1. Introduction
Accurate prediction and representation of the raindrop size distribution (DSD) in the microphysical schemes of numerical weather prediction models is essential for accurately representing cloud and precipitation processes. To this end, numerous methods have been developed to simulate the initial formation of the DSD via cloud droplet autoconversion and raindrop accretion processes, some of which use bulk distribution (Berry and Reinhardt 1974, hereafter BR74) bin-emulating (Tzivion et al. 1987; Meyers et al. 1997), or spectral-bin approaches (Khain et al. 2004). Bulk hydrometeor distribution and bin-emulating approaches assume a priori size distributions of hydrometeors, typically with an exponential or gamma distribution shape, while a computationally demanding spectral-bin approach permits the evolution of the size distribution with no assumed shape. There are various advantages and disadvantages to using these different approaches, the assessment of which is further complicated by the fact that they function alongside processes such as drop sedimentation, drop self-collection, and ice processes of raindrop production (via melting and shedding) for generating a representative DSD (e.g., Meyers et al. 1997; Morrison et al. 2009; Thompson et al. 2008; Khain et al. 2004). The synergy of these parameterized processes ultimately determines the prognosis of liquid water content (LWC), number concentration (Nr), and diameter of raindrops, with significant implications for research and forecasting applications.
Most microphysics schemes have parameters that are adjusted to permit better agreement between simulated and observed DSDs, as well as other hydrometeor quantities. This requires setting parameters within an acceptable physical range, while adjusting them to operate appropriately within the overarching microphysics scheme. As such, there are often multiple microphysics schemes using the same parameterization basis functions to represent processes such as raindrop collisional breakup, but that utilize model-customized coefficients that are calibrated to produce the most representative DSDs (Meyers et al. 1997; Thompson et al. 2004, 2008; Morrison et al. 2009, 2012; Lim and Hong 2010). Variations in such parameterization coefficients within a common parent microphysics scheme have been demonstrated to result in very different solutions due to complex nonlinear interactions of parameterized microphysical processes. As such they may benefit from calibration to improve their agreement with observations (Morrison et al. 2012; Planche et al. 2019).
One such microphysical process that has undergone parameterization adjustments and tuning in numerical models is that of raindrop collisional breakup (Ziegler 1985; Meyers et al. 1997; Khain et al. 2004; Thompson et al. 2004, 2008; Morrison et al. 2009, 2012; Lim and Hong 2010; Mansell et al. 2010). There is a general lack of theoretical formulations upon which to base the development of a rigorous parameterization for drop breakup. Seifert et al. (2005) note that models largely rely upon 1) parameterizations that seek to generate equilibrium DSDs that generally agree with observations, such as the use of DSDs from Zawadzki and de Agostino Antonio (1988, hereafter ZA88) in the formulation of Verlinde and Cotton (1993, hereafter VC93), or 2) data from the few laboratory studies of breakup (e.g., Pruppacher and Klett 1997; Low and List 1982, hereafter LL82). More recent laboratory observations (e.g., Barros et al. 2008) and refinements to the LL82 parameterization (e.g., McFarquhar 2004; Straub et al. 2010; Schlottke et al. 2010; Prat et al. 2012) have improved upon LL82 by extrapolating to more numerous drop-pair collisions, permitting drop eccentricity, and/or utilizing more updated collision kernels, among other things. Some of these refined parameterizations produce rain DSDs that tend to vary in the resulting number concentrations of drops toward the tails of the distribution compared to LL82. As such, many of these studies highlight the need for more robust laboratory work and observations on which to base a more theoretically formulated parameterization of drop collisions and breakup. Recent modeling studies have demonstrated that some microphysics schemes overpredict raindrop size and underpredict number concentration for differing reasons. It has been demonstrated that models directly benefit from adjustments to the drop breakup equations to modify collisional breakup, thereby producing DSDs in better agreement with their observations (Morrison et al. 2012; Planche et al. 2019).
We note here that the disdrometer observations are subject to the detection capabilities, sampling limitations, and quality control of the disdrometer datasets used. As discussed by Dolan et al. (2018), disdrometers such as 2DVD’s have difficulty measuring the smallest drops (<0.3 mm; Tokay et al. 2001), and the quality control process limits data in the smallest bin as well as samples with fewer than 100 drops in order to account for splashing, drop shatter, insects, and drop shadowing (Tokay et al. 2001; Thompson et al. 2015). Additionally, disdrometers likely undersample large drops (>5 mm) due to the small catchment cross section combined with the infrequency of drops of such sizes (Smith et al. 1993; Gatlin et al. 2015). The distribution of individual drops measured by the disdrometers are fit to a distribution with a given D0.
In this study we utilize an extensive archive of simulations, produced from the Regional Atmospheric Modeling System (RAMS) (Cotton et al. 2003), using two-moment bulk microphysics (Verlinde et al. 1990; Walko et al. 1995; Meyers et al. 1997; Walko et al. 2000; Saleeby and Cotton 2004; Saleeby and van den Heever 2013) to perform a similar statistical analysis of rain DSDs as was done for the suite of global disdrometer data by Dolan et al. (2018). Like the disdrometer data suite, the simulation archive covers a variety of precipitation systems ranging from continental to maritime systems and from warm-phase to mixed-phase systems as shown in Table 1. We seek to determine if this large sample of model-generated rain DSDs exhibits a similar raindrop mean diameter frequency distribution compared to the global disdrometer data while considering the limitations and numerical constraints within both the models and observations (e.g., disdrometers have minimum size and number detection thresholds for reliable results and models have parameterized numerical bounds and limits).
Simulations used for comparisons in this study.
Raindrop mean diameter frequency distributions expressed in logNw–Dm phase space from (a) global surface disdrometer data (from Dolan et al. 2018) and (b) RAMS simulation data with a reference frequency contour from (a) overlaid. The distinct peak seen for large logNw near Dm ∼ 1 mm, which is discussed in the text, is noted by the arrow and “spike” label and is referred to as the “spike” throughout the text.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
This analysis demonstrated that the spike was more prevalent in deep convective simulations, compared to shallow convection, due to the presence of larger sized drops that are subject to breakup. As such, the investigation presented here will focus solely on the supercell case from the simulation archive. Given the noted differences between the disdrometer observations and simulated rain distributions, this paper presents an investigation to 1) determine the cause of the prominent spike and the dominant frequency of occurrence of drop DSD with Dm ∼ 1 mm, 2) compare representative raindrop Dm frequency distributions produced from a suite of different microphysics schemes, and 3) present a generalized method of adjusting raindrop breakup parameterizations aimed at bringing simulated rain DSDs and observations into better agreement.
2. Results from supercell simulation
The RAMS-simulated supercell case was initialized with a modified Weismann–Klemp sounding as depicted by Grant and van den Heever (2014a). Additional details of this simulation are provided in Table 2. The simulated storm undergoes multiple splitting and generates rainfall in both the left and right mover cells, as seen in Fig. 2a. The associated plot of the raindrop Dm frequency distribution in logNw–Dm phase space is shown in Fig. 2b. A comparison of the plots of logNw–Dm between Fig. 2b and Fig. 1b demonstrate that the supercell simulation produces a similar Dm distribution compared to the full simulation archive, and the spike is clearly present. The spike at Dm ∼ 1 mm indicates a propensity for raindrop Dm to cluster at this size over a wide range of high logNw. This suggests that the microphysics parameterization responsible for this feature tends to generate drops of a specific Dm.
From the RAMS supercell simulation: (a) accumulated precipitation and (b) raindrop Dm frequency distribution in logNw–Dm phase space.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
Summary of model grid setup and simulation configuration.
To examine the frequency of occurrence of a particular Dm, the corresponding near-surface raindrop Dm frequency distribution (RDFD) is shown in Fig. 3. The Dm values were separated into 0.04 mm bins, and each grid cell in the lowest model layer containing rain mixing ratio of at least 0.01 g kg−1 was included for the duration of the simulation. Most of the sampled grid cells, regardless of rain LWC or number concentration, fall within a narrow range centered near 1 mm. While the dominant spike near 1 mm remains the focus of this paper, since it is associated with the clearest anomalous feature in comparison to the disdrometer observations, there is also a secondary a peak near 0.7 mm. It is suspected that the lesser peak is associated with either warm phase collision–coalescence growth of drops or melting of smaller ice particles.
Raindrop Dm frequency distribution (RDFD) represented as normalized bin counts of rain Dm across a range of size bins from the RAMS-2M supercell simulation. The counted data include grid cells in the lowest model layer to consider only raindrops impacting surface rainfall accumulation.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
To isolate the parameterization(s) responsible for this distinct Dm peak near 1 mm diameter, we performed an exhaustive set of additional supercell test simulations, with various microphysical parameterizations either turned on and off or with modified parameterization coefficients. From these tests, only modification or exclusion of the raindrop self-collection process led to a reduced or eliminated spike at Dm ∼ 1 mm. More specifically, the spike is directly linked to the representation of raindrop self-collisional breakup. While other processes, such as autoconversion, accretion, drop shedding of hail, and melting of ice (e.g., Brown et al. 2017) certainly impact the raindrop DSD, the drop self-collisional breakup parameterization is the primary cause of the spike, as will be demonstrated below.
3. Raindrop breakup
a. RAMS drop breakup parameterization
The raindrop breakup parameterization in the RAMS microphysics scheme follows Verlinde et al. (1990) and VC93, and it is guided by disdrometer observations of ZA88. These observations were used to assist in the development of the VC93 raindrop self-collection efficiency equation. The ZA88 observations, from tropical Brazil, measured DSDs over varying rain rates from rainfall systems whose precipitation characteristics resemble that of deep convection. Their observations indicate that an equilibrium exists between collisional growth of drops and collisional drop breakup. Their equilibrium DSDs indicate an overall peak in distribution frequency for drops with diameter D ∼ 1.1 mm, and secondary peaks at D ∼ 0.6 and 2.0 mm. Seifert et al. (2005) cite the observational study of ZA88 (regarding equilibrium rain DSDs) as a good benchmark for assessing simulated collisional breakup parameterizations. More recently, D’Adderio et al. (2018) also noted that an equilibrium drop distribution is persistent for higher precipitation rates in deep convection, but that for nonconvective precipitation, processes other than breakup have a large influence and can prevent equilibrium. However, we should note that for the lighter rain scenarios included in the RAMS archived analysis, Dm rarely exceeded 1.0 mm, and thus breakup would be minimal via the VC93 formulation.
Raindrop self-collection efficiency curves (Ec) relative to the raindrop distribution volume-number mean diameter (Dm). The black line depicts the default Ec in RAMS. The red and blue lines are experimental curves that delay drop breakup until drops grow to larger sizes. Drops begin to break up when the Ec < 0. The horizontal dashed line highlights the Ec = 0 point for each curve.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
b. Testing drop breakup in RAMS
To assess the impact that the RAMS raindrop breakup parameterization may exert on the raindrop size and frequency distribution, we introduced modified raindrop self-collection efficiencies as shown by the red and blue curves in Fig. 4. These modified curves were chosen to expand the exponential curve so that it becomes negative at larger Dm. The baseline black curve (original, A = 1485 m−1) crosses the Ec = 0 threshold at ∼1.1 mm (slightly modified VC93) while the red (test 1, A = 1097 m−1) and blue (test 2, A = 845 m−1) curves cross Ec = 0 at ∼ 1.24 and 1.40 mm, respectively. The resulting RDFDs from the RAMS supercell test simulations, associated with these varying representations of Ec, are shown in Fig. 5. In each simulation, there is a distinct peak in the RDFD that is associated with the diameter at which the curve of Ec becomes negative (indicating drop breakup). The peaks are also reduced in magnitude as their associated distributions broaden. As mentioned in VC93, the mean drop diameter, Dm, will tend to oscillate around the diameter at which Ec = 0, and settle at an equilibrium diameter that is near that size. Given the direct linkage between the diameter at which the spike is present in the logNw–Dm plots and the peak in the plots of RDFD in the control simulation, as well as the clear response in the peaks of the RDFD tests cases to varying Ec, it is highly likely that an overly efficient representation of raindrop breakup is the cause of the spikes in the previous figures of raindrop logNw–Dm. This is consistent with McTaggart-Cowan and List (1975), whereby they noted that coalescence and collisional breakup may be the two most dominant controls in the rain DSD.
Normalized counts of surface rain DSDs over a given range in Dm from RAMS supercell test simulations. The three distributions coincide with the raindrop self-collection equations for Ec in Fig. 4. Bin widths are 0.04 mm.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
4. Model intercomparisons of drop breakup
To determine if the distinct peak in the plots of RDFD are unique to the use of the RAMS bulk microphysics scheme, additional supercell simulations were performed using the Hebrew University Cloud Model with spectral bin microphysics (HUCM) (Khain et al. 2004) interfaced to RAMS (Igel and van den Heever 2017), as well as the Weather Research and Forecasting (WRF) Model version 3.9.1 (Skamarock 2006) using the Thompson (Thompson et al. 2004, 2008; Thompson and Eidhammer 2014), Morrison (Morrison et al. 2005, 2009, 2012), WRF double-moment 6-class (WDM6) (Lim and Hong 2010), and National Severe Storms Laboratory (NSSL) (Mansell et al. 2010) double-moment microphysics schemes. For the remainder of the discussion, these microphysics schemes, which are summarized in Table 3, will be identified by their namesakes or abbreviations without repetitive citation.
Summary of the microphysics schemes used in drop breakup intercomparison.
The additional supercell simulations using HUCM, Thompson, Morrison, WDM6, and NSSL microphysics schemes were run with the same grid configuration and initialization (see Table 2) as the RAMS simulations. (One difference from Table 1 for the WRF Model simulations is the use of a 1.5-order TKE turbulence parameterization.) While the RAMS and WRF parent models differ in numerous ways, the goal here is to assess if the various microphysics schemes generate a similar spike in raindrop logNw–Dm phase space and a peak in the RDFD, while also considering that general model variability can account for some of the differences. Default settings were used for each microphysics scheme tested herein. We recognize that various assumptions regarding single-moment versus double-moment approaches as well as the choice of raindrop size distribution type (e.g., inverse exponential versus gamma versus multimodal distributions) can influence the calculated diameters and the shape of the logNw–Dm frequency distribution and, thus, may impact the comparison to disdrometer observations. Likewise, many of the physical parameterizations within each microphysics scheme may contribute to the convergence of raindrops at an equilibrium drop diameter, including autoconversion and accretion, melting of ice, raindrop breakup, and falling-hydrometeor size sorting. However, as demonstrated above for the example from the RAMS model, drop breakup parameterizations are applied indiscriminately to the resulting drop distributions and they act to limit excessive drop growth. While keeping in mind these model limitations as well as the variability in processes that impact the rain DSD, we seek to determine if other commonly used models and microphysics schemes generate similar frequency distributions of raindrop Dm and to highlight differences and similarities among the results from the various schemes. Given the strong linkage between simulated raindrop breakup and the peaks in RDFD, the drop breakup parameterizations, associated with each of the tested microphysics schemes, are briefly summarized below.
a. HUCM drop breakup
HUCM simulates droplet self-collection using stochastic collection (Bleck 1970) with the coalescence efficiencies of Beard and Ochs (1995). Within this method, self-collisional drop breakup is represented by the method of LL82. The details of this breakup parameterization are given in Seifert et al. (2005). The drop self-collection in HUCM uses a combination of several coalescence efficiencies (Ec) over various size ranges. For larger drops, they rely upon the laboratory data of LL82 that involved collisions between 10 drop pairs. Ec from LL82 is an empirical function of collision kinetic energy and surface energy of colliding drop pairs [Seifert et al. 2005, Eq. (5)]. A modification for collisions involving large drops (D > 1.8 mm) is applied from Brown (1997).
b. Thompson, Morrison, and WDM6 drop breakup
The Thompson, Morrison, and WDM6 microphysics schemes employ drop breakup parameterizations that rely upon the representation of Ec for raindrop collisional breakup that are similar to VC93 used in RAMS. In each scheme’s drop breakup parameterization, the number concentration of raindrops is increased via the use of Ec < 0 to represent raindrop collisional breakup. The methods differ slightly in the details. The Thompson and Morrison schemes both use Eqs. (3) and (4) as they are presented here, but the Thompson scheme uses Dth = 1.6 mm (as the raindrop median volume diameter) and the Morrison scheme uses Dth = 0.3 mm (as the raindrop number-weighted mean diameter). Both schemes apply a weighting factor to the number of drops generated via self-collection collisional breakup. For raindrop exponential distributions in the default Thompson and Morrison schemes, their reported values of Dth are not dissimilar when expressed in the same rain mean/median diameter framework. WDM6 applies Eqs. (3) and (4) slightly differently than RAMS with respect to the representation of drop self-collection, but it uses the same basis of Eq. (4) for drop breakup such that the threshold diameter (Dth = 0.6 mm, volume-number mean diameter) is the same as that used in RAMS. However, WDM6 uses a collection efficiency factor A = 2500 m−1. This slightly modifies the representation of the self-collection efficiency curve compared to RAMS, but the essence and method of representing drop breakup is nearly the same. In summary, the RAMS, Thompson, Morrison, and WDM2 methods for representing drop self-collection and breakup use the same basic principles but include modifications to the collection efficiency curves.
c. NSSL drop breakup
The NSSL scheme parameterizes drop breakup following Mansell et al. (2010) and Ziegler (1985), which discuss drop breakup within the context of drop self-collection as represented by BR74. Within this self-collection method, drop breakup is represented in a similar manner to the previously mentioned parameterizations, such that the formulation of Ec considers the reduction in collisions of large drops as a means of preventing the formation of unrealistically large drops. Their specific formulation of Ec follows LL82 regarding the sizes of the most frequently colliding drop pairs and reduces Ec to 0 for a mean drop radius of 1 mm.
d. Simulation intercomparison of RDFD
Though not shown, all the supercell simulations, using RAMS, HUCM, Thompson, Morrison, WDM6, and NSSL microphysics schemes, generate splitting supercells with various amounts of accumulated surface precipitation. The RDFD for each supercell simulation using the various microphysics schemes is shown in Fig. 6. In this case, the RDFD is normalized such that the area under each curve equals one. Note first that the sharpest peaks with distinct cutoffs in RDFD occur in the simulations using the Thompson and WDM6 schemes. RAMS also has a sharp peak and does not generate many instances with Dm > 1.25 mm. The Morrison scheme also generates a sharp peak, but the curve is broader and permits more instances with larger Dm when compared with RAMS. These four schemes mentioned are those using the modifications of VC93 that permits Ec < 0 beyond a custom rain Dm threshold. The locations of the peaks are associated with the chosen thresholds and self-collection efficiency curves as discussed in VC93 and Planche et al. (2019). As mentioned earlier, these peaks are typically tuned to various cited observations as a means of choosing the most reliable value that works in conjunction with the other microphysical parameterizations in the respective schemes. The HUCM and NSSL schemes, both of which make use of the observations of colliding drop pairs in LL82, tend to have broader peaks in the RDFD. They also tend to favor a smaller peak frequency Dm, with a peak Dm ∼ 0.7 mm for HUCM and Dm ∼ 0.4 mm for NSSL. While individual rain DSDs shown in LL82 and Barros et al. (2008) are not directly comparable to the Dm frequency distributions shown here, we should note that the parameterizations associated with these studies of drop pair collisions, including more recently refined work (e.g., McFarquhar 2004; Schlottke et al. 2010; Straub et al. 2010; Prat et al. 2012), present a smaller modal diameter in the rain DSD compared to ZA88 (and thus the VC93 parameterization). This may account for the differences in the peak frequencies in Dm between the models using these different base parameterizations of drop breakup.
Normalized raindrop Dm frequency distributions (RDFD) from supercell simulations using the various models and microphysics schemes shown in the legend. The counted data include grid cells in the lowest model layer to consider only rain impacting surface rainfall accumulation. Bin widths are 0.04 mm.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
The Dm frequency distribution is also shown in logNw–Dm phase space in Fig. 7 for the supercell simulations generated from the various microphysics schemes. There are several key features to note (that are not necessarily tied to drop breakup), some of which mimic the distributions seen in Fig. 6:
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The Thompson and WDM6 schemes appear to have distinct rain Dm upper limits, near Dm ∼ 1.25. DSDs with Dm beyond these cutoff sizes are not produced. Such general hydrometeor constraints are put in place by microphysics developers of two-moment schemes to help preserve a balance between hydrometeor mass and number. In spite of these upper bounds, these schemes capture the large majority of the logNw–Dm frequency distribution seen in the disdrometer observations from two convective cases (in Figs. 9e and 9f).
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The RAMS and Morrison schemes permit the largest Dm (that approach 4 mm), although the frequency of occurrence of Dm larger than 3 mm is very low. Such large Dm drop distributions likely results from melted hail, but they are short-lived below the melting level as the drop breakup parameterizations force breakup into smaller drops. RAMS and Morrison also display the greatest frequency of occurrence near 1 mm diameter and a spike of larger logNw at this size, though, the spike in the Morrison simulation is less pronounced than in RAMS. Experiments by Planche et al. (2019) suggest that the Morrison scheme provides better agreement to observations when using a smaller equilibrium threshold diameter.
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The HUCM Dm frequency of occurrence is greatest near 0.6 mm diameter as also evident in Fig. 6. This most frequent Dm is substantially smaller than the frequently observed equilibrium drop size of 1 mm (ZA88; Dolan et al. 2018), which suggests that accretion and collisional growth are either too weak, or breakup is too strong in this scheme.
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The WDM6, Thompson, and NSSL schemes all generate some grid cells with very high concentrations (high max logNw) of small Dm. In contrast, RAMS, HUCM and Morrison all have more limited small Dm number concentrations (lower max logNw) that fall more within the range of logNw seen in the disdrometer observations associated with deep convection (Figs. 9e,f). As noted earlier, though, the disdrometer observations are limited in their detection of very small drops, and thus, may not be representing the smallest drop Dm produced in some of the simulations (e.g., Kathiravelu et al. 2016; Tokay et al. 2013). Furthermore, specific parameterizations and/or different delineations between cloud droplet and raindrop mean sizes in these schemes may permit formation of very small rain Dm.
Lowest-model-level raindrop logNw–Dm frequency distribution from the high-resolution supercell simulation using the various model microphysics schemes tested in this study.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
Each microphysics scheme generates a raindrop distribution, in logNw–Dm phase space, with its own unique set of constraints that shapes the range in the logNw and Dm dimensions in this phase space (Fig. 7). In the disdrometer observations, the zone with peak frequency of occurrence tends to fall within a Dm range from ∼0.50 to 1.25 mm and logNw range from 3 to 5 (mm−1 m−3). Most of the schemes tested in Fig. 7 have peak frequencies that largely fall in this range, suggesting that, in a broad sense, they are representing the rain DSD in a reasonable manner. However, there are various “spikes” or similar linear trends in the modeled logNw–Dm frequency distributions that are not seen in the equivalent disdrometer plots. It is important to note that numerous processes associated with each microphysics scheme contribute to the DSDs shown in Fig. 7. Differences in the assumed rain DSD shape parameters, drop size sorting, ice processes and subsequent melting to rain, as well as differences in warm-phase drop growth, all contribute to the final Dm frequency distributions. Each microphysics scheme has an array of parameterized processes that exert varying degrees of control over the final DSDs produced, as discussed for the Thompson and Morrison schemes in Planche et al. (2019). Our goal in this brief comparison among the schemes shown in Fig. 7 was to see if other microphysics schemes produce similar logNw–Dm raindrop frequency distributions to that seen from RAMS. While we were able to determine that the “spike” seen in RAMS logNw–Dm distribution is directly linked to the drop breakup parameterization, a more exhaustive investigation would be necessary to determine the dominant controls on the unique features of each microphysics scheme’s logNw–Dm distribution.
A “spike” type feature is clearly present in the RAMS results and is marginally present in the Morrison results. As discussed early, experiments with the Morrison drop breakup parameterization have been performed via changes to the threshold breakup diameter (Planche et al. 2019). In the section that follows, we will explore a method of potentially reducing the “spike” seen in the RAMS results by reducing the strength of drop breakup without modifying the threshold diameter established in VC93.
5. Adjusting raindrop breakup parameterizations
Given the limited laboratory studies (e.g., LL82; Barros et al. 2008) on which to formulate physically based parameterizations of drop breakup, modelers sometimes need to fine-tune parameterizations of breakup to keep drop sizes within a reasonable range (VC93; Morrison et al. 2012; Planche et al. 2019). Of the WRF schemes that use the VC93 approach, the primary method of tuning has been related to the value of the raindrop self-collection threshold diameter; this diameter has been modified to obtain better agreement with observed number concentrations of raindrops (i.e., Morrison et al. 2012; Planche et al. 2019). Tuning can be dependent upon the microphysics scheme since various parameterized processes can impact raindrop number concentration and diameter, as highlighted in Planche et al. (2019). Thus, no single cited tuned value can necessarily be applied to other microphysics parameterizations.
Another method of refining the VC93 parameterization of drop breakup involves applying limits to the maximum breakup rate, as determined by the minimum self-collection efficiency Emin, while retaining the equilibrium drop diameter at which Ec = 0. This type of tuning should limit the strength of the drop breakup process while keeping the equilibrium size in close agreement to ZA88. Since the RAMS model exhibits the most prominent spike and highest frequency of occurrence at the equilibrium drop size (Fig. 7), it was used for testing modifications to the maximum breakup rate via changes to the Emin parameter. However, the results shown here could also be applied to other microphysics schemes using a similar drop breakup parameterization.
Drop breakup test simulations were performed with RAMS using various values of the minimum drop self-collection efficiency, Emin, as applied from VC93. Recall that more negative values of Emin produce more efficient drop breakup. In these tests, Emin was varied incrementally from −5.0 (default in RAMS), toward the less negative values of −1.0, −0.5, −0.3, −0.1, and 0.0.
Figure 4 displays a minimum ordinate value of −5 corresponding with RAMS default Emin = −5.0. In the test where Emin = −1.0, for example, the collection efficiency curve is the same as the black line in Fig. 4, but with the ordinate minimum truncated at Ec = −1.0. Figure 8 displays plots of RDFD from these test simulations. It reveals a reduction in the height of the peak in RDFD as Emin becomes less and less negative (moving from −5.0 to 0.0), with the most noticeable change occurring for a change in Emin from −0.3 to −0.1. It may be inferred from this figure that drop breakup is still quite active for relatively small negative values of Emin. For an Emin = 0.0, there is still a peak in RDFD near 1.0 mm, but the Dm frequency distribution is broader.
Normalized counts of rain Dm from RAMS supercell test simulations. The counted data include grid cells in the lowest model layer to consider only raindrops impacting surface rainfall accumulation. The curves depict simulations with varying application of minimum collection efficiency (Ec). “Emin −5.0 (Orig)” required Ec > −5, while simulation “Emin −1.0” required Ec > −1.0, and so forth for the remaining experiments. Bin widths are 0.04 mm.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
The use of Emin = 0.0 is akin to that described for the NSSL scheme that does not use negative values of Ec. The NSSL plot of RDFD is quite broad (Fig. 6) as is the RDFD plot for the RAMS test simulation with Emin = 0.0. The main difference between these two scenarios is the location of the Dm peak. NSSL generates a propensity toward Dm ∼ 0.4 mm (Fig. 6) while RAMS with Emin = 0.0 produces the greatest occurrence of drops at Dm ∼ 1 mm (Fig. 8). Again, the greatest occurrence of Dm is controlled by the threshold diameters in the formulations of Ec as well as the diameter where Ec = 0, and these are generally tuned with respect to the parent microphysics scheme.
Plots of logNw–Dm for these supercell tests with varying Emin are shown in Figs. 9a–d. For comparison to observations, Figs. 9e and 9f display the results of disdrometer data from the iFloodS and MC3E field campaigns, both of which included deep isolated and organized convection. While we should not necessarily expect the supercell test results to exactly match those from these specific field campaign data, we can make some broad comparisons with regards to the range of expected drop sizes found in deep convection and the size drops with the greatest frequency of occurrence. Figure 9 demonstrates that a reduction in the drop breakup strength, controlled by changing Emin from −5.0 to 0.0, leads to 1) a reduction in the spike near 1 mm Dm, 2) greater frequency of occurrence of larger Dm, and 3) a broader peak in the higher frequency Dm denoted as a larger area of orange shaded pixels. The test with Emin = 0.0 offers, perhaps, too great of a reduction in drop breakup. Figure 9d depicts a distribution that still has its peak near 1 mm, but the diagonal shape of the distribution is somewhat lost in comparison to the disdrometer distributions and the other tests of Emin. While additional testing is necessary to determine an optimal and less ad hoc value of the Emin parameter in this drop self-collection parameterization, it appears that a reduction in the maximum allowed strength in the raindrop breakup parameterization does help reduce the persistence of the artificial spike of high frequency of occurrence of large logNw at Dm ∼ 1 mm. Perhaps a combination of modified Emin and a reduction in the breakup threshold diameter [similar to that tested in Planche et al. (2019) for the Thompson and Morrison schemes] would provide additional improvements.
(a)–(d) Lowest-model-level raindrop logNw–Dm frequency distribution from the RAMS supercell test simulations with varying raindrop minimum negative self-collection efficiency Emin. (e),(f) As in (a)–(d), but from disdrometer observations from the IFloodS and MC3E fields projects, respectively.
Citation: Journal of the Atmospheric Sciences 79, 11; 10.1175/JAS-D-21-0335.1
6. Summary and conclusions
In this study we have compared the raindrop size distributions, in logNw–Dm phase space, from a global disdrometer database to an extensive database of RAMS model simulations composed of tropical, maritime, shallow, and deep precipitating cloud systems. Here Dm is the volume-number mean diameter of the raindrop gamma DSD and Nw is the intercept parameter. It was noted that the simulations tended to produce 1) a narrower range of Dm than in the observations, 2) a lower frequency of Dm from 1.0 to 1.5 mm than observed, and 3) a “spike” of high logNw of rain DSD with Dm ∼ 1 mm diameter that is not evident in the observations. It was found that this spike was most prevalent in simulations of deep convection, where, in reality, drops can grow to appreciable size through vigorous collision–coalescence processes and melting of large ice particles.
Model experimentation revealed that the parameterization of raindrop self-collisional breakup was the cause of the persistent occurrence of rain with Dm ∼ 1 mm at high logNw. While other microphysical processes certainly contribute to the prediction of drop size, it was shown that the VC93 parameterization of drop breakup exerts a strong control on the mean drop size via the assignment of the threshold drop diameter and the assigned maximum strength of drop breakup via negative collection efficiencies.
Given that many microphysics schemes in numerical models use similar approaches to parameterize raindrop collisional breakup, a set of comparative numerical simulations of deep convection (idealized supercell) were run using different models and microphysics schemes as summarized in Table 3. These include the double-moment bulk microphysics schemes from RAMS, WRF-Thompson, WRF-Morrison, WRF-WDM6, and WRF-NSSL, as well as the HUCM-Bin scheme interfaced to the RAMS dynamic model. Analysis of the raindrop size distributions in logNw–Dm phase space from these simulations (Fig. 7) reveals that nearly all the model results display a degree of numerical constraint while broadly agreeing with the zone of peak frequencies in the logNw–Dm disdrometer observations (Figs. 1a, 9e,f). The apparent constraints vary, however, by microphysics scheme and may not always be clearly linked to the parameterization of drop breakup. For example, the rain Dm distribution from the WRF-Thompson and WRF-WDM6 simulations (Figs. 6, 7) display hard upper bounds and do not permit Dm beyond ∼1.3 mm in diameter. Meanwhile, the remainder of the microphysics schemes permit some Dm beyond this threshold. However, the disdrometer frequency distributions do not reveal many occurrences of Dm > 1.5 mm, though this could be due to the upper size limits of drop detection and subsequent fitting to gamma distributions.
Each of the microphysics schemes using a derivative of the VC93 approach to drop breakup (RAMS, WRF-Thompson, WRF-Morrison, WRF-WDM6) all exhibit sharp peaks in the rain Dm frequency distribution (Fig. 6) with the most frequently occurring Dm near 1 mm, as is formulated in the VC93 parameterization. The most prolific rain Dm from the WRF-NSSL and HUCM-Bin schemes occurs near 0.5–0.6 mm (Fig. 6). Both WRF-NSSL and HUCM use the LL82 drop breakup approach based on observed colliding drop pairs, though WRF-NSSL applies a breakup limitation such that the drop self-collection efficiency, Ec does not drop below zero. VC93 permits Ec < 0, with breakup becoming more efficient for increasingly negative values. This suggests that limiting the settings of Ec to values closer to zero, rather than more negative minimum values, may allow a VC93 type of breakup parameterization to reduce the forcing of large drops to Dm ∼ 1 mm.
To investigate this possibility, supercell test simulations were run with the RAMS microphysics with perturbations to the minimum value to Ec (Emin). These tests used the same simulation setup as those that were run to isolate the microphysical process(es) responsible for the “spike” in high logNw for Dm ∼ 1 mm. In the VC93 drop breakup application in RAMS, an arbitrary value of Emin = −5 is set. Recall that WRF-NSSL uses Emin = 0.0 (in combination with the LL82 approach). In this set of test simulations, Emin was varied from 0 to −5. Figures 8 and 9 indicate that as Emin is modified from −5 to 0 (becoming less negative), the “spike” becomes less prominent. While these figures cannot definitively determine the optimal value of Emin to use in the VC93 parameterization in the RAMS microphysics, values of Emin closer toward Emin = 0.0 (though, perhaps, not Emin = 0.0 itself) do provide a drop size trend that is more comparable to the general disdrometer observations. In the future, direct case study comparisons between disdrometer observations and model simulations could provide a more quantitative determination of the optimal upper limit to apply to drop breakup in microphysics schemes that parameterize breakup as VC93.
Acknowledgments.
This work was supported by the Department of Energy under Grant DE-SC0017977.
Data availability statement.
The datasets from the suite of numerical simulations and global disdrometers on which this paper is based is too large to be retained or publicly archived with available resources. Model and instrument output as well as documentation and methods used to support this study are available from the manuscript authors at Colorado State University Department of Atmospheric Science. The archive of the available files and tools related to the analyses herein is available at https://doi.org/10.25675/10217/235397.
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