a. Initiation of cloud ice

A related, fundamental shift in ice initiation pertains to the necessary conditions to nucleate ice. Previously, ice was allowed to initiate by Eq. (1) as soon as ice saturation was attained for all temperatures less than 0°C. In the current scheme, ice does not form by Eq. (2) until the air is saturated with respect to water and T < −5°C or until the water vapor mixing ratio exceeds 5% supersaturation with respect to ice. However, as in RRB, ice continues to be formed by freezing of cloud droplets (T < −5°C) and by a secondary ice-nucleation method, commonly referred to as rime-splinter ice production, based on work by Hallet and Mossop (1974).

b. Autoconversion

The collision and coalescence of cloud droplets to form raindrops is parameterized by autoconverting between the mixing ratios of the two hydrometeor species, q_c and q_r, following Kessler (1969) and given by

View Expanded

where a = 1 × 10⁻³ s⁻¹ is a time constant, H is a Heaviside function, and q_co = 0.35 × 10⁻³ is a threshold value. Previously, the threshold used in RRB was 0.5 × 10⁻³ but is reduced based on results by RG. Besides testing the old and revised thresholds, an additional sensitivity test is performed with q_co = 0.1 × 10⁻³.

As an alternative to the Kessler autoconversion scheme, the methodology described by Berry (1968) is also evaluated using the relationship

View Expanded

where Q_r is the rain water content (g m⁻³), D_b = 0.3 is the dispersion factor, N_b is cloud droplet concentration (cm⁻³), and Q_c is the cloud water content (g m⁻³).

In another, alternative autoconversion scheme, Walko et al. (1995) adapted a Berry and Reinhardt (1974) parameterization using the relationship¹

View Expanded

where υ represents a gamma distribution shape parameter, ρ_a and ρ_w are the density of air and water (kg m⁻³), respectively, and D_mean is the mean diameter (m) of cloud droplets computed from cloud water mixing ratio (q_c) and concentration (N_c) using

View Expanded

In our application of Eq. (6), υ is set to 3, and both the numerator and denominator must be positive. Substituting various droplet concentrations of 50, 100, 200, and 500 cm⁻³ into Eqs. (6) and (7), we compute minimum cloud water mixing ratios of 0.171, 0.343, 0.686, and 1.71 g kg⁻¹, respectively, before cloud water converts to rain. Hence, Eq. (6) simplifies to a form similar to the Kessler autoconversion scheme with constant N_c, but the rates of rain conversion tend to be lower using Eq. (6) compared to Eq. (4). Nonetheless, this alteration is desireable because of its physical basis and for other/future modeling studies where N_c could be prognosed.

c. Treatment of graupel

In RRB, the size distribution of graupel assumed an exponential form [N(D) = N_o,g e^−λ_gD] with a constant intercept parameter (N_o,g = 4 × 10⁶ m⁻⁴), whereas, in the current study, the distribution is altered in two ways. First, the distribution assumes the following generalized gamma form

NDN_o,gD^(υ−1)e^−λ_gD(8)

where

View Expanded

replace the slope and intercept parameters of the exponential distribution, υ = 2, and ρ_g = 400 kg m⁻³ is the density of graupel. Second, N_o,g depends on q_g similar to the RRB approach for determining N_o,s as a function of q_s. Whereas the RRB study used observations by Sekhon and Srivastava (1970) to derive N_o,s = f(q_s), we derive Eq. (10) using observations from Brown and Swann (1997). Note that because N_o,g → ∞ as q_g → 0, we limit the magnitude of N_o,g such that it cannot exceed a fixed maximum value (5 × 10⁷ m⁻⁴) while also imposing a lower limit of 1 × 10⁴ m⁻⁴.

Besides the modification to the shape of the graupel distribution, the conversion of rimed snow into graupel is altered from the RRB study. In RRB, Eq. (A.43) contains the model time step, Δt, potentially requiring tuning when the time step is adjusted. In the current study, we follow the treatment found in Murakami (1990) and evaluate the larger of two terms: depositional growth (PSDEP) and riming growth (PSACW) of snow, computed as in Rutledge and Hobbs (1983) using

View Expanded

respectively, where A and B are thermodynamic terms given in Pruppacher and Klett (1978), S_c = 0.6 is the Schmidt number, a_s = 11.72 m^(1−b_s) s⁻¹ and b_s = 0.41 are constants in the snow fall speed relation, E_sc is the collection efficiency between snow and cloud water, λ_s is the slope of the snow size distribution (m⁻¹) and μ is the dynamic viscosity of air (kg m⁻¹ s⁻¹). If riming growth exceeds depositional growth, then graupel increases at the rate given by PSACW, otherwise snow increases at this rate. To illustrate the relative contributions by these two terms, Fig. 2 presents PSDEP contours as a function of snow mixing ratio and temperature (Fig. 2a), PSACW contours as a function of snow and cloud water mixing ratios (Fig. 2b), and the ratio of the two at T = −10°C (Fig. 2c). In general, riming growth does not exceed depositional growth until cloud liquid water exceeds 0.1 g kg⁻¹. Rutledge and Hobbs (1984) required a threshold snow mixing ratio of 0.1 g kg⁻¹ and a cloud water mixing ratio threshold of 0.5 g kg⁻¹ before producing graupel. These thresholds approximately correspond to PSDEP/PSACW = 0.2 curve shown in Fig. 2c, implying that riming growth must exceed depositional growth by a factor of 5 before rimed snow transitions to the graupel category.

d. Intercept parameter of the snow size distribution

RRB determined that a fixed snow intercept parameter led to the depletion of too much cloud water, therefore motivating the mass-dependent N_o,s relationship used previously in MM5. Similarly, Swann (1998) utilized snow and graupel intercept parameters that depended on mixing ratio in a single-moment microphysics scheme; however, he speculated that a temperature or height dependence may improve the scheme to match results from a double-moment scheme. By analyzing 37 particle-size spectra from aircraft flights through frontal clouds at virtually all temperatures aloft, Houze et al. (1979) found that mean particle diameter increased with increasing temperature, and, more importantly, N_o and λ decreased with increasing temperature as a result of growth by aggregation. Thus, we decided to implement an explicit temperature-dependent N_o,s into the scheme using the curve for total precipitation water content 0.03 ≤ M < 0.3 in Fig. 7 of Houze et al. (1979), resulting in the following relationship:

View Expanded

where T_o = 273.15 K, and T is the ambient temperature (K). Considering that this version of the microphysics code lacks a snow aggregate species, perhaps a temperature-dependent N_o,s is the simplest way to parameterize this effect. Alternatively, the addition of an aggregate species and associated prognostic equations could be developed.

The largest impact of the new relationship for N_o,s pertains to depositional growth of snow [PSDEP; Eq. (11)], which is illustrated in Fig. 3. In Fig. 3a, the vertical profile of snow mixing ratio varies from 0.002 to 0.2 g kg⁻¹, corresponding to a hypothetical, shallow, mixed-phase cloud. Note that the maximum N_o,s exceeds the old value by an order of magnitude at low temperatures; thus, the depositional growth is larger at temperatures < −20°C using the new method. However, in relatively warm air (T > −20°C), the intercept parameter is less using the new method, and therefore depositional growth is reduced. On the other hand, when the vertical profile of snow mixing ratio more closely mimics a deep snow cloud with q_s ranging from 0.05 to 0.5 g kg⁻¹ (corresponding to Fig. 3b), then PSDEP is always larger using the temperature-dependent relationship over the mass-dependent N_o,s.

Whereas the maximum depositional growth of a single ice crystal generally peaks around T = −14°C (see, e.g., Wallace and Hobbs 1977 or Young 1993), Figs. 2a and 3 represent the aggregate effect of depositional growth on an entire snow size distribution. The very broad minimum centered at −35°C in Fig. 2a and maximum at approximately −20°C in Fig. 3 are a result of the increase in N_o,s with decreasing temperature [Eq. (13)]. In other words, a population of large numbers of small snow crystals at T = −30°C grows nearly as rapidly by deposition as a reduced number of larger crystals at higher temperatures.

e. Intercept parameter of the rain size distribution

Unlike the intercept parameter for snow, previous studies do not support a temperature-dependent rain size distribution. Instead, it is quite reasonable to assume that water drops undergo a gradual transition from cloud droplet sizes (diameter less than approximately 50 μm) through drizzle drops (diameter approximately 50–500 μm) on their way to becoming raindrops. However, nearly all single-moment bulk microphysics schemes simply make an abrupt transition from cloud water to rain with the associated Marshall–Palmer size distribution and intercept parameter of 8 × 10⁶ m⁻⁴. Thus liquid drops undergo a transition from nonsettling (most bulk microphysics schemes do not sediment cloud droplets) to typical rain terminal velocities of 1–4 m s⁻¹ instantaneously. This leaves little time for water drops to interact as drizzle drops with other microphysical species such as snow, graupel, and cloud water. Instead, raindrops race to hit the earth as precipitation and rarely remain suspended within gentle stratiform updrafts. With these considerations in mind, we alter the rain size distribution via the intercept parameter to replicate a drizzle transition whereby the size distribution of rain consists primarily of drizzle-size drops for very low rain mixing ratios. On the other hand, when rain mixing ratio increases, the intercept parameter decreases, thus broadening the rain distribution and replicating the original formulation. The following function encapsulates the transition of the intercept parameter from drizzle to rain:

View Expanded

where N_1,r = 1 × 10¹⁰ m⁻⁴ is an upper-intercept limit, N_2,r = 8 × 10⁶ m⁻⁴ is a lower-intercept limit, and q_ro = 1 × 10⁻⁴ is essentially the transition value between the two limits. The terminal velocity that results when N_o,r spans this range is shown in Fig. 4 (labeled as “new rain”) along with the curve for the original terminal velocity using the previously fixed value of N_o,r and curves for terminal velocities of snow and graupel. The graph shows the primary result of a varying N_o,r is that small q_r (theoretically more common of drizzle rather than rain) produce a terminal velocity between 0.2 and 2 m s⁻¹, whereas large rain mixing ratios produce terminal velocities between 2 and 8 m s⁻¹. According to Young (1993), the former velocities correspond to drops with diameters between 50 and 200 μm, while the latter velocities correspond to drops with diameters between 200 μm and 1 mm. Results of sensitivity tests for this and all other alterations are presented in section 4.

a. CONTROL experiment

During the initial 30 min, a small cloud composed of water forms approximately two-thirds of the way up the barrier. This liquid cloud grows horizontally and vertically while a small amount of cloud ice is initiated near cloud top. Cloud water and cloud ice continue to increase during the first two hours of the simulation, with vertical growth to 2 km (approximately −13°C). Cloud ice rapidly grows by deposition to form snow that sediments and precipitates. Once snow forms, it accretes cloud water and rimes, thus increasing the mass of snow but also creating a comparable amount of graupel. The formation of graupel triggers ice multiplication (within the temperature range −3° to −8°C), which increases the background value of ice number concentration from 0.05 to 0.7 L⁻¹. These new ice crystals form directly within the liquid portion of the cloud and rapidly grow to snow sizes and accrete more cloud water. As snow and graupel continue to increase in mass, cloud water slowly depletes. Two hours into the CONTROL simulation, the cloud water peaks at 0.364 g kg⁻¹, just crossing the threshold quantity for autoconversion to the rain category (essentially becoming freezing drizzle). Thereafter, cloud water decreases as glaciation dominates, while snow and graupel precipitate in nearly equal proportions. A snapshot of the microphysical species: cloud water, cloud ice, snow, rain, and graupel at 3 h, along with a plot of precipitation type and amount at hours 3 and 4 are shown in Fig. 6, while 3-h domain-maximum values of all hydrometeor species are listed in Table 2, along with 6-h simulation maxima shown in parentheses. The third value found in square brackets in each column is the rmse (L2 norm) computed as the square root of the sum (over all grid points) of squared differences between the bulk and bin models at 3 h.

b. Bin model

To compare directly between results of the bulk versus the bin models, we performed a new bin-model simulation using the CTT = −13°C sounding. While the bin model is capable of depleting ice nuclei, the bulk model is not; so, for proper comparison, we disabled ice nuclei depletion (as in RG simulation 10). In this manner, both the bin and bulk schemes initiate new ice crystals as the number concentration falls below the prescribed Cooper amount [Eq. (2) and Fig. 1]. As discussed in RG and graphically shown here in Fig. 7 and Table 2, this has important consequences to the resulting cloud water, rain, snow, and graupel amounts. The new bin-model simulation contains 4 times as much frozen hydrometeors (snow and graupel) and approximately one-half as much liquid compared to results shown in RG with ice nuclei depletion active. The sensitivity experiments described below illustrate the key modifications to the bulk scheme that bring the simulation into closer agreement with results of this new bin-model simulation.

c. Ice initiation: Meyers and Fletcher experiments

To illustrate the sensitivity of the microphysics parameterization to primary ice initiation, the model is modified to use the ice nucleation schemes of Meyers et al. (1992) and Fletcher (1962). The experiment called Meyers produces at least an order of magnitude more ice crystals throughout the cloud compared to CONTROL. The increase in ice number produces the anticipated result of less cloud water (∼16%) and 14% more snow (Table 2). The Fletcher experiment, on the other hand, produces an order of magnitude reduction in ice number concentration at cloud top than CONTROL, resulting in marginally more cloud liquid water.

d. Autoconversion: Kessler1, Kessler5, Berry, and BandR experiments

The next series of tests involves the treatment of converting cloud water to the rain category by autoconversion using Kessler's methodology in Eq. (4), the Berry scheme in Eq. (5), and the Berry and Reinhardt scheme in Eq. (6). The Kessler autoconversion threshold is 0.35 × 10⁻³ in CONTROL, 0.1 × 10⁻³ in Kessler1, and 0.5 × 10⁻³ in Kessler5. Not unexpectedly, Kessler1 produces far less cloud water (maximum 0.133 g kg⁻¹), a lot more rain, and less graupel than CONTROL, as cloud water is readily converted to rain that precipitates quickly onto the ground. Kessler5 is hardly different from CONTROL since the updraft produced by this flow regime is only strong enough to produce a limited amount of cloud water that is depleted by snow and ice. The Berry experiment produces drastically smaller amounts of cloud water mixing ratio (maximum 0.067 g kg⁻¹), much more rain (accumulation ≈ 0.4 mm), and slightly less snow/graupel than CONTROL. The BandR experiment nearly matches CONTROL except for a slight increase in maximum cloud water and less rain because of its low autoconversion rate (when compared to the Kessler rate).

To see the true sensitivities of these autoconversion schemes, one needs to disable all the ice species/interactions and simulate the warm-rain process by itself. Results from this suite of tests with ice physics disabled produces the results shown in Fig. 8a. The same trend as mentioned above occurs with Kessler1 and Berry, showing very aggressive rain production initiating from the lowest cloud water amounts. CONTROL is next (not shown), followed by Kessler5, then BandR. It is also clear from this figure that BandR has the slowest rate of cloud water to rain conversion of all the experiments.

e. CCN spectra: Maritime, Continental1, and Continental2 experiments

The sensitivity of the microphysics to CCN spectra is addressed using three simulations with various cloud droplet concentrations (N_c, a proxy variable for CCN spectra). Since the Kessler (1969) autoconversion scheme does not include the effects of N_c, these tests are combined with the Berry and Reinhardt (1974) autoconversion method discussed above in experiment BandR. Whereas CONTROL used N_c = 100 cm⁻³, the Maritime experiment uses N_c = 50 cm⁻³, Continental1 uses N_c = 200 cm⁻³, and Continental2 uses N_c = 500 cm⁻³. Like the previous test above, we disable all ice physics to prevent water depletion by ice and to compare against results of RG. As expected, the Maritime experiment produces the least cloud water and the most rain, while Continental2 produces the greatest cloud water mixing ratio and no rain (Fig. 8b). Direct comparisons to results by RG are found below (section 4i).

f. Treatment of graupel: Graupel1 and Graupel2 experiments

The treatment of graupel has major impacts on a mixed-phase simulation such as this one. Besides the assumed graupel size distribution, the treatment of snow riming and subsequent conversion to graupel is also important. In experiment Graupel1, the original exponential or Marshall–Palmer size distribution employed by RRB replaces Eqs. (8)–(10). Furthermore, the conversion of rimed snow to graupel is altered from the new methodology discussed in section 2 back to its original formulation as specified in RRB. Results of this test reveal a 14% reduction of cloud water, a 30% increase in snow, and 51% less graupel. Graupel is reduced primarily because its intercept parameter is constant and relatively low in Graupel1; therefore, depositional growth of graupel is reduced from that of CONTROL. Instead of growing graupel, deposition onto snow dominates, as evidenced by the accumulated precipitation plot (Fig. 9f) showing snow dominating between the third and fourth hour. None of the results discussed thus far matches those of RG, where the primary precipitation was rain with a small amount of snow.

In the experiment called Graupel2, riming growth of snow must exceed depositional growth by a factor of 3 before rimed snow is transferred to the graupel category, whereas CONTROL required a unity ratio. The difference between these two threshold ratios is shown in Fig. 2c, with CONTROL represented by the 1.0 curve and Graupel2 represented approximately halfway between the 0.2 and 0.4 curves. Results of this test reveal no graupel but 73% more snow, 18% less cloud water, and 34% less cloud ice than CONTROL (see Table 2). The decrease in cloud ice is due to the lack of ice multiplication, a direct consequence of eliminating graupel since riming growth does not attain the new threshold requirement. Similar to Graupel1, snow mass increases due to deposition at the expense of cloud water.

g. Version2 experiment

As discussed in section 2, a significant number of modifications have been made to the MM5 microphysics scheme since RRB. In an experiment referred to as Version2, the code is modified to approximate RRB; however, an exact match is not possible because of bug fixes. In its simplest form, the modifications to CONTROL combine three of the sensitivity experiments above: Fletcher, Kessler5, and Graupel1. Not surprisingly, the resulting hydrometeor amounts (Table 2) are very similar to the Graupel1 experiment since little sensitivity was noted between CONTROL and Fletcher or Kessler5.

h. Snow intercept parameter: SON and SONV experiments

In sensitivity experiment SON, N_o,s is set constant to its maximum value, 2.0 × 10⁷ m⁻⁴. This simulation produces only 9% more snow but no other discernible differences in resulting hydrometeor mixing ratios versus CONTROL. This is logical because the relatively small mixing ratio of snow produced by this shallow cloud is insufficient to reduce N_o,s in CONTROL (essentially N_o,s is constant in CONTROL); however, the impacts of this sensitivity test are apparent in the deeper and colder cloud systems discussed later.

In experiment SONV, N_o,s depends on temperature via Eq. (13) replacing the RRB mass-dependent relationship, resulting in significant differences versus CONTROL. The maximum cloud water mixing ratio realized in this test is 0.397 g kg⁻¹, with an order of magnitude less snow, 22% less graupel, and dramatically increased rain (nearly half of the precipitation is freezing drizzle) compared to CONTROL. This result (shown in Fig. 10) compares favorably to the RG study except for the larger amounts of graupel in this simulation. The dramatic decrease in snow mixing ratio is due to a reduced depositional growth of snow (recall Fig. 3a) because the snow size distribution is shifted toward large sizes at relatively high temperatures (and the slope of the distribution decreases).

i. Rain intercept parameter: RON and RONV experiments

Similar to the previous modifications to the intercept parameter of snow, the intercept parameter of rain, N_o,s is altered from 8.0 × 10⁶ m⁻⁴ in CONTROL to 1.0 × 10¹⁰ m⁻⁴ in the sensitivity experiment referred to as RON. Testing this parameter without significant rain is meaningless, so this experiment also combines the modifications of SONV, whose simulation produces the most rainwater. From the discussion in section 2e and Fig. 4, note that the impact of this change to N_o,r alters the terminal velocity of rain from approximately 2 to 0.5 m s⁻¹ (for the amount of rain produced in SONV). The resulting cloud water at 3 h shown in Fig. 11a is 4% less than the cloud water produced in SONV (Fig. 10) because rain falls more slowly in RON, thus accreting more cloud water. Accordingly, the resulting rain accumulation is ∼50% greater in RON (Fig. 11e), and the amount of rain suspended within the cloud is an order of magnitude larger (∼0.07 g kg⁻¹; Fig. 11c). The suspended rain mixing ratio is significantly increased in this simulation as compared to SONV because of the lower terminal velocity of raindrops.

In the experiment referred to as RONV, N_o,r varies between the values used in experiments RON and CONTROL according to Eq. (14). As shown in Table 2, the resulting mixing ratios are essentially identical compared to RON because the rain mixing ratio does not increase sufficiently to impact (decrease) N_o,r.

To see the ramifications of a variable intercept parameter, we repeated the RONV experiment without any ice microphysics active, thus allowing higher cloud water and rain mixing ratios to develop. Furthermore, we aim to reproduce results by RG in association with CCN spectra sensitivities duplicated here in Fig. 12a. Note that while using a maritime CCN spectrum, their cloud water increased to ∼0.4 g kg⁻¹ before the onset of rain (drizzle) at approximately 1 h. When RG switched to a continental CCN spectrum, their cloud water rose to ∼0.7 g kg⁻¹ and required 3 h before producing rain. In either case, the rain mixing ratio rapidly increased to approximately 0.1 g kg⁻¹ then remained nearly constant. When the RG sounding is used in an all-warm version of the bulk model using the code in experiment BandR (recall section 4d), the resulting cloud water mixing ratios are in reasonable agreement with results by RG, but the rain mixing ratios are a factor of 10 too low (cf. Fig. 8b to Fig. 12a). This is due to the large terminal velocity of rain (∼3 m s⁻¹) when the intercept parameter is set constant at its classical value (8 × 10⁶ m⁻⁴); hence, rain is rapidly precipitating to the ground and not remaining suspended aloft like drizzle, as it is in the RG study. When the intercept parameter is altered to depend on mixing ratio, an experiment combining the all-warm BandR and RONV codes produces results in closer agreement to RG as shown in Fig. 12b.

j. Final experiment

Finally, in the last sensitivity simulation, the code modifications of BandR (with N_c = 100 cm⁻³), Graupel2, SONV, and RONV combine to produce the experiment called Final. Results of this test (see Fig. 13 and Table 2) show a slight increase in cloud water (5%), a sharp decrease in rainwater (73%), significantly more snow (nearly an order of magnitude), and less graupel (14%) compared to RONV. Changes to the liquid portion are primarily due to swapping the autoconversion scheme, while the balance between snow and graupel is primarily due to the higher threshold for producing graupel in the Graupel2 portion of the code.

More important than comparing Final to RONV is the comparison of the Final experiment to the bin model (recall Fig. 7). While individual mixing ratios of each microphysical species do not perfectly agree, the balance of liquid and frozen species matches more closely than any other experiment. This is confirmed by the rmse values found in Table 2 as well as visual inspection of Figs. 7a–f and 13a–f.

k. Deeper/colder cloud systems

Besides testing a shallow cloud with cloud-top temperature of −13°C, tests are performed with deeper and colder cloud systems. In the remainder of this section, the temperature profile remains the same as before, but the moisture profile is altered to produce cloud systems of various depths and temperatures. Furthermore, a subset of the sensitivity studies (see Table 1) are repeated to reveal responses due to both cloud depth/temperature as well as the treatment of certain aspects of the microphysical parameterization. There is little reason to perform the full suite of tests because a few of the previous tests require sufficient cloud water or rain to exist, which, as will soon be shown, is lacking in these deeper/colder clouds.