories as functions of diameter (unit: μm) in the Thompson, Morrison, P3 and SBM_fast schemes, and velocity–diameter relationships assuming the area–diameter relationship in (b) and the fitted mass–diameter relationship. The IWC, PSD, and total area data measured in the fourth and fifth spirals with temperatures lower than −5°C were used. The V–D relationships have been adjusted to the value at the same air density.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
The measured total ice particle cross-sectional areas and the areas calculated using the fitted area–diameter (A–D) relationship are compared in Fig. 3b. The fitted A–D relationship agrees better with the observation than the m–D relationship shown above. This improved fitting result seems to stem from the fact that the area of a particle, which is based on the two-dimensional structure of the particle, is measured more accurately than the density of the particle and its three-dimensional structure, which are used to calculate mass.
Figure 3c presents several V–D relationships for ice particles. The colored lines represent the V–D relationships of ice and snow categories in the Thompson, Morrison, P3, and SBM_fast schemes. The V–D relationships adopted in microphysics schemes rely on observation results of unrimed ice-phase particles (Locatelli and Hobbs 1974; Ferrier 1994) or are calculated from observationally fitted m–D and A–D relationships following Mitchell and Heymsfield (2005). Note that the V–D relationship of the P3 scheme shown in Fig. 3c is a combined V–D relationship of small spherical ice particles and large unrimed particles. The critical diameter separating these two kinds of ice particles is 66 μm; thus, there is an abrupt change of velocity at this size as shown in Fig. 3c. The black line in Fig. 3c displays the V–D relationships derived from the m–D and A–D relationships mentioned above. Note that all the V–D relationships have been adjusted to the value with the air temperature of 263.15 K and the air pressure of 490 hPa, which are the observed values at about 6000 m. As shown in Fig. 3c, the V–D relationship derived from the m–D relationship with the exponent b = 2 is close to those adopted in the microphysics schemes, especially the Thompson scheme. The m–D and V–D relationships are used to verify the model simulation results in the following sections.
b. Verification of model results
The stratiform cloud was measured from 0927 to 0942 UTC and from 0949 to 1005 UTC for the fourth and fifth spirals, respectively. The corresponding simulation results at 0940 and 1000 UTC are used for comparison. The simulated precipitating system (Fig. 4) is close to the observations (Figs. 1e,f), with convection over mountainous areas and stratiform clouds northeast of these convective clouds. It seems that the column-maximum reflectivities predicted by the model with the particle property–evolving schemes are smaller than other schemes, and are closer to the observations. All the simulated data shown in the following sections are extracted from all grid points in a 10 km × 10 km model area (cyan boxes in Fig. 4), which were centered in the fourth and fifth spirals with a radius of approximately 5 km.
The column-maximum reflectivity simulated by the WRF Model configured with the (a),(c) Thompson, (b),(d) Morrison, (e),(g) P3_1ice, (f),(h) P3_2ice, (i),(k) ISMMAEL, and (j),(l) SBM_fast schemes at (first column),(second column) 0940 and (third column),(fourth column) 1000 UTC. The black circles are flight tracks at the fourth and fifth spirals. The cyan boxes represent the sampling region of the simulation results at responding time.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
Figure 5 compares the temperature profiles simulated by the WRF Model configured with different microphysics schemes with the observations. Generally, the simulated temperature is close to the observations, despite the simulated temperature being approximately 1°C higher than the observations in the fourth spiral. The disparities among the temperature profiles provided by the different schemes are quite small above 4000 m, while the temperature simulated by WRF_SBM_fast is warmer than the others from 2000 to 3500 m, especially in the fourth spiral. This colder temperature produced by the WRF Model with the bulk schemes may be caused by that bulk schemes produce a larger rain evaporation rate than bin schemes, as suggested by Li et al. (2009) and Wang et al. (2013). Images collected by CPI show that aggregates are dominant above the freezing level in both spirals. As discussed below, the domination by such low-density ice-phase particles is reproduced by most simulations configured with different microphysics schemes. The consistency between the observed and simulated temperature and dominating hydrometeors ensured that the simulations provided good conditions for analyzing the microphysical properties of these schemes.
Observed (black lines) and simulated (colored lines) temperature (unit: °C) at the (a) fourth and (b) fifth vertical spirals. The simulated temperature profiles were extracted from the red boxes shown in Figs. 1d and 1e at 0940 and 1000 UTC, respectively. Particle images measured by the CPI at different levels are also shown.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
c. Comparison of the simulated LWC and TWC with the observations
Figure 6 shows the observed and simulated LWC and TWC along the fourth (0940 UTC) and fifth (1000 UTC) vertical spirals. Notably, the selected data for comparison of the models are representative since they are not only consistent with those extracted from a larger area (20 km × 20 km, the third and fourth columns in Fig. S1 in the online supplemental material) but also close to those extracted from an early time (0930 UTC for the fourth spiral and 0950 UTC for the fifth spiral, shown in the first two columns in Fig. S1 in the supplemental material). This consistency in time and space indicates that the particle properties in the simulated stratiform cloud are fairly horizontally homogeneous, similar to the observed clouds. Notably, the water content calculated from all the categories of hydrometeors (i.e., cloud, rain, ice, snow, graupel, ICE1, ICE2, and ICE3) are plotted in Fig. 6, but the values of some hydrometeors are too small to be visible in this figure.
Observed TWC (black line, unit: g m−3) and LWC (gray line, unit: g m−3) along the (first column),(second column) fourth and (third column),(fourth column) fifth vertical spirals vs simulated ice and water content using the (a),(c) Thompson, (b),(d) Morrison, (e),(g) P3_1ice, (f),(h) P3_2ice, (i),(k) ISHMAEL, and (j),(l) SBM_fast schemes. The LWCs measured by the Nevzorov hotwire and calculated from the FCDP and CDP probes are shown as gray solid, dotted, and dashed lines, respectively. The median value of the water content for each simulated particle type is shown with colored dashed lines. The orange-shaded area and dashed line represent the 25th and 75th percentiles and the median value of the simulated TWC. The simulation results are extracted from the red box shown in Figs. 1e and 1f.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
The TWCs observed in the fourth and fifth spirals gradually decrease with height above the melting layer (approximately 3720 m), and most are less than 0.4 g m−3. The LWCs measured by the Nevzorov hotwire agree well with those calculated from the FCDP and CDP probes, and most are less than 0.05 g m−3 above the freezing level (approximately 3720 m), especially in the fifth spiral, which indicates that liquid water is rarely measured and ice particles dominate above the freezing level. Below the melting layer the TWC also decreases rapidly due to the acceleration of the terminal fall velocities of raindrops that have melted from aggregates. In general, the profiles of the TWCs and LWCs above 3000 m observed in the fourth spiral are quite similar to those in the fifth spiral, indicating that the observed stratiform cloud is fairly homogeneous in space and time.
WRF_Thompson, WRF_Morrison, and WRF_P3 (including P3_1ice and P3_2ice) accurately simulated the IWCs above the melting layer and a slowly decreasing mass content with height, similar to the observed. The IWCs predicted by WRF_ISHMAEL and WRF_SBM_fast are also similar to the observations in the fifth spiral, but they are larger than the observations in the fourth spiral. For WRF_SBM_fast, the overestimation arises from too many snow-sized particles. However, for the ISHMAEL scheme, too many particles that belongs to the ICE1 (planar-nucleated) and ICE2 (columnar-nucleated) categories contribute to the overestimation of the IWC. The IWC of ICE3, which represents the low-density aggregates in this scheme, is relatively low compared to the low-density particles in the observations and the other schemes.
All the simulations accurately reproduce the decreasing trend of the TWC due to melting between 3000 and 4000 m. Simulated cloud droplets are also concentrated in this layer, indicating that the melting process occurred in a saturated environment. The simulated TWC and LWC show a discrepancy with observations below 3000 m, especially in the fifth spiral, where the observed LWC increases downward, while the simulated LWC remains nearly constant or lower than the observed. This discrepancy may have been caused by a lower relative humidity predicted by the WRF Model. Therefore, in the following sections, the evaluation focused on the layers above 3000 m to ensure that the differences between simulation and observation mainly arise from microphysics rather than other undesired factors.
d. Comparison of the m–D relationship
For most bulk microphysical schemes, the m–D relationship is crucial to calculating the PSD parameters and microphysical processes. For the SBM scheme, it also serves as a bridge that links the mass and number concentrations. Figure 7 compares the IWC measured in the fourth and fifth spirals with that integrated over the observed PSDs using the m–D relationships of snow or ice categories in these microphysics schemes to evaluate whether these predefined m–D relationships are suitable for describing the properties of particles observed in this stratiform cloud case. The “calculated” IWC in Fig. 7 is simply defined as
IWC measured with the Nevzorov hotwire vs the IWC integrated over the observed PSDs in the fourth and fifth vertical spirals with the m–D relationship of the snow category from the (a) Morrison, (b) Thompson, (c) SBM_fast and ice particles from the (d) P3_1ice and P3_2ice and (e) ISHMAEL schemes.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
Since the snow category in the Thompson and Morrison schemes contributes the most to the total (or combined) ice-phase particle mass, and the contributions from the ice or graupel categories are negligible, Figs. 7a and 7b only compare the observed IWCs with those calculated using the m–D relationships of the snow category in these two schemes. It is shown that if these two predefined snow-category m–D relationships in these two schemes are applied over the observed PSDs, they will slightly produce more mass than observed. However, their overestimations are caused by different reasons. Particles of the snow category in the Morrison scheme are assumed to be spherical (b = 3). Given the same parameter a, the spherical assumption leads to an overestimation of mass content, especially for particles with large diameters (and IWCs). Unlike the Morrison scheme, the exponent b in the m–D relationship for the snow category in the Thompson scheme is fixed to 2, following Cox (1988). The overestimation shown in Fig. 7b is caused by the fixed coefficient a (0.069 kg m−2), which is almost 2 times larger than that fitted from the observations (a = 0.0321 kg m−2 for the fourth and fifth spirals). The overestimation of the coefficient a used in this scheme is also reported by Lin and Colle (2009).
The SBM_fast scheme also adopts the spherical assumption for snow-sized particles, but their bulk particle density decreases with particle size. It is expected that this method should be more realistic because snow-sized particle densities are shown to be related to particle size (Locatelli and Hobbs 1974). However, Fig. 7c shows that the m–D relationships for snow-sized particles implemented in this scheme overestimate the IWC much more than the above two schemes. This may be caused by the overlarge equivalent density, the density of an isotropic spherical particle having the same mass and maximum particle length as the actual particle, used in the SBM_fast scheme, which varies from 400 to 110 kg m−3 in the first eight snow size bins. In comparison, the equivalent density is 100 kg m−3 in the Morrison scheme.
The m–D relationship adopted in the P3 scheme varies over a range of particle sizes and is related to the bulk rime mass fraction. For small spherical ice particles, the m–D relationship is
The m–D relationship for ice particles in the ISHMAEL scheme is controlled by the microphysical processes that the particles have undergone and can be derived from the shape and density of particles. The method of deriving the m–D relationships of ice-phase particles in this scheme is detailed in appendix C. The coefficients a and b for each category vary with time and space in the WRF Model. Here, each observed PSD is multiplied by the m–D relationship whose coefficients a and b are the median value at the model level closest to the corresponding height of the observed PSD, within the sampling area (red boxes in Figs. 1e,f) and at the corresponding time. Figure 7e shows the IWC integrated over the observed PSDs with the m–D relationships for three ice-phase categories in the ISHMAEL scheme. The IWCs calculated with the m–D relationship of the ICE3 category, which refers to aggregates, are close to the observations, while those of the other two categories (ICE1 and ICE2) overestimate the masses of the observed particles. This discrepancy results from the fact that the predicted particle densities of the ICE1 and ICE2 categories range from 550 to 700 kg m−3 between 5000 and 7000 m, while that of the ICE3 category is about 50 kg m−3, which is close to the observation.
e. Comparison of ice-phase PSDs
Figure 8 compares PSDs observed in the fourth and fifth vertical spirals at three selected heights with those from the simulations configured with different microphysics schemes at the corresponding times. To ensure the representativeness of the sampling, the observed PSDs collected in the ±100 m range at each height are shown in each panel in Fig. 8. As shown in this figure, the PSDs collected in these two vertical spirals (approximately 14 km and 15 min apart) were quite similar, indicating a homogeneity of particle properties in this stratiform cloud (at least around these two sampling areas). Obviously, the PSDs observed in the fourth and fifth spirals are in a fairly stable shoulder-like form at the three height levels, which is commonly reported in aircraft observation studies (e.g., Field et al. 2005). We can see that none of these microphysics schemes represent this shoulder-like form, except the Thompson scheme, which captures the bimodal distribution form but with a larger number concentration of the small particles. In the Thompson scheme, the PSDs of the snow category contribute the most to the total PSDs, which is the combination of PSDs of all the ice-phase categories. This scheme uses a combination of the M–P and gamma distributions to represent the PSD of the snow category. However, the snow category is modeled with one-moment, i.e., only the mass of snow is predicted, and the other parameters are fixed. These fixed parameters are derived from aircraft observations of stratiform clouds sampled around the British Isles (Field et al. 2005). In this study, it appears that these fixed parameters are not suitable for this frontal precipitation case in North China. The simulated number concentrations are significantly larger than the observations for particles smaller than 200 μm, although the portion with large-size particles is relatively accurate.
The median PSDs (colored lines, deep color for the fourth and light color for the fifth spiral; unit: μm−1 cm−3) of different hydrometeor categories simulated by the WRF Model configured with the Thompson, Morrison, P3_1ice, P3_2ice, ISHMAEL, and SBM_fast schemes and the observed PSDs (round dots, black for the fourth and gray for the fifth spiral) at approximately 6707 (6868), 5922 (6040), and 5198 (5280) m for the fourth (fifth) spiral. The observed PSDs displayed at each height are a combination of PSDs at a depth of 200 m centered at the height. The square-dotted lines represent the total PSDs which are the combined PSDs of all the ice-phase hydrometeor categories shown in each panel.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
The combined PSDs predicted by WRF_Morrison are consistent with the observations at all levels for ice particles larger than 2 mm, but it underestimates the number concentrations of smaller particles. The difference in the number concentration of small particles between the observations and simulation results could not be offset by the ice category, as the ice crystal number concentration is even less than that of the snow category. As shown in Fig. 6a, the snow category dominates in this area, and both the number concentration and mass content of ice crystals are negligible.
Compared with other simulations, WRF_P3_1ice provides the best PSD simulation at all heights, especially for the particles larger than 1 mm. With decreasing height, the predicted PSD changes from a gamma distribution form to an M–P distribution form when the size spectrum is broadened. The PSDs simulated with WRF_P3_2ice match the observations very well at a higher level, but they seem to exhibit a faster spectral broadening trend than the observation, leading to a higher (lower) number concentration of particles with the diameter larger (smaller) than 2 mm at about 5200 m. Meanwhile, since the amount of the ICE2 category particles is negligible, the corresponding PSDs are invisible in these panels.
WRF_ISHMAEL produces fewer particles larger than 1 mm at all heights than the observed. The ICE1 and ICE2 categories contribute excessively to the total PSD for particles smaller than 1 mm. The ICE3 category, which represents aggregates, underestimates the number concentration for particles larger than 1 mm. WRF_SBM_fast severely underestimates the number density at 6707 (6859) m for the fourth (fifth) spiral, especially for ice particles smaller than 2 mm, which is at least one order lower than the observations. At lower levels, the simulated PSDs are comparable to the observations of the large particle end (D > 2 mm), but the number concentrations of ice particles from 0.1 to 2 mm are still underestimated.
f. Comparison of ice particle PMD with observations
The particle mass distribution (PMD) relies on the PSDs and the m–D relationship. Figure 9 depicts the observed and simulated PMDs, including the PMDs of each individual ice-phase category and the total (or combined) PMDs, at different heights. It is noted that the m–D relationship for observed data has been derived in section 3. The observed PMD peaks at approximately 1 mm, indicating that the particles at approximately 1 mm contribute the most to the total mass content. WRF_Thompson significantly overestimates the mass of particles smaller than 0.3 mm due to its overestimation of the number concentration in this size range and its m–D relationship that overestimates the mass of particles at all sizes. The built-in shoulder-like form of PSD in this scheme forms a bimodal PMD, one peaking at approximately 0.1 mm and the other at 1 mm. WRF_Morrison predicts a lower number concentration for particles approximately 1 mm in size. As a result, the corresponding PMD is somewhat lower than the observations, and the PMD peak is shifted to approximately 2 mm. In addition, for particles larger than 2 mm, where WRF_Morrison produces a comparable PSD, the particle mass is several times larger than the observations due to an inappropriate m–D relationship, which slightly overestimates the mass of particles (Fig. 7a).
As in Fig. 8, but for the PMDs (unit: kg μm−1 cm−3) of the observed and simulated ice particles.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
Figures 9g–i depict the PMDs produced by WRF_P3_1ice. Note that the m–D relationship for calculating the PMDs for the P3 scheme is a piecewise method, that is,
WRF_SBM_fast provides a PMD that generally agrees with the observations. However, considering that the PMD relies on the PSD and m–D relationship, and that its m–D relationship overestimates the mass of snow-sized particles (Fig. 7c), this scheme is unable to accurately represent the PMD and PSD at the same time. For example, the simulated PMDs for particles larger than 0.5 mm in both the fourth and fifth spirals are close to the observations. However, the corresponding simulated PSDs were lower than the observed PSDs. In contrast, PSDs for particles larger than 2 mm in lower levels are accurately represented, but the corresponding PMDs are larger than the observations. The simulated peak diameter is slightly larger than the observations, especially at lower levels.
g. Comparison of mass-weighted mean diameter (Dm) and terminal velocity (Vm)
Results obtained from observations for the mass-weighted mean diameter (Dm; black for the fourth and gray for the fifth spiral; unit: mm) along the fourth and fifth vertical spiral vs the simulated Dm (colored, deep color for the fourth and light color for the fifth spiral) using the (a) Thompson, (b) Morrison, (c) P3_1ice, (d) P3_2ice, (e) ISHMAEL, and (f) SBM_fast schemes. The colored dashed lines represent the median Dm of each ice-phase hydrometeor categories. The orange filled areas represent the 5th and 95th percentiles of Dmt.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
As in Fig. 10, but for the mass-weighted mean fall velocity (Vm; unit: m s−1).
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
The Vm derived from observed data is narrowly constrained between 1.0 and 1.3 m s−1 over the range from 5000 to 7000 m (Fig. 11). WRF_Morrison provides the best estimations of Vmt, which ranges between 1.0 and 1.25 m s−1 (Fig. 11b). Although the Vmt values simulated by WRF_Thompson, WRF_P3_1ice and WRF_SBM_fast show a slightly increasing trend with decreasing height, which is not present in the observations, they match the observations well especially for those at the heights lower than 6000 m. The Vm values of ICE1 and ICE3 in WRF_ISHMAEL are smaller than the observations, with nearly constant values of 0.8 and 1.0 m s−1, respectively, and that of ICE2 increases from 0.75 to approximately 1.1 m s−1 with decreasing height. As a result, the combined Vmt values in WRF_ISHMAEL are smaller than the observations. The WRF_P3_2ice simulation provides slightly larger Vmt values than the observations and WRF_P3_1ice.
h. Statistical verification for ice layers
The median (5000–7000 m) value of MAPEs and WMAPEs (unit: %) of the different ice particle property parameters simulated with these microphysics schemes, calculated against the aircraft measurements. The first (second) value in each cell represents the MAPE (and WMAPE) for the fourth (fifth) spiral. The boldface font indicates the lowest MAPE (and WMAPE) among these schemes.
As shown in Table 2, the discrepancy between the observations and the simulation results of the P3_1ice scheme is the smallest, especially in aspects of the PSD (WMAPE: 1.5% and 1.9% for the fourth and fifth spirals, respectively), PMD (WMAPE: 1.9% and 2.1%), and Dm (MAPE: 19.5% for the fifth spiral). This agreement originates from the successful representation of the PSD and m–D relationship. The P3_2ice scheme also produces comparable results, but does not exhibit its superiority compared with the P3_1ice scheme, despite that it is designed to reduce the dilution degree of ice particle properties in the P3_1ice scheme and could be deemed as an improved version of this scheme. The reason for WRF_P3_2ice not producing improved predictions will be explained in section 4.
The simulation configured with the Morrison scheme is consistent with the observations, especially in terms of the IWC (MAPE: 25.4% in the fifth spiral) and Vm (MAPE: 4.8% and 5.8%). WRF_Thompson overestimates the number concentration of small particles, but since these small particles contribute little to the total mass, the WMAPEs of its PSD and PMD are relatively small, 4.5% (3.8%) and 2.3% (2.5%) for the fourth (fifth) spiral, respectively.
The PSD (WMAPE: 34.8% and 30.8%) and PMD (WMAPE: 16.7% and 7.2%) produced by WRF_ISHMAEL differed from the observations to a greater extent than did the other schemes. This scheme produces too few aggregates, although the properties of the aggregates it produced are close to the observations. The SBM_fast scheme does not exhibit its superiority in modeling the PSD (WMAPE: 28.6% and 41.0%) and PMD (WMAPE: 4.7% and 7.6%). The m–D relationship adopted in the SBM may be unsuitable (MAPE: 296.6% and 219.9%), and this scheme tends to simulate a larger Dm (MAPE: 43.3% and 35.8%).
4. Further investigation of the P3_2ice scheme
The P3_2ice scheme, which was designed to reduce the dilution of bulk physical properties (see appendix B) in the P3_1ice scheme and deemed as an improved version, did not show its superiority in simulating ice-phase particle properties. WRF_P3_2ice produces a larger Dm and spectrum width, and a lower number concentration of small particles than WRF_P3_1ice. Huang et al. (2021) also found that the model configured with the P3_2ice scheme underestimated the number concentration of particles smaller than 1 mm and overestimated that of larger particles.
The major difference between these two configurations is that P3_2ice has an additional ice category; thus, we look into possible reasons in the interaction between these two ice categories in this scheme. There are two main microphysics processes between these two categories, collection and merging. According to Milbrandt and Morrison (2016), the category with the higher fall velocity for a given diameter collects the particles in the other category with the lower fall velocity at the same diameter, and if these two categories are sufficiently similar in terms of the bulk density and mass-weighted mean diameter, the ice in one category will merge into the other. Milbrandt and Morrison (2016) also acknowledges that the collection efficiency Eii between these two categories is of some uncertainty. In the previous version of the P3_2ice scheme, Eii ranges from 0.1 to 1. In the current version, it is reduced to a range from 0.001 to 0.3.
To investigate the role of collection efficiency Eii and the merging process on the modeling results, three sensitivity experiments (EiiHigh, NoMerge, and Eii0) were conducted, with the original simulation as a control experiment (CTRL).
In EiiHigh the collection efficiency Eii was set to range from 0.1 to 1, while in Eii0 Eii was set to 0. The merging process was turned on in these two experiments as in the CTRL simulation. In NoMerge, Eii was set to values varying from 0.001 to 0.3 and the merging process is turned off.
Figure 12 depicts the PSDs at approximately 5200 m in the fourth and fifth vertical spirals simulated by these three sensitivity experiments. It demonstrates an apparent trend of the simulated PSDs getting closer to the observations as Eii decreases. Comparing the total PSDs of NoMerge with the CTRL simulations, it can be concluded that the merging process does not exert significant influences on the total PSDs, but only makes the ICE2 category empty by merging the particles in ICE2 into the ICE1 category. Among all the sensitivity experiments, Eii0 produces the closest PSDs to the observations. It infers that the Eii (0.001–0.3) adopted in the current version of the P3_2ice scheme is still not low enough for this stratiform cloud case, despite the fact that the CTRL and NoMerge experiments produce much better total PSDs than the EiiHigh experiment.
Observed (round dots) vs simulated median PSDs modeled by (a) CTRL, (b) EiiHigh, (c) NoMerge, and (d) Eii0 at approximately 5200 m along the fourth and fifth vertical spiral. The black (gray) dots represent the PSDs observed in the fourth (fifth) spiral. The orange and pink lines are the median PSDs of ICE1 and ICE2, respectively. The square-dotted lines represent the total (ICE1 + ICE2) PSDs. The simulated PSDs in the fourth (fifth) spiral are in dark (light) color.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
Figure 13 shows the IWC, Dm, and Vm of each ice-phase category and the combined, simulated by Eii0. They are closer to the observations compared with the CTRL run, and are very similar to those produced by WRF_P3_1ice. It means that at least for this stratiform cloud case, reducing the collection efficiency or even completely prohibiting the collection process of these two ice-phase categories can significantly improve the performance of the P3_2ice scheme to simulate all the properties of ice-phase particles.
Observed (a) IWC, (b) Dm, and (c) Vm vs the results simulated by Eii0 in the fourth and fifth spirals. The black (gray) solid lines represent the data observed or retrieved from the observation in the fourth (fifth) spiral. The colored dashed lines represent the median value of different particle properties of each ice-phase category. The orange filled areas represent the 5th and 95th percentiles of the combined particle properties. The simulated data in the fourth (fifth) spiral are plotted in dark (light) color.
Citation: Journal of the Atmospheric Sciences 80, 6; 10.1175/JAS-D-22-0155.1
5. Summary and discussion
This study evaluates the simulation of particle properties of five microphysics schemes using the aircraft data measured in two vertical spirals in a stratiform cloud in North China. The particle properties simulated by the same microphysics scheme in these two spirals are similar, and both are in agreement with the observations.
It is found that the P3_1ice scheme provides a good representation of ice particle properties in all aspects, similar to those reported by Naeger et al. (2017) and Hou et al. (2020). However, considering the negligible simulated rime mass fraction, perhaps the good performance of the P3_1ice scheme in this stratiform cloud case is not caused by its particle property evolving characteristic. That means in this rarely rimed stratiform cloud case, the P3_1ice scheme behaves similarly to a traditional ice-phase scheme. As inferred in this study, the traditional ice-phase bulk schemes (the Thompson and Morrison schemes) also have a similar capability to represent the ice-phase particle properties well for this stratiform cloud case.
The P3_2ice scheme, which is designed to reduce the dilution of the bulk physical properties of the ice-phase particles in the P3_1ice scheme as an improvement, does not significantly outperform the P3_1ice scheme for this stratiform cloud. Sensitivity experiments show that the overestimated collection efficiency between ice-phase categories, even though it has been reduced from 0.1–1 to 0.001–0.3 in the newer version, causes the simulation results of the P3_2ice scheme to fall short of expectations. By comparing the results of sensitivity experiments with the observations, we provisionally estimate that the collection efficiency has to be reduced to as low as 0 to match the observations measured in this stratiform cloud. We note that perhaps for convective clouds the collection efficiency is not necessary to be as small as in this stratiform cloud case. More accurate value of the collection efficiency could be derived following the Bayesian approach proposed by Morrison et al. (2020) or be estimated through heuristically conducting numerous single-column sensitivity experiments as Karrer et al. (2021) does. Thus, further studies on this issue are desired in the future. Maybe more factors should be considered in parameterizing the collection efficiency, such as the relative humidity over ice (Khain and Sednev 1996) and the mass-weighted mean diameters (Milbrandt and Yau 2005). The collection computation in the current P3_2ice scheme depends on temperature and the bulk rime mass fraction only.
It is also found that the SBM_fast scheme did not generate better simulation results than the bulk schemes. It overestimates Dm and IWCs compared to the observations. The snow-sized particles are assumed spherical in the SBM_fast scheme, that is, the coefficient b of the m–D relationship equals 3. However, assuming b = 3 will lead to a deviation from the observations in aspects of PSDs of snow-sized particles (Mitchell 1988), an overestimation of diffusion growth rate of snow particles (Lin and Colle 2009) and an unrealistically weak melting rates of the snow category and slower rain fall speeds (Naeger et al. 2020). For the SBM_fast scheme, the spherical assumption and the overestimated bulk densities for snow-sized particles result in an unexpected representation of PSDs although its predicted PMDs are relatively close to the observations. In addition, the SBM_fast scheme (and many other bin schemes) also use predefined ice-phase categories as the traditional bulk schemes and thus has to deal with the conversion process between categories that is purely artificial and often leads to an abrupt change of particle properties. However, the change of particle properties in nature is gradual. Our results echo Xue et al. (2017) that the SBM scheme with technically detailed treatment of the PSDs does not guarantee more accurate simulation results than the bulk schemes for this case. We would like to mention that the numerical simulation of a microphysical scheme is affected by many aspects of the scheme, including the algorithm designs, the numerical representations of microphysical processes and particle properties (e.g., m–D and V–D relationships), the strategy adopted to deal with the conversion problem between categories, and so on.
All the evaluated bulk schemes failed to represent the shoulder-like form of the observed PSDs. The Thompson scheme uses a combined distribution form of the gamma and M–P distributions to describe the PSDs of the snow category, and predicts bimodal PSDs as observed, but it overestimates the number concentration of small particles. This overestimation may be caused by the inappropriate fixed parameters of the combined distribution form that are fitted based on aircraft observations over the British Isles, which may be unsuitable for this stratiform cloud case in North China. The Morrison, P3, and ISHMAEL schemes use M–P or gamma distribution to describe PSDs for each category and cannot describe the observed bimodal PSDs. The total PSDs combined from different ice-phase categories may be bimodal, but for the Morrison scheme the number concentration of the other categories is too small to form the observed bimodal form. The failure to represent the observed bimodal PSDs may arise from the incomplete parameterization of the secondary ice production (SIP) process in the current version of these evaluated microphysics schemes, where only the Hallett–Mossop mechanism is considered. If additional SIP mechanisms, such as the fragmentation during ice–ice collisions and shattering of freezing droplets, are taken into consideration, the predicted number concentration of small ice-phase particles may be raised to form the observed bimodal PSDs, as suggested by Huang et al. (2022).
Finally, we point out that the conclusions in this study are made based on a fairly homogeneous stratiform cloud with light precipitation. The microphysics schemes evaluated may exhibit different behavior for other cloud types. In the future, research should be expanded to include clouds in other regions and convective mixed-phase clouds. More knowledge of these detailed properties will be helpful for further understanding cloud microphysics and improving cloud microphysical schemes.
Acknowledgments.
This study was supported by the National Key R&D Program of China (2019YFC1510305), the National Natural Science Foundation of China (41775132), the Northwest Weather Modification Capabilities Development Program (ZQC-R19081), and the S&T Program of Hebei (19275420D). We also acknowledge support from the CMA Key Innovation Team (CMA2022ZD10). The authors would like to express their sincere thanks to the three anonymous reviewers who meticulously inspected our original manuscript and provided very useful suggestions, advice, and encouragement that helped us to significantly improve the manuscript.
Data availability statement.
Aircraft observation and simulation data in this paper are available at this link: https://doi.org/10.6084/m9.figshare.16968532.v1.
APPENDIX A
Retrieving the V–D Relationship from Observation
The air density exerts an influence on the V–D relationship; thus, to compare the observation-derived V–D relationship with those adopted in microphysics schemes, one must ensure that they are at the same air density. The V–D relationships shown in Fig. 3c have been adjusted to the value with the air temperature of 263.15 K and the air pressure of 490 hPa, which are the observed values at about 6000 m.
The air density effect must be considered when comparing Vm at different heights. The air density factor F is calculated in different ways and with different values in these five microphysics schemes. For these four bulk schemes, it is calculated as
APPENDIX B
Introduction of Five Microphysics Schemes
In this paper, five microphysical schemes were evaluated with their model outputs for a domain with 1-km grid spacings. They were the two-moment Morrison scheme (Morrison et al. 2009), the Thompson scheme with constant cloud number concentration (Thompson et al. 2008), the 1-ice-category and 2-ice-category configurations of the P3 scheme (Morrison and Milbrandt 2015; Milbrandt and Morrison 2016), the ISHMAEL Jensen scheme (Jensen et al. 2017), and the HUJI spectral bin fast version (SBM_fast) microphysics scheme (Khain et al. 2009).
The two-moment Morrison scheme adopts the gamma distribution to describe the PSDs of each category. For the rain, ice, snow, and graupel categories, the shape parameters are all set to 0; thus, the corresponding PSDs become the inverse exponential distributions. For the cloud category, the shape parameter is calculated following Martin et al. (1994), which is a function of pressure, temperature, and the predicted droplet number concentration. All the categories are assumed to be spherical (m ∼ D3) with prescribed bulk densities in this scheme. The Thompson scheme is partially two-moment, since only the rain and ice categories are two-moment. For other categories (cloud, snow, and graupel), only the mass mixing ratio is predicted. However, the snow category is described by a combination of the M–P and gamma distributions, which is very different from other categories. This combined distribution form is considered to be more accurate in representing ice particles larger than 100 μm than the solo M–P or gamma distribution (Field et al. 2005). These two microphysics schemes can be deemed traditional bulk schemes in which ice-phase hydrometeors are artificially partitioned into different categories (ice, snow, and graupel) with predefined properties such as density and terminal fall velocity.
The third scheme is the P3 scheme. Unlike the two traditional microphysical schemes, the P3 scheme freely predicts the evolution of various physical properties, e.g., the bulk density and degree of riming of ice particles in space and time. It avoids the unphysical and problematic conversion between ice particle types present in traditional schemes. For example, in traditional schemes, the density and terminal fall velocity of ice particles may change abruptly when snow is converted to graupel during riming. In the P3 scheme, the density and fall velocity change in a more realistic way due to riming. In this paper, we evaluated the one- and two-category configurations of the P3 scheme, which were referred to as the P3_1ice and P3_2ice schemes. The P3_2ice scheme was designed to reduce the detrimental effects of property dilution in the P3_1ice scheme, which represents two or more populations of particles with different bulk properties using a single ice-phase category and a single set of physical properties (e.g., bulk density, fall velocity, etc.). The P3_2ice scheme is not deemed a traditional scheme despite having two ice-phase categories. The reason is that the properties, e.g., bulk density, riming degree, and terminal fall velocity, of ice-phase particles in this scheme also evolved freely with time and space, rather than being predefined in the traditional scheme. The version of the P3_2ice scheme used in this paper is version 4.2.3.
The fourth scheme is a more complicated bulk microphysics scheme (the ISHMAEL scheme) that predicts crystal axis growth rates and effective crystal densities. According to Jensen et al. (2017), ice particles are partitioned into 3 categories: planar-nucleated ice (ICE1), columnar-nucleated ice (ICE2), and aggregates (ICE3). The particle properties of these ice-phase categories, such as the bulk density, fall velocity and axis ratio, also vary with time and space. As a result, a planar (columnar)-nucleated ice could evolve into a column (plane)-like particle and still be in the ICE1 (ICE2) category. Notably, the particle density of ice-phase particles is related to the microphysics processes that the particles undergo, which is very different from the traditional schemes in which the bulk density is predefined. The ISHMAEL scheme and the P3 scheme (P3_1ice and P3_2ice) are regarded as the particle property–evolving microphysics schemes in this study, in contrast to the abovementioned traditional schemes.
The SBM_fast scheme, a computational timesaving spectral bin scheme, was also evaluated in this study. Unlike the above bulk schemes, the evolution of the number concentration and microphysical processes are predicted in each mass bin in the SBM_fast scheme. Particles in each mass bin have their own density and fall velocity. The ice particles are portioned into 3 categories (ice, snow and graupel) in the SBM_fast scheme. The ice crystals and snow (aggregates) are calculated using one 33-bin distribution function, where the first 18 mass bins (radius < 150 μm) correspond to ice crystals and the last 15 bins correspond to snow. Note that the partitioning of ice crystals and snow in the SBM_fast scheme is completely diagnostic, which does not affect the simulations directly.
APPENDIX C
Deriving the m–D Relationships of Ice-Phase Particles of the ISHMAEL Scheme
These derived m–D relationships of the ISHMAEL scheme are different for each model grid point. For calculating the “calculated IWC” in section 3d, each observed PSD is multiplied by the m–D relationship whose coefficients a and b are the median value at the model level closest to the corresponding height of the observed PSD, within the sampling area (red boxes in Figs. 1e,f) and at the corresponding time. For calculating the PMD, the m–D relationship at each 3D model grid point is multiplied by the PSD at the corresponding grid point.
REFERENCES
Andrejczuk, M., J. M. Reisner, B. Henson, M. K. Dubey, and C. A. Jeffery, 2008: The potential impacts of pollution on a nondrizzling stratus deck: Does aerosol number matter more than type? J. Geophys. Res., 113, D19204, https://doi.org/10.1029/2007JD009445.
Brown, P. R. A., and P. N. Francis, 1995: Improved measurements of the ice water content in cirrus using a total-water probe. J. Atmos. Oceanic Technol., 12, 410–414, https://doi.org/10.1175/1520-0426(1995)012<0410:IMOTIW>2.0.CO;2.
Cotton, R. J., and Coauthors, 2013: The effective density of small ice particles obtained from in situ aircraft observations of mid-latitude cirrus. Quart. J. Roy. Meteor. Soc., 139, 1923–1934, https://doi.org/10.1002/qj.2058.
Cox, G. P., 1988: Modelling precipitation in frontal rainbands. Quart. J. Roy. Meteor. Soc., 114, 115–127, https://doi.org/10.1002/qj.49711447906.
Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 3077–3107, https://doi.org/10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.
Fan, J., L. R. Leung, Z. Li, H. Morrison, H. Chen, Y. Zhou, Y. Qian, and Y. Wang, 2012: Aerosol impacts on clouds and precipitation in eastern China: Results from bin and bulk microphysics. J. Geophys. Res., 117, D00K36, https://doi.org/10.1029/2011JD016537.
Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249–280, https://doi.org/10.1175/1520-0469(1994)051<0249:ADMMPF>2.0.CO;2.
Field, P. R., R. J. Hogan, P. R. A. Brown, A. J. Illingworth, T. W. Choularton, and R. J. Cotton, 2005: Parametrization of ice-particle size distributions for mid-latitude stratiform cloud. Quart. J. Roy. Meteor. Soc., 131, 1997–2017, https://doi.org/10.1256/qj.04.134.
Fontaine, E., A. Schwarzenboeck, J. Delanoë, W. Wobrock, D. Leroy, R. Dupuy, C. Gourbeyre, and A. Protat, 2014: Constraining mass–diameter relations from hydrometeor images and cloud radar reflectivities in tropical continental and oceanic convective anvils. Atmos. Chem. Phys., 14, 11 367–11 392, https://doi.org/10.5194/acp-14-11367-2014.
Garvert, M. F., C. P. Woods, B. A. Colle, C. F. Mass, P. V. Hobbs, M. T. Stoelinga, and J. B. Wolfe, 2005: The 13–14 December 2001 IMPROVE-2 event. Part II: Comparisons of MM5 model simulations of clouds and precipitation with observations. J. Atmos. Sci., 62, 3520–3534, https://doi.org/10.1175/JAS3551.1.
Grabowski, W. W., P. Dziekan, and H. Pawlowska, 2018: Lagrangian condensation microphysics with Twomey CCN activation. Geosci. Model Dev., 11, 103–120, https://doi.org/10.5194/gmd-11-103-2018.
Grabowski, W. W., H. Morrison, S.-I. Shima, G. C. Abade, P. Dziekan, and H. Pawlowska, 2019: Modeling of cloud microphysics: Can we do better? Bull. Amer. Meteor. Soc., 100, 655–672, https://doi.org/10.1175/BAMS-D-18-0005.1.
Harrington, J. Y., K. Sulia, and H. Morrison, 2013: A method for adaptive habit prediction in bulk microphysical models. Part I: Theoretical development. J. Atmos. Sci., 70, 349–364, https://doi.org/10.1175/JAS-D-12-040.1.
Heymsfield, A. J., A. Bansemer, C. Schmitt, C. Twohy, and M. R. Poellot, 2004: Effective ice particle densities derived from aircraft data. J. Atmos. Sci., 61, 982–1003, https://doi.org/10.1175/1520-0469(2004)061<0982:EIPDDF>2.0.CO;2.
Heymsfield, A. J., C. Schmitt, A. Bansemer, and C. H. Twohy, 2010: Improved representation of ice particle masses based on observations in natural clouds. J. Atmos. Sci., 67, 3303–3318, https://doi.org/10.1175/2010JAS3507.1.
Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341, https://doi.org/10.1175/MWR3199.1.
Hou, T., H. Lei, Z. Hu, J. Yang, and X. Li, 2020: Simulations of microphysics and precipitation in a stratiform cloud case over northern China: Comparison of two microphysics schemes. Adv. Atmos. Sci., 37, 117–129, https://doi.org/10.1007/s00376-019-8257-0.
Hua, S., X. Xu, and B. Chen, 2020: Influence of multiscale orography on the initiation and maintenance of a precipitating convective system in North China: A case study. J. Geophys. Res. Atmos., 125, e2019JD031731, https://doi.org/10.1029/2019JD031731.
Huang, Y., and Coauthors, 2021: Microphysical processes producing high ice water contents (HIWCs) in tropical convective clouds during the HAIC-HIWC field campaign: Evaluation of simulations using bulk microphysical schemes. Atmos. Chem. Phys., 21, 6919–6944, https://doi.org/10.5194/acp-21-6919-2021.
Huang, Y., and Coauthors, 2022: Microphysical processes producing high ice water contents (HIWCs) in tropical convective clouds during the HAIC-HIWC field campaign: Dominant role of secondary ice production. Atmos. Chem. Phys., 22, 2365–2384, https://doi.org/10.5194/acp-22-2365-2022.
Jensen, A. A., J. Y. Harrington, H. Morrison, and J. A. Milbrandt, 2017: Predicting ice shape evolution in a bulk microphysics model. J. Atmos. Sci., 74, 2081–2104, https://doi.org/10.1175/JAS-D-16-0350.1.
Jensen, A. A., J. Y. Harrington, and H. Morrison, 2018a: Impacts of ice particle shape and density evolution on the distribution of orographic precipitation. J. Atmos. Sci., 75, 3095–3114, https://doi.org/10.1175/JAS-D-17-0400.1.
Jensen, A. A., J. Y. Harrington, and H. Morrison, 2018b: Microphysical characteristics of squall-line stratiform precipitation and transition zones simulated using an ice particle property-evolving model. Mon. Wea. Rev., 146, 723–743, https://doi.org/10.1175/MWR-D-17-0215.1.
Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898–918, https://doi.org/10.1175/MWR-D-11-00056.1.
Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170–181, https://doi.org/10.1175/1520-0450(2004)043<0170:TKCPAU>2.0.CO;2.
Karrer, M., A. Seifert, D. Ori, and S. Kneifel, 2021: Improving the representation of aggregation in a two-moment microphysical scheme with statistics of multi-frequency Doppler radar observations. Atmos. Chem. Phys., 21, 17 133–17 166, https://doi.org/10.5194/acp-21-17133-2021.
Khain, A. P., and I. Sednev, 1996: Simulation of precipitation formation in the eastern Mediterranean coastal zone using a spectral microphysics cloud ensemble model. Atmos. Res., 43, 77–110, https://doi.org/10.1016/S0169-8095(96)00005-1.
Khain, A. P., L. R. Leung, B. Lynn, and S. Ghan, 2009: Effects of aerosols on the dynamics and microphysics of squall lines simulated by spectral bin and bulk parameterization schemes. J. Geophys. Res., 114, D22203, https://doi.org/10.1029/2009JD011902.
Khain, A. P., and Coauthors, 2015: Representation of microphysical processes in cloud-resolving models: Spectral (bin) microphysics versus bulk parameterization. Rev. Geophys., 53, 247–322, https://doi.org/10.1002/2014RG000468.
King, W. D., D. A. Parkin, and R. J. Handsworth, 1978: A hot-wire liquid water device having fully calculable response characteristics. J. Appl. Meteor., 17, 1809–1813, https://doi.org/10.1175/1520-0450(1978)017<1809:AHWLWD>2.0.CO;2.
Korolev, A., 2007: Reconstruction of the sizes of spherical particles from their shadow images. Part I: Theoretical considerations. J. Atmos. Oceanic Technol., 24, 376–389, https://doi.org/10.1175/JTECH1980.1.
Korolev, A., J. W. Strapp, G. A. Isaac, and A. N. Nevzorov, 1998: The Nevzorov airborne hot-wire LWC–TWC probe: Principle of operation and performance characteristics. J. Atmos. Oceanic Technol., 15, 1495–1510, https://doi.org/10.1175/1520-0426(1998)015<1495:TNAHWL>2.0.CO;2.
Lawson, R. P., 2011: Effects of ice particles shattering on the 2D-S probe. Atmos. Meas. Tech., 4, 1361–1381, https://doi.org/10.5194/amt-4-1361-2011.
Lawson, R. P., S. Woods, and H. Morrison, 2015: The microphysics of ice and precipitation development in tropical cumulus clouds. J. Atmos. Sci., 72, 2429–2445, https://doi.org/10.1175/JAS-D-14-0274.1.
Li, X., W.-K. Tao, A. P. Khain, J. Simpson, and D. E. Johnson, 2009: Sensitivity of a cloud-resolving model to bulk and explicit bin microphysical schemes. Part II: Cloud microphysics and storm dynamics interactions. J. Atmos. Sci., 66, 22–40, https://doi.org/10.1175/2008JAS2647.1.
Lin, Y., and B. A. Colle, 2009: The 4–5 December 2001 IMPROVE-2 event: Observed microphysics and comparisons with the Weather Research and Forecasting Model. Mon. Wea. Rev., 137, 1372–1392, https://doi.org/10.1175/2008MWR2653.1.
Lin, Y., and B. A. Colle, 2011: A new bulk microphysical scheme that includes riming intensity and temperature-dependent ice characteristics. Mon. Wea. Rev., 139, 1013–1035, https://doi.org/10.1175/2010MWR3293.1.
Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79, 2185–2197, https://doi.org/10.1029/JC079i015p02185.
Martin, G. M., D. W. Johnson, and A. Spice, 1994: The measurement and parameterization of effective radius of droplets in warm stratocumulus clouds. J. Atmos. Sci., 51, 1823–1842, https://doi.org/10.1175/1520-0469(1994)051<1823:TMAPOE>2.0.CO;2.
Milbrandt, J. A., and M. K. Yau, 2005: A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J. Atmos. Sci., 62, 3065–3081, https://doi.org/10.1175/JAS3535.1.
Milbrandt, J. A., and H. Morrison, 2016: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part III: Introduction of multiple free categories. J. Atmos. Sci., 73, 975–995, https://doi.org/10.1175/JAS-D-15-0204.1.
Mitchell, D. L., 1988: Evolution of snow-size spectra in cyclonic storms. Part I: Snow growth by vapor deposition and aggregation. J. Atmos. Sci., 45, 3431–3451, https://doi.org/10.1175/1520-0469(1988)045<3431:EOSSSI>2.0.CO;2.
Mitchell, D. L., and A. J. Heymsfield, 2005: Refinements in the treatment of ice particle terminal velocities, highlighting aggregates. J. Atmos. Sci., 62, 1637–1644, https://doi.org/10.1175/JAS3413.1.
Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 663–16 682, https://doi.org/10.1029/97JD00237.
Molthan, A. L., and B. A. Colle, 2012: Comparisons of single- and double-moment microphysics schemes in the simulation of a synoptic-scale snowfall event. Mon. Wea. Rev., 140, 2982–3002, https://doi.org/10.1175/MWR-D-11-00292.1.
Molthan, A. L., W. A. Petersen, S. W. Nesbitt, and D. Hudak, 2010: Evaluating the snow crystal size distribution and density assumptions within a single-moment microphysics scheme. Mon. Wea. Rev., 138, 4254–4267, https://doi.org/10.1175/2010MWR3485.1.
Morrison, H., and W. W. Grabowski, 2007: Comparison of bulk and bin warm-rain microphysics models using a kinematic framework. J. Atmos. Sci., 64, 2839–2861, https://doi.org/10.1175/JAS3980.
Morrison, H., and W. W. Grabowski, 2008: A novel approach for representing ice microphysics in models: Description and tests using a kinematic framework. J. Atmos. Sci., 65, 1528–1548, https://doi.org/10.1175/2007JAS2491.1.
Morrison, H., and J. Milbrandt, 2011: Comparison of two-moment bulk microphysics schemes in idealized supercell thunderstorm simulations. Mon. Wea. Rev., 139, 1103–1130, https://doi.org/10.1175/2010MWR3433.1.
Morrison, H., and J. Milbrandt, 2015: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part I: Scheme description and idealized tests. J. Atmos. Sci., 72, 287–311, https://doi.org/10.1175/JAS-D-14-0065.1.
Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon. Wea. Rev., 137, 991–1007, https://doi.org/10.1175/2008MWR2556.1.
Morrison, H., J. A. Milbrandt, G. H. Bryan, K. Ikeda, S. A. Tessendorf, and G. Thompson, 2015: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part II: Case study comparisons with observations and other schemes. J. Atmos. Sci., 72, 312–339, https://doi.org/10.1175/JAS-D-14-0066.1.
Morrison, H., M. Witte, G. H. Bryan, J. Y. Harrington, and Z. J. Lebo, 2018: Broadening of modeled cloud droplet spectra using bin microphysics in an Eulerian spatial domain. J. Atmos. Sci., 75, 4005–4030, https://doi.org/10.1175/JAS-D-18-0055.1.
Morrison, H., and Coauthors, 2020: Confronting the challenge of modeling cloud and precipitation microphysics. J. Adv. Model. Earth Syst., 12, e2019MS001689, https://doi.org/10.1029/2019MS001689.
Naeger, A. R., B. A. Colle, and A. Molthan, 2017: Evaluation of cloud microphysical schemes for a warm frontal snowband during the GPM Cold Season Precipitation Experiment (GCPEx). Mon. Wea. Rev., 145, 4627–4650, https://doi.org/10.1175/MWR-D-17-0081.1.
Naeger, A. R., B. A. Colle, N. Zhou, and A. Molthan, 2020: Evaluating warm and cold rain processes in cloud microphysical schemes using OLYMPEX field measurements. Mon. Wea. Rev., 148, 2163–2190, https://doi.org/10.1175/MWR-D-19-0092.1.
Riechelmann, T., Y. Noh, and S. Raasch, 2012: A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision. New J. Phys., 14, 065008, https://doi.org/10.1088/1367-2630/14/6/065008.
Saleeby, S. M., and W. R. Cotton, 2008: A binned approach to cloud-droplet riming implemented in a bulk microphysics model. J. Appl. Meteor. Climatol., 47, 694–703, https://doi.org/10.1175/2007JAMC1664.1.
Schmitt, C. G., and A. J. Heymsfield, 2010: The dimensional characteristics of ice crystal aggregates from fractal geometry. J. Atmos. Sci., 67, 1605–1616, https://doi.org/10.1175/2009JAS3187.1.
Seifert, A., and K. D. Beheng, 2006: A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteor. Atmos. Phys., 92, 45–66, https://doi.org/10.1007/s00703-005-0112-4.
Seifert, A., A. Khain, A. Pokrovsky, and K. D. Beheng, 2006: A comparison of spectral bin and two-moment bulk mixed-phase cloud microphysics. Atmos. Res., 80, 46–66, https://doi.org/10.1016/j.atmosres.2005.06.009.
Shima, S., K. Kusano, A. Kawano, T. Sugiyama, and S. Kawahara, 2009: The super-droplet method for the numerical simulation of clouds and precipitation: A particle-based and probabilistic microphysics model coupled with a non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 135, 1307–1320, https://doi.org/10.1002/qj.441.
Shima, S., Y. Sato, A. Hashimoto, and R. Misumi, 2020: Predicting the morphology of ice particles in deep convection using the super-droplet method: Development and evaluation of SCALE-SDM 0.2.5-2.2.0, -2.2.1, and -2.2.2. Geosci. Model Dev., 13, 4107–4157, https://doi.org/10.5194/gmd-13-4107-2020.
Shipway, B. J., and A. A. Hill, 2012: Diagnosis of systematic differences between multiple parametrizations of warm rain microphysics using a kinematic framework. Quart. J. Roy. Meteor. Soc., 138, 2196–2211, https://doi.org/10.1002/qj.1913.
Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for Weather Research and Forecasting applications. J. Comput. Phys., 227, 3465–3485, https://doi.org/10.1016/j.jcp.2007.01.037.
Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 5095–5115, https://doi.org/10.1175/2008MWR2387.1.
vanZanten, M. C., and Coauthors, 2011: Controls on precipitation and cloudiness in simulations of trade-wind cumulus as observed during RICO. J. Adv. Model. Earth Syst., 3, M06001, https://doi.org/10.1029/2011MS000056.
Wang, Y., J. Fan, R. Zhang, L. R. Leung, and C. Franklin, 2013: Improving bulk microphysics parameterizations in simulations of aerosol effects. J. Geophys. Res. Atmos., 118, 5361–5379, https://doi.org/10.1002/jgrd.50432.
Westbrook, C. D., R. C. Ball, P. R. Field, and A. J. Heymsfield, 2004: Theory of growth by differential sedimentation, with application to snowflake formation. Phys. Rev., 70E, 021403, https://doi.org/10.1103/PhysRevE.70.021403.
Xue, L., and Coauthors, 2017: Idealized simulations of a squall line from the MC3E field campaign applying three bin microphysics schemes: Dynamic and thermodynamic structure. Mon. Wea. Rev., 145, 4789–4812, https://doi.org/10.1175/MWR-D-16-0385.1.