1. Introduction
Cloud-resolving mesoscale models using bulk-microphysics parameterization have been used to simulate single clouds, cloud ensembles, sea breezes, severe storms, and synoptic and tropical storms. These models have also been used in cloud-seeding studies, and for calculating radiative transfer retrievals (see, e.g., Anthes et al. 1982; Yau and Michaud 1982; McCumber et al. 1991; Brooks et al. 1992; Simpson and Tao 1993; Bélair et al. 1994; Ferrier 1994; Alpert et al. 1996; Meyers et al. 1995; Molders et al. 1995; Wicker and Wilhelmson 1995; Ferrier et al. 1996; Chen et al. 1997; Panegrossi et al. 1998; Halverson et al. 1996, 1999; Zhang and Altshuler 1999; Tremblay and Glazer 2000; Lynn et al. 2001; Montmerle et al. 2001; Wang 2001; Zeng et al. 2001; Braun 2002; Coleman and Marwitz 2002; Elmore et al. 2002; Sassen et al. 2002).
In bulk-microphysics schemes, it is assumed that the shape of the raindrop size spectrum (and other hydrometeors) follows the findings of Marshall and Palmer (1948). As a result, only a limited number of integral parameters are required to describe cloud microphysical processes. These include either the time evolution of mass contents (single-moment schemes) or the mass contents and the mean number concentrations (double-moment schemes). The relatively small number of integral parameters makes the bulk parameterization computationally efficient.
At the same time, the simplifications used when introducing the integral parameters imposes some limitations on the abilities of these schemes to adequately reproduce cloud microphysical processes. For instance, the utilization of “mean” sedimentation velocities independent of the particle size may lead to an inadequate description of the spatial distribution of different cloud hydrometeors. This can introduce errors in the interaction between hydrometeors of different types. Moreover, the shape of the drop size spectrum can change during the course of the simulation, since the particle size spectra is dependent on the concentration and the size distribution of active aerosols [or cloud condensation nuclei (CCN)]. This can affect the evolution of precipitation development.
In fact, evidence that aerosol composition affects the shape of the droplet spectrum has been noted in a number of sources. For example, Kaufman and Nakajima (1993) found a significant decrease in droplet size (from 15 to 9 μm), accompanied by an increase in drop concentration, in “smoky,” continental clouds (see also Martinsson et al. 1999; Pawlowska and Brenguier 1998). Harshvardhan et al. (2002) observed an increase in cloud droplet number concentration and a decrease in cloud droplet radius associated with a sulfate incursion over the mid-North Atlantic. Observations (e.g., Rosensfeld and Woodley 2000; Rosenfeld et al. 2001, 2002) and numerical simulations (Khain et al. 1999, 2001a) show that that the aerosol effect can be a substantial factor affecting the type, rate, and distribution of precipitation in convective systems.
Yet most bulk-parameterization schemes preclude any dependence of raindrop production on cloud droplet size and width of the initial droplet size spectrum. Instead, many bulk schemes are based on Kessler's (1969) autoconversion parameterization, according to which the rate of rainwater production by cloud droplet collisions is proportional to the cloud water content (CWC), and does not depend on the width of the droplet spectrum. Thus, according to the Kessler approach, CWCs being equal, the rates of raindrop formation in smoky air and clean air would be the same.
Yet, droplet collisions in clouds forming in a smoky air environment are ineffective. Hence, cloud water content, as compared to rainwater content, in these clouds is usually higher than in clouds growing under cleaner, more maritime conditions. As a result, the Kessler formula tends to overestimate the rate of precipitation formation from continental-like clouds developing in smoky air. In fact, Khain et al. (1999) showed that the rate of rainfall formation simulated using the Kessler formula can be in error by as high as a factor of 10. Since the size of water drops affects the rate of freezing, the error in raindrop production can lead to errors in the prediction of supercooled water and/or frozen hydrometeors (Khain et al. 2000).
To avoid this problem the autoconversion parameterization of Berry and Reinhardt (1974) might be used, which includes explicit dependencies on the mean size of cloud droplets and the width of the spectrum. Yet, even here, the cloud spectrum parameters must be tuned to a particular observational dataset.
Another approach is referred to as spectral (bin) microphysics (SBM). Each type of cloud particle/hydrometeor is described using size (mass) distribution functions containing several tens of bins of masses (e.g., Khvorostyanov et al. 1989; Hall 1980; Reisin et al. 1996; Ovtchinnikov and Kogan 2000; Yin et al. 2000; Rasmussen et al. 2002). In this approach, the shapes of the size distributions in SBM models are not determined a priori, but are calculated in the course of the model integration. Another example of this type of model is the Hebrew University Cloud Model (HUCM) (Khain et al. 2000, 2001b), which solves an equation system for eight size distribution functions for CCN, water drops, three types of ice crystals, snowflakes, graupel, and hail/frozen drops.
Until now, computer limitations have precluded the development of mesoscale three-dimensional models with spectral microphysics, which limits the utilization of these models as research tools and in prognostic models. There are a limited number of 3D mixed-phase spectral microphysics models (e.g., Khvorostyanov and Sassen 1998; Ovtchinnikov and Kogan 2000) that have been used for simulation of individual clouds for a comparatively short period of time. During this time environmental conditions are considered as time independent. In most cases, the cloud is triggered by a temperature (or humidity) impulse. Moreover, the cited models use only one size distribution for the description of cloud ice.
This paper describes the first attempt to use a “fast” version of spectral (bin) microphysics in a three-dimensional nested grid mesoscale model. The model was used for the simulation of the initial stage of convective system formation over Florida on 27 July 1991, during the Convective and Precipitation Electrification Experiment (CaPE). Spectral microphysics was used for the first time in a model that has a realistic land surface and atmospheric environment. The structure of the rest of the paper is as follows. In section 2 the spectral microphysics mesoscale model is described. In section 3, the design of numerical experiments is presented with the model setup, etc., while section 4 is dedicated to the description of results of simulations. A summary and discussion can be found in section 5.
2. Spectral microphysics mesoscale model
a. Model dynamics
The nonhydrostatic mesoscale modeling system, the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model (MM5), was chosen as the dynamical platform for the spectral (bin) microphysics. The MM5 (Dudhia 1993; Grell et al. 1994) is the latest in a series of mesoscale models developed by Penn State–NCAR. The standard model predicts the three wind components, temperature, mixing ratios for water vapor, cloud water/ ice, and rain/snow (using bulk parameterizations), and a pressure perturbation. The perturbation pressure is the departure from a temporally invariant reference state described by Dudhia (1993). The latest general version of MM5, version 3, has only a nonhydrostatic option (this study used version 3.4). Second-order centered differences describe spatial finite differencing for most equations. A fourth-order scheme is applied for diffusion terms. Temporal finite differencing uses a second-order leapfrog time step scheme. The fast terms in the momentum equation responsible for sound waves use a shorter time step than for the advection of, for example, the horizontal wind. The model uses a terrain-following sigma coordinate in the vertical, and a stretched vertical coordinate with the highest vertical resolution closest to the ground surface.
b. Model microphysics
1) Spectral microphysical package
The coupling of MM5 to SBM originally used the original microphysical package contained within HUCM (Khain and Sednev 1996; Khain et al. 1996, 1999, 2000, 2001b, 2004). In the full SBM approach, eight size (number) distributions are used to describe water drops, ice crystals (columnar, platelike, and dendrites), snowflakes (aggregates), graupel, and hail/frozen drops, and CCN. The size distribution functions are defined the same as in Berry and Reinhardt (1974) and Bott (1998). Each size distribution is represented by 33 mass doubling categories (bins), so mass mk in the category k is determined as mk = 2mk−1, where k = 2, … , 3. The size distribution for water drops includes all drop sizes from small cloud droplets to raindrops. So, in the SBM approach there is no need for separate cloud species and rain species (as in bulk-microphysics schemes). The minimum mass in the hydrometeor mass grids (except aerosols) corresponds to that of a 2-μm-radius droplet. The mass grids used for hydrometeors of all types are identical. This simplifies calculations concerning interactions between hydrometeors of different bulk densities. The model microphysics is specifically designed to account for the effect of atmospheric aerosols on cloud development and precipitation formation. Likewise, the model can be used to study the effects of clouds on CCN concentration in the atmosphere.
We assume that aerosol particles (APs) consist of sodium chloride. The utilization of another chemical composition of AP is also possible. Note that since the Raoult term in the equation of diffusional growth (and droplet nucleation) is proportional to the third power of the radius of dry aerosol particles, any changes in other parameters in this term related to the chemical composition will result in a comparatively small change in the “equivalent” radii of APs (see, e.g., Mazin and Shmeter 1983).
Nucleation (CCN activation) of droplets is based on the utilization of a separate size distribution function for CCN. There are a very limited number of cases when CCN size distributions are directly measured (and available). It is usual practice to characterize CCN properties by an empirical dependence on the number of activated CCN as a function of supersaturation with respect to water Sw. In particular, the empirical dependence (Pruppacher and Klett 1997) of CCN concentration N on supersaturation can be written as N = No
During the course of the model integration (t > 0), the critical size of dry CCN rNcrit that must be surpassed to trigger nucleation is determined at each model time step using the supersaturation Sw. Aerosol particles with radii rN > rNcrit are activated and converted into droplets, while corresponding bins of the CCN size distributions become empty. In case there are no aerosol particles in the CCN spectra at a particular grid point with rN > rNcrit, no new droplet nucleation takes place at this point.
The size of fresh nucleated droplets is calculated as follows. In case the radii of dry CCN rN < 0.03 μm, the equilibrium assumption (according to the Köhler equation) is used to calculate the radius of a nucleated droplet corresponding to rN (see Khain et al. 2000 for more details). In case rN > 0.03 μm, the radius of water droplet formed on these CCN is assumed to be equal to 5 times the radius of the dry aerosol particle (Kogan 1991; Khain et al. 1999). Since large CCN do not reach their equilibrium size at cloud base, this approach prevents the nucleation of unrealistically large droplets and unrealistically fast raindrop formation. In the current version of microphysics, aerosol particles are not recovered when cloud drops evaporate.
The type of ice crystals nucleated depends on air temperature. According to Takahashi et al. (1991): platelike crystals form between −8°C > Tc ≥ −14°C and −18°C > Tc ≥ −22.4°C, columnar crystals between −4°C > Tc ≥ −8°C, Tc < −22.4°C, and dendrites (branch-type crystals) between −14°C > Tc ≥ −18°C.
The description of secondary ice generation follows the measurements described by Hallett and Mossop (1974). At T = −5°C, 250 collisions of droplets having radii exceeding 24 μm with graupel particles lead to the formation of one ice splinter. The number of formed splinters varies linearly to zero toward −3° and −8°C. We assume that the density of splinters is the same as that of pure ice (0.9 g cm−3), and, hence, the splinters are assigned to plate-type ice crystals.
The rate of drop freezing follows the observations of immersion nuclei by Vali (1975, 1994) and homogeneous freezing by Pruppacher (1995). The rate of freezing is calculated using a semi-Lagrangian approach as written in Khain et al. (2000). Contact freezing in the freezing of drops is neglected. According to Meyers et al. (1992), the number of immersion and contact IN are of the same order. At the same time, while immersion IN are located inside of drops and lead to drop freezing when temperature decreases to a certain value, contact nuclei lead to droplet freezing as a result of collisions with drops. However, the collision efficiency is usually evaluated as small as ∼10−3. As a result, contact freezing seems to be less efficient when compared to droplet freezing associated with immersion nuclei.
Melting occurs by instantaneous conversion of all ice particles into liquid drops of equal mass at the grid points just below the freezing level. Ovtchinnikov and Kogan (2000) also use this approach.
A system of differential equations is used to calculate supersaturation with respect to water and ice at each model time step (Khain and Sednev 1996). Besides being used for droplet and ice nucleation, these values of supersaturation are used to calculate the diffusional growth/evaporation of water droplets and deposition/ sublimation of ice particles. The diffusional growth of ice crystals also takes into account their shape.
An efficient and precise method of solving the stochastic kinetic equation for droplet collisions (Bott 1998) was extended to a system of stochastic kinetic equations that are used to calculate water–water, water– ice, and ice–ice collisions. The model uses height-dependent drop–drop and drop–graupel collision kernels that are calculated using a hydrodynamic method valid within a wide range of drop and graupel sizes (Khain et al. 2001b; Pinsky et al. 2001). Ice–water and ice–ice collision kernels account for the shapes of ice crystals and a dispersion of terminal velocities of crystals of the same mass but different shape. Ice–ice collision rates are assumed to be temperature dependent.
To take into account the effect of turbulence on drop– drop collision, the collision rate between droplets was increased in clouds following Pinsky and Khain (2002). The enhancement factor depends on droplet size. The maximum value of the enhancement is ∼5. Collision rate for graupel–drop collisions was increased as compared to pure gravitational values following Pinsky et al. (1998). Collision rate between ice particles was increased several times following Pinsky and Khain (1998). The enhancement in the collision rate for ice particles was taken larger than that for droplets because ice particles have larger inertia and lower terminal fall velocity.
The collision enhancement factors were developed for typical conditions in cumulus clouds and are applied to collision processes in modeled clouds without accounting for possible changes in turbulent intensity, which can vary during cloud evolution. Thus, these factors can be considered as a first approximation. Recent theoretical studies indicate that the turbulence effect is underestimated in the model, especially for drops with sizes of about 40–70 μm (e.g., Pinksy and Khain 1998; Wang 2001; Falkovich et al. 2002). More detailed treatment of turbulent effects on collisions will be developed as part of future improvement of model microphysics.
As a result of riming, ice crystals and snowflakes can convert to graupel or to hail depending on temperature. At comparatively low temperatures, the collision of hail (frozen drops) with water drops leads to graupel formation. Collisions between ice crystals lead to snow (aggregates) formation. Khain and Sednev (1996) describe in detail the procedure for the conversion of hydrometeor types that result from different kinds of collisions.
Recently, a description of collisional breakup has been implemented in the HUCM microphysics (Seifert et al. 2005). Changes to drop size distributions due to breakup are represented by the well-known stochastic breakup equation (Pruppacher and Klett 1997). The coalescence efficiency and the fragment size distributions are parameterized following Low and List (1982) with some corrections for small raindrops using parameterizations given by Beard and Ochs (1995). For the discretization of the breakup terms, the backward variant of Bleck's method is applied (Bleck 1970; Hu and Srivastava 1995).
To decrease the computer resources required to simulate the SBM, a faster version of the spectral microphysics (referred to hereafter as SBM Fast) was developed. The main features of the full microphysics are valid in the fast version. The main difference is that the number of size distributions for ice is decreased from six to three. In each size distribution, small ice particles are either plates, columns, or dendrites, while large ice particles are either graupel, snowflakes (aggregates), or hail. The definition of graupel, snowflakes, and hail particles as large particles with sizes exceeding several hundreds of microns is generally accepted in the subject of cloud physics (Pruppacher and Klett 1997).
Such separation of ice types along size distributions simplifies the description of deposition/sublimation of ice particles. For instance, it is natural to assume that diffusional growth of branch-type crystals (dendrites) should lead to the formation of particles with characteristics close to snow (or aggregates), while diffusional growth of plates leads to the formation of hail with the same density. Similarly, columns grow into graupel, while the process of sublimation leads to the opposite conversion of large ice particles to small ice particles.
The results of collisions have been modified slightly. For example, if two ice particles collide, they will not become snowflakes unless their combined mass exceeds the minimum mass we associate with snowflakes (in the 17th bin ∼100 μm of melted radius). Similarly, the collision of a water droplet with an ice crystal gives another ice crystal, unless the combined mass exceeds the minimum mass we associate with graupel (again in the 17th bin). Figure 1 summarizes the scheme of microphysical processes in the SBM model. Microphysical processes are treated in a sequence that is determined by the characteristic time scales of each of the various microphysical processes.
The results from the full SBM and SBM Fast were compared. The SBM Fast gave similar precipitation and simulated radar reflectivity results as the slower, full SBM model. The results from the SBM Fast model are presented in this paper.
2) Running SBM in MM5
The coupling of SBM to MM5 adapted code already in use in MM5. The advection of size distribution functions uses the standard MM5 code written for advection of integral contents and other parameters. Note that the advection of one size distribution corresponds to the advection of the 33 fields corresponding to each bin (actually advection of only nonempty mass bins is conducted). Particles of different mass and type fall with different terminal velocities, and the height dependence of terminal velocities is also taken into account.
Size distributions were integrated over all mass bins to obtain corresponding integral values. These integral values were used to calculate the “loading” term of hydrometeors in the nonhydrostatic equation for vertical velocity and for the purposes of radiative transfer in the MM5 atmospheric radiation schemes. SBM Fast, like bulk schemes, also calculates the effect of microphysics on temperature and moisture tendencies. Through these couplings, the SBM Fast affects the dynamics, radiation balance, and surface hydrology.
The model time step was set to 9 s. Hence, each simulation was run with a dynamical/advection time step of 18 s (since MM5 uses the leapfrog prognostic method). The dynamical time step is then divided into several microphysical time steps (each 3 s long), and each “microphysical” time step is assigned a fraction of the dynamical tendencies of supersaturation. These tendencies are then used while diffusional growth and/ or evaporation are calculated.
The nucleation was also calculated with a 3-s time increment. Yet, the microphysical time step itself can be further broken up to provide greater precision for certain processes. For example, the time integration of the diffusional growth/evaporation equation is conducted using the method of Khain and Sednev (1996). Here the sub–time step varies, but a minimum substep value for diffusion/evaporation was chosen to be equal to 0.4 s. Supplemental experiments showed that a further decrease in the duration of the sub–time step did not affect the results. Regarding collisions, the model results showed sensitivity to time step when the time step was longer than 9 s. Hence, collisions and breakup were called twice during every dynamical time step of the MM5 model.
3) Bulk-microphysics schemes
A large number of bulk parameterizations exist in the MM5. Different schemes can be employed for warm rain, simple ice, and mixed-phase microphysics. At most, though, these schemes deal with five types of cloud particles/hydrometeors: cloud water, rainwater, a generic type of cloud ice, snow, and graupel or hail. Currently, the most advanced bulk-microphysics options in MM5 consist of those labeled in MM5 as “GSFC” (Goddard Space Flight Center) (Tao et al. 2003), “Reisner2” (Reisner et al. 1998), and “Schultz” (Schultz 1995). Supplemental simulations (see Lynn et al. 2005, hereafter Part II) show that the Reisner2 scheme produced the best agreement between precipitation amount and observed precipitation. Therefore we chose the Reisner2 scheme as the bulk model comparison for this study.
The Reisner2 scheme predicts cloud, rainwater, snow, graupel, ice, and ice number concentration. Marshall– Palmer distributions are used for rain, snow, and graupel. The current version of the scheme allows the intercept parameter to vary with amount for graupel and rain, and with temperature for snow. Condensation adjusts to exact water saturation. The autoconversion in the MM5 3.4 version is based on the Kessler parameterization. Riming, melting, and multiplication processes are also considered.
3. Design of case study
a. Description of simulated day
Halverson et al. (1996), Lynn et al. (2001), and Baker et al. (2001) each discuss in various detail the convective development that occurred on 27 July 1991. Prior to the onset of west coast sea-breeze formation, though, convective clouds developed mostly over water and approached the west coast of Florida, north of St. Petersburg and south and west of Gainesville. These clouds were relatively short-lived. For example, Fig. 2 shows the radar reflectivity from several clouds. For example, cloud “A” developed on the west-central coast at 12.25 UTC, with radar reflectivity reaching 35 to 40 dBZ at 12.50 (henceforth decimal hours are used for time, e.g. 12.50 = 1230) UTC. Radar indicated that this cloud then redeveloped in the next 15 min (1275 UTC), eastward of its previous position, with a convective core of 25 to 30 dBZ radar echoes. Radar showed that another cloud, “B,” approached the northwest coast at 13.00 UTC. It had peak radar reflectivity values between 45 and 50 dBZ at 13.50 UTC (which was near the time of sea-breeze formation).
b. Model setup
The model grid geometry (Fig. 3) consists of a coarse domain (9 km) with a nested 3-km domain. Within the 3-km domain, there is also nested a 1-km grid domain. These are referred to as domains 1, 2, and 3, respectively. Each of the domains is centered over Florida. Domain 1 covered 100 × 84 grid elements, or 900 km in the west-to-east direction and 756 km in the north-to-south direction. This domain was used to generate lateral boundary conditions for domain 2 of 184 × 160 grid elements, which covered 552 km west to east and 480 km north to south. In turn, domain 2 was used to generate lateral boundary conditions for domain 3, which covered 400 × 199 grid elements, or 400 km west to east and 199 km north to south. Each domain had 35 atmospheric layers. Within domain 1, the model was integrated with a time step of 27 s. It was run from 0000 UTC 27 July to 0100 UTC 28 July 1991 using standard MM5 input files from the MM5 preprocessor programs. These programs take NCEP reanalysis data and interpolate them to the MM5 grid. Additional “massaging” of the MM5 atmospheric fields is done using radiosonde data. The model was initialized using this interpolated data field, but after model initialization only the data at the boundaries were updated every 6 h.
The first nested domain, domain 2, was run separately (one-way interaction) with a time step of 9 s from hours 1000 to 0100 UTC on 27 July 1991. The boundary conditions were updated every 15 min using the output from domain 1.
The SBM Fast was implemented on the 1-km grid of domain 3, and it is referred to as domain 4. To save computer time, it was not activated along the borders of the domain. Instead, the Reisner2 option was used on the border of domain 3 (see Fig. 3). The SBM Fast microphysics encompassed an area of 320 by 99 grid elements or 320 km west to east by 99 km north to south, while the outer border was of size 40 km (on the western and eastern sides of the domain) and 50 km (northern and southern sides of the domain). The model domain with Reisner2 (run separately for comparison) and Reisner2/SBM was run from 1000 to 1400 UTC, using 9-s time steps. The simulation with Reisner2 used 15-min output from domain 2 at the lateral boundaries, while the simulation with SBM also used information from domain 3 at its boundaries.
The MM5 has a five-layer soil model (Dudhia 1993), which was used here with a soil moisture availability distribution derived with the Parameterization for Land– Atmosphere–Cloud Exchange (PLACE) (see Lynn et al. 2001). The Gayno–Seaman (Shafran et al. 2000) turbulent kinetic energy parameterization was used to calculate the fluxes in the atmospheric boundary layer and mixing within clouds.
Note that on the 9-km simulation domain the Kain– Fritsch (1990) convective parameterization was used, but this parameterization was not used on the 3- or 1-km grid. The Reisner2 option was used on each grid except on the 1-km grid where SBM Fast was activated.
As noted, SBM Fast was used on domain 4 (at the same 1-km resolution) within domain 3, which required that the coupling address the problem of the penetration of clouds through the boundary separating it from the bulk microphysics. Since the fine-resolution grid covers the main convective zone, the effect of such penetrations is not significant. Nevertheless, in case such penetration took place, size distributions of hydrometeors were restored using the (mean) mass contents (see Rogers and Yau 1989, p. 104) of the penetrating clouds, and assuming that the distributions of rainwater, columnar ice particles, snow, and graupel follow the Marshall–Palmer (1948) distribution.
In the present study, radiosonde data indicated that the wind direction was off the ocean. Hence, an aerosol concentration typical of maritime conditions was used for the calculation of the initial CCN size distribution. In this case, the coefficient A was set equal to 100 cm−3, while coefficient k was set equal to 0.462. It was also assumed that there were no small CCN in the CCN spectrum that could be activated at supersaturation values exceeding 1.1%. This assumption is based on measurements of maritime CCN (Hudson 1984, 1993; Hudson and Frisbie 1991). This limitation allows us to keep droplet concentration to be typical of maritime clouds. This experiment will be referred to hereafter as SBM FastM.
A simulation to test the sensitivity of precipitation to initial aerosol concentration (hereafter SBM FastC) was also produced. Here, we chose coefficients that could be used to represent continental initial conditions (A = 1260 cm−3, while k = 0.308). In the restored initial CCN size distribution function, CCN particles with dry radii exceeding 0.4 μm were eliminated. This excludes the elongated tail of large CCN distribution, which can accelerate the formation of large droplets. No effects of giant and ultragiant CCN were considered. Note that at each grid point CCN distribution changes with time during model integration due to nucleation scavenging and advection.
Additionally, a simulation was produced using the Reisner2 bulk parameterization, hereafter referred to as Reisner2, with parameters in the Kessler autoconversion formula already preset for maritime conditions.
c. Calculation of radar reflectivity
The calculation of radar reflectivity from model data uses an algorithm supplied by W.-K. Tao (described in Tao and Simpson 1984; McCumber et al. 1991). This algorithm uses empirical equations that calculate the radar reflectivity from the modeled fields of cloud and rainwater (or frozen hydrometeors). These modeled values represent the grid-element mean values of cloud particles/hydrometeors obtained directly from the MM5 simulations with bulk parameterizations, or by integrating the SBM size distributions over all bins. The radar reflectivity was calculated at ∼3 km level. We tested also another algorithm from Rutledge and Hobbs (1984). It gave very similar radar reflectivity for cloud/ rain at the same height.
d. Dataset
The model results were compared to radar observations, which were obtained from the University Corporation for Atmospheric Research (UCAR) courtesy of Weather Services International (WSI). They are planar two-dimensional, extending across the Florida peninsula. No other data were available for comparison with model results. However, the main emphasis here is to compare the model results to each other, and the observations will be used to emphasize these differences.
4. Results
a. Cloud structure
In each of the simulations described below, the thermodynamic conditions were similar. Thus, differences in results between spectral microphysics runs can be attributed to aerosol effects. The aerosol effects on microphysics and dynamics of single clouds are best revealed by comparison of the evolution of first clouds that experience similar forcing environments. For the sake of convenience, we refer to clouds that developed with the maritime aerosol concentrations as “maritime,” while clouds that developed with the continental aerosols are referred to as “continental.” However, since thermodynamic conditions were similar in each simulation, the latter are not fully typical of clouds that develop in a continental air mass.
Figure 4 shows CWC, cloud rainwater content (RWC) (drops with radii exceeding 70 μm are referred to as raindrops), and total water/ice content at 11.50 UTC for SBM FastM, SBM FastC, and Reisner2. These were the first clouds that formed in each simulation, and they formed near the location of cloud A in Fig. 2. SBM FastM produced both cloud water and cloud rainwater, but SBM FastC produced mostly cloud water with almost no rainwater. Yet, the CWC in SBM FastC was larger than in SBM FastM. Typically, at the initial stage of development continental clouds contain more cloud water than maritime clouds. This feature can be attributed to the fact that droplets in continental clouds are smaller than in maritime clouds and the efficiency of collisions (to produce raindrops) is lower. As a result, a larger mass of cloud droplets remains in the air and ascends in cloud updrafts, instead of falling out as raindrops. These are in agreement with those from the two-dimensional model of Khain et al. (1999, 2001b). In contrast to both SBM simulations, Reisner2 produced both relatively large values of CWC and RWC at the same time. Hence, the Reisner2 cloud had characteristics similar to both maritime and continental clouds.
Figure 5 shows the model results 20 min later at 11.83 UTC. The maximum of RWC in SBM FastM reached between 5 and 7 g kg−1, which is more than the 3 to 5 g kg−1 in the continental cloud of SBM FastC. Much less rainwater is shown in Reisner2, and in fact this cloud had nearly dissipated by this time. Note that no cloud produced ice [the freezing level was at 5.1 km (Halverson et al. 1996)]; only quite deep clouds can produce significant amounts of ice under these conditions.
The first clouds described above arose in the vicinity of the seashore and were probably caused by vertical velocity fluctuations associated with sea–land surface temperature differences. Dissipation of the first cloud in both SBM FastM and SBM FastC led to the formation of downdrafts and to convergence in the boundary layer. This convergence fostered the formation of a secondary cloud in each case. Aerosol effects were more pronounced for the secondary clouds than the first cloud, since they developed over more homogeneous surface conditions and were not forced by significant sea surface differences.
Figure 6 shows that the secondary cloud in SBM FastC had maxima of CWC and RWC larger than in SBM FastM, and SBM FastC produced more ice mass than SBM FastM. In fact, although the maximum vertical velocity in the first clouds was very similar, a comparison of Figs. 7 and 8 shows that SBM FastC had larger vertical velocity at the time of maximum cloud development than SBM FastM.
Interestingly, the droplet concentration in secondary clouds in SBM FastM (Fig. 9) was lower than in the first clouds. This is related to smaller updrafts in the secondary clouds than primary clouds, as smaller updraft velocity leads to smaller supersaturation values. In the maritime case, fewer drops imply a faster conversion of cloud droplets to raindrops. Hence, the cloud in SBM FastM grows relatively fast and rainfall loading hinders convective development under even greater convective instability (over land as compared to the ocean). In the continental case, there was also a reduction in the number of cloud droplets (not shown). Here, though, there are sufficient cloud droplets to delay raindrop formation enough time to allow a strong secondary cloud to develop. These dynamical and microphysical effects of aerosols on cloud development were also found in simulations with the two-dimensional HUCM as well.
Reisner2 does not have explicit dependence on aerosol concentration, although governing scheme parameters were preset for maritime clouds. Figure 10 shows that Reisner2 produced a maximum vertical velocity of 9 to 12 m s−1 within 10 min (i.e., from 11.50 to 11.67 UTC). In fact, the maximum value of vertical velocity obtained was larger than in the first clouds in either SBM FastM or SBM FastC. Figures 5 and 6 indicate a rapid dissipation of the first cloud. Relatively short forcing of the first cloud on the environment is one of the reasons that secondary clouds in Reisner2 turn out to be weaker than those in SBM FastM and FastC.
As noted, the duration of cloud life (evolution) when the bulk-parameterization model was used was much shorter than when spectral (bin) microphysics was used. It should be noted that a short lifetime of simulated clouds is a typical feature of most bulk-parameterization schemes. We attribute this result to the fact that in the bulk parameterization the sedimentation of precipitating particles begins if the mean fall velocity exceeds the updraft velocity. In this case the cloud produces short-lasting, intense precipitation. In spectral microphysics, fall velocities depend on particle size. Hence, larger drops start falling earlier (even if cloud updrafts are large), while small raindrops fall later, when cloud updrafts decrease due to general cloud dissipation.
b. Spatial structure of clouds
Figure 11 shows the rainfall “footprints” of the convective clouds described above, extending until 13.50 UTC. These figures show the accumulated rainfall obtained every 5 min averaged over 5 km in the north and south direction from the center of each cloud. The SBM FastM and Reisner2 simulations produced rainfall earlier than SBM FastC. This agrees with the developmental sequence of RWC shown in Figs. 4–6. One can see, though, that clouds developing in continental aerosols produce stronger peaks of precipitation under the particular thermodynamic conditions used in the study.
Figure 12 shows calculated radar obtained from SBM FastM, SBM FastC, and Reisner2 from 13.50 to 14.00 UTC. In Fig. 12, we focus on the model-simulated cloud (cluster) “B′.” This corresponds to the observed cloud “B” marked in Fig. 2, shown from 12.75 to 13.50 UTC. The sequence of clouds shown in Fig. 12 developed about a half hour later in the model than observed. This is the reason that the times in Fig. 12 do not overlap with the last three time frames shown in Fig. 2. All figures suggest an eastward progression of clouds toward the west coast. The clouds formed in SBM FastM propagated eastward, with a speed closer to the observed than those formed in SBM FastC and Reisner2. This can be attributed to the different heights of clouds that developed in these simulations. The clouds that formed in SBM FastM did not reach as high as those in the other simulations, and remained mainly in low-level westerly flow. We see, therefore, that different aerosol conditions affect the cloud propagation speed within a sheared background flow. It should be mentioned that the features of the Reisner2 parameterization were typical of other mixed-phase bulk parameterizations implemented into MM5.
5. Summary
A novel mesoscale model with spectral (bin) microphysics has been developed. The spectral (bin) microphysics was implemented into a widely used mesoscale model, the MM5. The microphysics package is based on solving a system of equations for size distribution functions for cloud condensational nuclei (CCN), water drops, three types of ice crystals, and three ice hydrometeors: snowflakes (aggregates), graupel, and hail.
The model has been used to simulate initial cloud development on 27 July 1991, during the CaPE experiment. The experiments with spectral (bin) microphysics showed some aerosol effects on first clouds, and very strong effects on secondary cloud microphysics, as well as on cloud dynamics.
High aerosol (continental) concentration in the first cloud led to some delay in the formation of raindrops as compared to a first cloud in a maritime case. The top heights of the first clouds that developed in continental and maritime air were quite similar, as the intensity and depths of the first clouds responded more to the dynamical (coastal) forcing than to differences in aerosol concentration. Nevertheless, significant differences in cloud microphysics (droplet concentration, level and time of raindrop formation, etc.) show that aerosol effects are important even in cases of similar dynamic forcing. In secondary clouds, the effect of aerosol concentration was even more pronounced. Here, the forcing caused by horizontal temperature gradients was weaker, and aerosols played a greater role in cloud development.
The clouds with spectral (bin) microphysics have generally longer lifetime than clouds formed with the Reisner2 bulk parameterization. A qualitative comparison of cloud lifetimes with those apparent from radar observations suggests that spectral (bin) microphysics described cloud development and movement in a more realistic way than Reisner2. A more in-depth analysis and comparison will be made in Part II.
Acknowledgments
This study was supported by the Binational U.S.–Israel Science Foundation (Grant 2000215), the Israel Ministry of Science (German-Israel collaboration in water technology, Grant WT 0403), and the European project SMOCC. The authors wish to thank the reviewers for their very helpful comments concerning the original manuscript. The authors express their deep gratitude to Robert Rilling at UCAR for providing WSI radar data and to Dennis Buechler and Bill Crosson for processing this data. We also thank the Israeli High Powered Computing Center for help in utilization of their computer resources.
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Scheme of microphysical processes used in spectral (bin) microphysics model
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Scheme of microphysical processes used in spectral (bin) microphysics model
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Scheme of microphysical processes used in spectral (bin) microphysics model
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Observed radar reflectivity on 27 Jul 1991 (note time in decimal hours)
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Observed radar reflectivity on 27 Jul 1991 (note time in decimal hours)
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Observed radar reflectivity on 27 Jul 1991 (note time in decimal hours)
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Model geometry used in simulations
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Model geometry used in simulations
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Model geometry used in simulations
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross section of cloud liquid water, cloud rainwater, and total cloud water/ice content for the times and simulations shown. The cross sections are from the simulated cloud that developed in each simulation near the location of cloud “A” in Fig. 2 at about 1200 UTC. Note that there was no ice content below 5 km
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross section of cloud liquid water, cloud rainwater, and total cloud water/ice content for the times and simulations shown. The cross sections are from the simulated cloud that developed in each simulation near the location of cloud “A” in Fig. 2 at about 1200 UTC. Note that there was no ice content below 5 km
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross section of cloud liquid water, cloud rainwater, and total cloud water/ice content for the times and simulations shown. The cross sections are from the simulated cloud that developed in each simulation near the location of cloud “A” in Fig. 2 at about 1200 UTC. Note that there was no ice content below 5 km
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Same as Fig. 4, but for the time shown
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Same as Fig. 4, but for the time shown
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Same as Fig. 4, but for the time shown
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Same as Fig. 4, but for the time (decimal hours) shown
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Same as Fig. 4, but for the time (decimal hours) shown
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Same as Fig. 4, but for the time (decimal hours) shown
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross sections of vertical velocity at the times shown for SBM FastM. The cross section is the same as for Fig. 4
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross sections of vertical velocity at the times shown for SBM FastM. The cross section is the same as for Fig. 4
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross sections of vertical velocity at the times shown for SBM FastM. The cross section is the same as for Fig. 4
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross sections of droplet concentration obtained in SBM FastM
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross sections of droplet concentration obtained in SBM FastM
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Vertical cross sections of droplet concentration obtained in SBM FastM
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Rainfall footprints for the clouds shown in Figs. 4–6, extending to 13.30 UTC. The rainfall is the accumulated rain amount obtained every 5 min, after being averaged over a 5-km north–south axis centered on the west-to-east cross sections of the clouds shown above
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Rainfall footprints for the clouds shown in Figs. 4–6, extending to 13.30 UTC. The rainfall is the accumulated rain amount obtained every 5 min, after being averaged over a 5-km north–south axis centered on the west-to-east cross sections of the clouds shown above
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Rainfall footprints for the clouds shown in Figs. 4–6, extending to 13.30 UTC. The rainfall is the accumulated rain amount obtained every 5 min, after being averaged over a 5-km north–south axis centered on the west-to-east cross sections of the clouds shown above
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Simulated horizontal cross sections of radar reflectivity for the model simulations shown. The radar reflectivity is at 3-km height. The cloud cluster labeled B′ is compared in the text to the cloud cluster labeled B in Fig. 2
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Simulated horizontal cross sections of radar reflectivity for the model simulations shown. The radar reflectivity is at 3-km height. The cloud cluster labeled B′ is compared in the text to the cloud cluster labeled B in Fig. 2
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
Simulated horizontal cross sections of radar reflectivity for the model simulations shown. The radar reflectivity is at 3-km height. The cloud cluster labeled B′ is compared in the text to the cloud cluster labeled B in Fig. 2
Citation: Monthly Weather Review 133, 1; 10.1175/MWR-2840.1
