A mesoscale model simulation of a wide cold-frontal rainband observed in the Pacific Northwest during the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-1) field study was used to test the sensitivity of the model-produced precipitation to varied representations of snow particles in a bulk microphysical scheme. Tests of sensitivity to snow habit type, by using empirical relationships for mass and velocity versus diameter, demonstrated the defectiveness of the conventional assumption of snow particles as constant density spheres. More realistic empirical mass–diameter relationships result in increased numbers of particles and shift the snow size distribution toward larger particles, leading to increased depositional growth of snow and decreased cloud water production. Use of realistic empirical mass–diameter relationships generally increased precipitation at the surface as the rainband interacted with the orography, with more limited increases occurring offshore. Changes in both the mass–diameter and velocity–diameter relationships significantly redistributed precipitation either windward or leeward when the rainband interacted with the mountain barrier.
A method of predicting snow particle habit in a bulk microphysical scheme, and using predicted habit to dynamically determine snow properties in the scheme, was developed and tested. The scheme performed well at predicting the habits present (or not present) in aircraft observations of the rainband. Use of the scheme resulted in little change in the precipitation rate at the ground for the rainband offshore, but significantly increased precipitation when the rainband interacted with the windward slope of the Olympic Mountains. The study demonstrates the promise of the habit prediction approach to treating snow in bulk microphysical schemes.
Regional mesoscale models have become the central tools for operational quantitative precipitation forecasts (QPFs) for periods of 0–72 h. Such models have increasingly relied on bulk microphysical schemes originally developed for cloud research (e.g., Cotton 1982; Lin et al. 1983; Rutledge and Hobbs 1983, 1984) for the representation of clouds and precipitation. Although bulk schemes carry a set of prognostic equations for typically three to six different water species (e.g., water vapor, cloud water, rainwater, cloud ice, snow, and graupel), in many situations it is the snow species that is the most active participant in the simulated microphysics of an overall storm. Colle et al. (2005) found that the interactions of snow with water vapor, cloud water, rain, and graupel were among the most active production terms in the bulk scheme for the simulation of an orographic precipitation event, and that the QPF was most sensitive to the assumption of snow size distribution, as well as the assumed snowfall velocity.
Snow particles take on highly varied habit types, densities, fall velocities, and degrees of aggregation and riming. Other precipitation species (rain and graupel) have much less variable characteristics. Despite the complexity of snow in nature, the representation of snow in bulk schemes has generally been highly simplified, utilizing static parameters in the mass–diameter relationship for snow particles (often assuming spheres of constant density), the fall velocity–diameter relationship, and other characteristics. Whereas observational and theoretical studies of snow particles have quantified the habit-dependent variability of the mass–diameter and velocity–diameter relationships (see citations in section 2), as well as the shape of the size distribution (Woods et al. 2007), typically little or none of this variability is incorporated into microphysical schemes. And yet all the production terms for snow are dependent on (and sensitive to) the specification of these characteristics.
Considering the importance of snow in the process of precipitation production, and the complexity of snow in nature, it is important to understand how this complexity affects precipitation production in bulk microphysical schemes. As a first step, this study examines the effects of different mass–diameter and velocity–diameter relationships for different snow particle types. The study takes two different approaches. The first approach is to alter assumptions about snow particles universally, by changing their mass–diameter and velocity–diameter relationships to be consistent with a single particle habit type, as determined from previous observational studies of snow particle characteristics. This approach is designed by intention to create highly variable results. The sensitivity of the simulated precipitation field to different universal particle assumptions (e.g., treating all snow particles as slow falling dendrites versus treating all snow particles as fast falling columns) should give a sense of the outer bounds to the potential improvement gained by a fully realistic representation of snow particles. The second approach is a preliminary attempt at an actual solution to the difficulty of realistic representation of snow particles in the model, namely, the testing of a bulk microphysical scheme with snow habit prediction. In this approach, separate prognostic equations for the mixing ratios of snow of different habit types are integrated, and the predicted mixing ratios are used to determine locally the habit-dependent mass–diameter and velocity–diameter relationships for the snow particles. In this manner, the habit prediction feeds back into the behavior of the microphysical scheme, potentially improving QPF. This approach builds on previous attempts at accounting for varying snow particle habits in microphysical schemes by Meyers et al. (1997), Straka and Mansell (2005), and Lynn et al. (2005). An interesting by-product of habit prediction is a forecast of the habit-dependent properties of snow accumulating at the ground, which has interesting potential applications to forecasting of snow density, snow depth, and avalanche potential, described in more detail in the discussion section.
The two approaches outlined above were applied to a mesoscale model simulation of a wide cold-frontal rainband (Evans et al. 2005) that approached the Washington coast on 1–2 February 2001, observed during the IMPROVE-1 field study (Stoelinga et al. 2003). This storm represents a good case for experimentation on the microphysical parameterization scheme, because the microphysical processes were relatively simple and steady state, and because it was well documented by observations, including a fairly complete set of measurements of the microphysical structure obtained at various levels within the rainband.
The next section describes the model used in this study, with emphasis on aspects of the microphysical scheme that are altered in sensitivity tests. A brief description of the rainband that is examined in this study is given in section 3. Section 4 describes the setup and results of the habit-related sensitivity tests. Section 5 describes the methodology of snow habit prediction that was added to a bulk scheme, and results of a test of that new scheme. A discussion of habit prediction, and overall conclusions, are presented in sections 6 and 7.
2. Model description
The mesoscale model utilized in this paper is version 3.7.0 of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) (Grell et al. 1994). The MM5 is a limited area, nonhydrostatic model with a terrain-following “sigma” vertical coordinate. The particular configuration of the model used in this study employs the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1993), a cloud radiation scheme described by Dudhia (1989), and the Medium-Range Forecast (MRF) planetary boundary layer scheme (Hong and Pan 1996).
The microphysical scheme used in this study is the five-species, single-moment1 bulk microphysical scheme developed by Reisner et al. (1998), drawn largely from previous work of Lin et al. (1983), Rutledge and Hobbs (1983, 1984), Ikawa and Saito (1991), and others. The scheme was recently modified by Thompson et al. (2004), and is therefore referred to herein as the Reisner–Thompson (or R-T) scheme. In the R-T bulk microphysical scheme, the exponential size distribution assumed for snow particles takes the form
where Ns is the number of snow particles per unit volume per unit size range, and N0s and λs are the intercept and slope of the exponential size distribution, respectively. The diameter, D, is usually defined as the maximum diameter for irregularly shaped particles, and that is what is assumed here. In general, care must be taken to insure consistency of (or account for differences in) the definitions of D when combining observed and modeled expressions for particle size distributions, mass–diameter relationships, velocity–diameter relationships, etc., as discussed by Potter (1991) and McFarquhar and Black (2004). By integrating (1) across all sizes, one obtains N̂s = N0s/λs, where N̂s is the snow particle number concentration.
From the perspective of the single-moment bulk scheme, the two parameters N0s and λs are significant in that they enter into nearly every production term in the scheme that involves snow. In single-moment schemes, either N0s or λs must be specified. Various approaches have been used, such as setting N0s constant (Dudhia 1989), diagnosing it from mixing ratio [e.g., Reisner et al. (1998), employing a relationship from Sekhon and Srivastiva (1970)], or diagnosing it from temperature [e.g., the R-T scheme used in the present study, employing a relationship from Houze et al. (1979)]. With N0s specified or diagnosed and the mixing ratio of snow predicted, λs is determined. An expression for λs is obtained by relating the predicted mixing ratio to the size distribution, which requires integration over all sizes of (1) multiplied by a relationship of the form m = amDbm that relates the mass of a snow particle to its maximum dimension:
where ρair is the air density, qs is the snow mixing ratio, and Γ is the gamma function. The quantity ρair qs is referred to as the snow water content or mass concentration of snow. Solving for λs yields
Similar to many other schemes, the R-T scheme assumes that snow particles are spheres of constant density, giving am = πρs/6 = 0.0524 mg mm−bm (where ρs is the density of snow, taken to be 100 kg m−3) and bm = 3. However, a host of observational studies (e.g., Nakaya 1954; Heymsfield and Knollenberg 1972; Locatelli and Hobbs 1974; Heymsfield 1975; Heymsfield and Kajikawa 1987; Kajikawa 1989; Mitchell et al. 1990; Mitchell 1996) have provided empirically derived mass-diameter relationships for unrimed snow particles, and these relationships differ substantially among different particle types. Table 1 lists several different classes of snow particle habit types considered in this study (including model-assumed snow spheres), and gives a mass–diameter power law corresponding to each habit type. Power laws published in the literature generally have finite size ranges of validity, and are usually based on the behavior of either single crystals or aggregates. To keep matters simple in this study, we assigned a single mass–diameter power law to each habit category, as indicated in Table 1. In some cases this makes good sense, such as for cold-type crystals, for which published power laws for single crystals overlap well with those for aggregates. In other cases (e.g., dendrites and needles), there is some disagreement between published power laws for single crystals and aggregates (single crystals generally being less massive), and we chose a power law that represented the “average” behavior of single crystals and aggregates. In the case of bullets and columns, no observational studies have quantified the behavior of aggregates, and so single-crystal power laws were used. No relationship was available for the “sectors and broad-branched” category, so the “cold type” mass–diameter law was substituted, since this type is probably most similar in form to “sectors and broad-branched” crystals.
For the particle types listed in Table 1, am ranges from 0.0092 to 0.0524 mg mm−bm, and bm ranges from 1.9 to 3.0. Since λs depends on both am and bm, the snow size distribution varies considerably with the choice of am and bm for a fixed value of mixing ratio and number concentration, as shown in Fig. 1 for four of the different habit types in Table 1. The size distribution implied by the R-T scheme’s assumption of snow particles as constant-density spheres yields a slope that is steeper than that yielded by any of the empirically derived mass–diameter relationships shown, and significantly so in some cases. Also shown in Fig. 1 is the “envelope” of ∼9000 snow particle size distributions observed by Field et al. (2005) using an aircraft-mounted imaging probe. While all of the habit-specific lines fall within this envelope, the variability among them is substantial compared to the total observed variability in particle size distributions, especially considering that the lines are derived from a single value of mixing ratio and number concentration, whereas the Field et al. data are taken from wide ranges of observed mixing ratios and number concentrations.
Another important aspect of the bulk scheme is that it assigns a single “bulk” terminal fall velocity (specifically, a mass-weighted mean terminal velocity) to each species of hydrometeor. The fall speed affects not only fallout of precipitation, but also interactions between the various hydrometeor species. Calculation of the mass-weighted mean terminal velocity for snow requires not only a mass–diameter relationship, but also a velocity–diameter relationship for snow particles, typically also expressed as a power law of the form V = aυDbυ. As with the mass–diameter relationship, several observational studies have shown the velocity–diameter relationship for unrimed snow particles to vary with habit types (Nakaya 1954; Bashkirova and Pershina 1964; Brown 1970; Jiusto and Bosworth 1971; Zikmunda 1972; Locatelli and Hobbs 1974; Kajikawa 1976; Heymsfield and Kajikawa 1987; Kajikawa 1989; Hanesch 1999). The habit-dependent velocity–diameter power laws used in this study are listed in Table 1. As was done for the mass–diameter power laws, we assigned one velocity–diameter power law to each habit category without regard to aggregates or single crystals. Again, this made sense for cold-type crystals, but required some compromise for dendrites, radiating assemblages of dendrites, and needles. For columns, we used a power law for single crystals, as no data on column aggregates were available. Little or no data were available for bullets or sectors/broad-branched (either single crystals or aggregates), so the Locatelli and Hobbs (1974) “cold type” velocity–diameter relationship was substituted. The choices for both the mass and velocity power laws are imperfect due to limited observations, but were made with the goal of “proof of concept” in mind for the habit sensitivity and habit-prediction applications described later in this paper. These relationships will be refined in future applications, using new field observations that we are presently gathering, as well as incorporating theoretically derived mass–diameter and velocity–diameter relationships (e.g., Mitchell 1996; Heymsfield et al. 2002; Mitchell and Heymsfield 2005).
The mass-weighted mean terminal velocity for snow is determined by multiplying the right-hand side of (1) by both the mass–diameter and velocity–diameter power laws, integrating over all sizes, dividing by the snow water content, and substituting (2), to yield
Note that this expression is dependent on am, bm, aυ, and bυ, all of which vary with particle habit type. Figure 2 shows how VS varies as a function of particle habit type and snow mixing ratio, using (4) and the power laws in Table 1. Also shown is a curve for “spheres,” which uses the mass of constant-density spheres but the fall velocity of cold-type particles. This combination of mass and velocity assumptions originated in the Rutledge and Hobbs (1983, 1984) scheme and is still used in the R-T scheme. While the differences in VS are small between the model-assumed spheres and the fully consistent approach for cold-type and needle-type particles, the differences are more substantial for dendritic snow particles (−50%) and columnar snow particles (+50%). Therefore, it appears that making greater and more consistent use of the empirically derived mass–diameter and velocity–diameter relationships in the bulk scheme could lead to significant improvements in the predicted precipitation.
3. Synoptic and mesoscale aspects of the observed and modeled storm
On 1–2 February 2001, during the first Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-1) field project, a cyclonic storm system located in the northeastern Pacific moved east toward the Pacific Northwest. The frontal structure, microphysical structure, and precipitation processes resulting from this system have been documented and extensively analyzed in Evans et al. (2005) and Locatelli et al. (2005), so only a basic summary of the synoptic and mesoscale aspects of the storm are given here. The event was characterized by a warm-type occlusion, with an upper cold front that extended ahead of the surface occluded front. At 500 hPa (Fig. 3a), the baroclinic zone associated with the upper cold front was characterized by a thermal gradient of 2°C (100 km)−1 behind its leading edge, compared to ≪1°C (100 km)−1 ahead of it. Upward motion immediately ahead of this baroclinic zone aloft produced the rainband that is the subject of the present study. The precipitation field of this rainband is seen in a radar summary at 0100 UTC 2 February 2001 (Fig. 3c).
The model simulation used in this study is identical to that described in Locatelli et al. (2005) in terms of time period, domain configuration, and physics options, with the following two exceptions. First, the initial and boundary conditions used for the simulation described in Locatelli et al. (2005) were interpolated directly from the National Centers for Environmental Prediction (NCEP) operational Eta Model forecast for the same time period. We later experimented with several different final analysis products [NCEP, European Centre for Medium-Range Weather Forecasts (ECMWF), etc.], and found the best simulation (in terms of position and orientation of the rainband) was obtained when initial and boundary conditions were produced using the NCEP–National Center for Atmospheric Research (NCAR) reanalysis gridded dataset as a first guess, enhanced on the model grid with all available surface and upper-air observations. As in Locatelli et al., the simulation was initialized at 1200 UTC 1 February 2001. Second, the simulation in Locatelli et al. (2005) used the Reisner et al. (1998) bulk microphysical scheme, whereas the present study used the R-T scheme as previously discussed.
In terms of synoptic features, such as height and thermal fields at standard synoptic pressure levels, the model simulation matched observations as well as or better than that seen in Figs. 2 and 3 of Locatelli et al. (2005). The 12-km model simulation (nested within a 36-km parent domain) produced an upper-level thermal field with enhanced baroclinicity behind the upper cold front, similar to observed (Figs. 3a,b). It also produced a banded precipitation field whose general location and orientation matched fairly well that of the observed rainband (Figs. 3c,d). Despite some errors in the model simulation (e.g., the model-depicted rainband is somewhat wider than observed, and the back edge of the simulated band is ∼1.5 h or 100 km behind the observed), the key characteristic for the present study is that there was a broad region of steady stratiform precipitation similar in character and intensity to the observed.
Subsequent analyses of the model-simulated rainband focus on two times: 0100 and 0200 UTC 2 February 2001. At 0100 UTC, the band was still primarily offshore (Fig. 4) and the University of Washington (UW) Convair-580 research aircraft was conducting a series of horizontal flight legs at various altitudes in the rainband to gather microphysical measurements. The precipitation in the rainband at this time was steady, moderate, widespread, and stratiform. The particle habit types observed by the Convair-580 within the vertical cross section are depicted in Fig. 5, taken from Evans et al. (2005). The habit types in Fig. 5 will be referred to later in this paper. An hour later (0200 UTC), the band approached the Olympic Mountains, resulting in significant orographic influence on the vertical velocity and microphysics of the band. Although there are no in situ observations to verify the microphysical behavior of the simulated band at this time and location, it is of interest to test the sensitivity of the model to different treatments of the microphysics in this dynamically more active environment.
4. Model sensitivities to realistic snow particle masses and velocities
a. Description of sensitivity tests
In this section, we explore the sensitivity of the model-simulated rainband to different universally applied snow particle habit types (in terms of particle mass and velocity assumptions). For each of the four different habit types shown in Fig. 1, two experiments were run (listed in Table 2): a “υ only” experiment, in which the constant density sphere assumption is retained for snow particle mass, but the velocity–diameter relationship for that habit (given in Table 1) is used; and an “m and υ” experiment, in which both the mass–diameter and velocity–diameter relationship for that habit (given in Table 1) are used. The “cold-type (υ)” experiment is the control run, utilizing the unmodified R-T scheme.
b. Model sensitivities in the rainband offshore
A plot of the 1-h accumulated precipitation from the control run at 0100 UTC 2 February (Fig. 4) shows the location of the rainband, and a line marking the location of vertical cross sections that are presented later in the paper. This line is approximately perpendicular to the rainband, and is also collocated with the vertical stack of flight legs flown by the Convair-580 at approximately this same time.
Because of the relative simplicity and steady-state nature of the microphysics in the rainband when it was offshore, the sensitivity tests showed only small differences in precipitation at the surface. However, there were significant differences in the microphysics aloft, primarily between the sensitivity tests that did or did not use the habit-based mass–diameter relationship. Fewer significant differences were seen between the different habit types assumed. Therefore, for the rainband offshore, we limit the presentation here to the differences between the “cold-type (υ only)” experiment and the “cold-type (m and υ)” experiment.
Note from Table 1 that bm for spheres is 3, whereas for cold-type particles, it is much closer to 2. This implies that, while the sphere assumption requires proportional growth in all three dimensions, cold-type particles grow in a two-dimensional fashion (although not in a flat plane), allowing them to become larger in terms of maximum diameter for the same amount of mass growth. The use of the mass–diameter relationship for cold-type particles resulted in what we interpret to be positive changes in the overall microphysics of the rainband. One such change was the reduction of the relative humidity with respect to ice (RHi) to values closer to 100% near 500 hPa, as expected for steady-state stratiform precipitation with modest vertical velocities (Locatelli et al. 2005).
The reduction in RHi in the midtroposphere in the cold-type (m and υ) experiment (Fig. 6) resulted from the effect of the new mass–diameter relationship on the slope parameter, λs. For the same mixing ratio, the cold-type mass–diameter relationship results in an increase in the number of particles and a shift in the size distribution to larger particles (due largely to the effect of bm discussed above), resulting in a reduction of λs (as illustrated in Fig. 1). While the dependence of the vapor deposition production term on λs is highly nonlinear, it can be qualitatively described as an inverse relationship, meaning larger particles more readily take up water vapor, and consequently, RHi is reduced. This occurred even in the presence of a slight increase in vertical velocity (not shown) in the cold-type (m and υ) simulation, confirming the microphysical cause of the RHi decrease. It is also consistent with the lack of dendritic crystals observed in their preferred temperature range for growth (−13° to −18°C) in the Evans et al. (2005) analysis (Fig. 5), since dendritic crystals also require high RHi (at or above water saturation) for growth (Magono and Lee 1966).
The increased efficiency of depositional growth within the primary band also acted to limit the vertical extent of the cloud water field in the cold-type (m and υ) run compared to the control run (Fig. 6). Cloud water mixing ratios exceeded 0.10 g m−3 at levels above the melting layer in the control run, compared to values closer to 0.02 g m−3 in the cold-type (m and υ) simulation. In both simulations, a band of increased cloud water existed immediately beneath the melting layer, associated with warm-frontal lifting (Evans et al. 2005). Above the melting layer, the presence of cloud water and subsequent riming of snow in the control run (Fig. 6a) resulted in the formation of graupel, whereas negligible graupel developed in the cold-type (m and υ) run (Fig. 6b). The cold-type (m and υ) run limited the condensation of cloud water above the melting layer by more efficiently taking up excess water vapor for snow growth, leaving little or no cloud water for riming. This result concurs with the absence of graupel shown in the Evans et al. (2005) analysis of this case and the slight increase in the precipitation rate across the band for the cold-type (m and υ) simulation.
c. Model sensitivities in the orographically influenced rainband
At 0200 UTC 2 February, the rainband approached the Olympic Mountains, and was affected by the orography. In this environment, more significant differences among all the experiments were seen. Figure 7 illustrates how the spatial distribution of precipitation at the ground varied for the different experiments. For the “υ only” experiments (Fig. 7, left column), alteration of the fall velocity alone resulted in significant horizontal displacements of precipitation, with the slowest falling particle type, dendrites, enhancing precipitation in the lee of the Olympics. All of the experiments that used habit-consistent velocity and mass relationships (“m and υ” experiments, Fig. 7, right column) produced heavier precipitation than the “υ only” experiments, particularly near the mountain barrier (with the exception of columns, whose mass–diameter relationship is close to that of spheres). Unfortunately, this result is in the opposite direction of what is needed to address the recurring finding in previous studies that the MM5 model generally overpredicts precipitation on the windward side of mountain barriers (Colle et al. 1999, 2005).
Further insight into the behaviors of the sensitivity tests is gained by examining a vertical cross section (Fig. 8) that cuts across both the rainband and the Olympic Mountains at 0200 UTC 2 February, as the forward portion of the rainband was interacting with the orographic barrier. The influence of snowfall velocity alone is evident in comparisons of the υ only experiments (Fig. 8, left column), with the least massive, slowest falling particle type (dendrites, Fig. 8c) resulting in precipitation rates of up to 1.5 mm h−1 extending into the lee of the Olympic Mountains. The dendrite experiment also resulted in higher cloud water mixing ratios off the Washington coast and upwind and downwind of the Olympic Mountain barrier, as a result of reduced collection by the slowly falling snow particles. On the other hand, the simulation using the fall velocity of columns (Fig. 8g), which fall most quickly of the different particle habit types, produced a relatively large and localized precipitation maximum on the lower windward slope.
More significant effects are seen in the experiments where both the mass and velocity of the snow particles were set to the habit-dependent values (Fig. 8, right column). Aloft, RHi levels decreased when the empirical mass–diameter relationship was introduced, for all habit types (cf. right column to left for each habit type). This occurred because for a given mixing ratio, the empirical mass–diameter relationship for all habits caused a shift in the size distribution to more and larger particles compared to spheres (see Fig. 1), and the more numerous and larger particles were able to take up excess water vapor more readily. The effect is strongest for needles, which had the largest size distribution shift (Fig. 1). This effect also is apparent in the cloud water field near the freezing level, which was reduced in the m and υ experiments (Fig. 8, right column) due to the enhanced ability of snow particles to take up excess water vapor. Additionally, the resultant graupel field (not shown) was greatly reduced for the cold-type, dendrite, and needle runs due to the reduction in cloud water above the melting level (Figs. 8b,d,f), thus limiting riming.
In terms of precipitation rate, the dendrite m and υ experiment (Fig. 8d) shows not only more precipitation reaching the ground, but also a more obvious shift of the precipitation toward the crest and lee of the mountain barrier than in the dendrite υ only experiment or any of the other experiments. This is because both the mass– and velocity–diameter relationships for dendrites act to reduce the mass-weighted mean fall velocity of snow compared to other habit types (or spheres). The needles m and υ experiment had the largest precipitation rate near the melting level, probably due to the efficient growth by vapor deposition mentioned above.
It is a testament to the complexity of feedbacks in the microphysical scheme that, even though all of the changes made in these sensitivity experiments directly affect only snow processes at or above the melting level, significant differences in precipitation rate below the melting level (i.e., the rain rate) are seen among the different experiments. These differences indicate the potential value of using more realistic representations of snow particle habit types in bulk microphysical schemes, particularly in terms of precipitation forecasts in regions of significant terrain. A first attempt at such a scheme is described in the next section.
5. An enhanced bulk microphysical scheme with snow habit prediction
a. Model description
The variability in behavior of the different habit sensitivity tests described above motivates the development of a bulk microphysical scheme that can predict the spatial and temporal variability of snow habit type, so that the predicted habits can be used to locally set habit-dependent parameters, instead of setting them universally to those of a single-habit type (as was done in the sensitivity tests). Although some attempts have been made at treating ice or snow particles of different habit types in microphysical schemes (see the discussion section), bulk schemes that have been developed to date generally do not predict the habit composition of the snow field.
For this study, we chose to predict seven habit types, described in Table 1. These habits were selected since they were thought to represent the most abundantly observed types of snow particles, according to our experience with both ground and aircraft observations. They also cover most of the depositional growth “phase space” defined by temperatures below 0°C and the relative humidity range from ice saturation to above water saturation, according to Magono and Lee (1966) and Bailey and Hallett (2002). The chart in Fig. 9 is used to assign depositional growth conditions for the seven habits represented. To keep the problem tractable, the chart is simplified in some regards compared to the depositional growth chart of Magono and Lee (1966), but as a first attempt, it captures the fundamental behavior of observed depositional growth habits.
Our approach for habit prediction in a single-moment bulk scheme is to replace the single prognostic equation for snow mixing ratio in the R-T scheme with seven prognostic equations, each of which predicts the mixing ratio of snow of a particular habit:
In the above, the subscript i refers to the ith habit of snow. The sum of these seven mixing ratios is the total snow mixing ratio, and the sum of the seven prognostic equations is equivalent (in both a continuous and discretized form) to the single prognostic equation for the total snow mixing ratio in the R-T scheme.
At each grid point and time step, the production terms arising from depositional growth and autoconversion of cloud ice are calculated based on the total snow mixing ratio (the sum of all the habits), but are added only to the habit whose depositional growth is expected to occur under the local conditions of temperature and humidity, as indicated by Fig. 9. This is represented by the switch ai in (5), which is equal to 1 for the habit that will grow locally, and 0 for all other habits. Each habit is also separately transported by advection and fallout as represented by the first line in (5). Thus, one habit type can grow under one set of conditions, and subsequently fall into a region of different conditions where its depositional growth ceases, but it can coexist with other habits that are now growing under the new conditions.
All other production terms for snow aside from depositional growth and autoconversion (such as collection of cloud water, sublimation, etc.) are also calculated based on the total snow mixing ratio (the sum of all the habits), but are distributed among the various habits in proportion to their local fraction of the total snow mixing ratio. This is represented by the third line in (5), where ri is the local mass fraction of the ith habit, that is, ri = qi/qs = qi/Σqi and Σri = 1. There is no obviously more physically plausible way to distribute these production terms, considering the simple manner in which coexisting habits are represented as described in the next paragraph.
In a standard bulk scheme, aggregation is essentially a self-collection mechanism, and so is not explicitly dealt with. It is implicitly represented by the fact that the empirically derived relationships for size distribution, fall velocity, etc., are based on observations of snow populations that were affected by the aggregation process (e.g., the temperature-dependent value of the size distribution intercept parameter used in the R-T scheme). In nature, particles of different habits obviously interact, but to keep track of all the different interactions in our scheme would rapidly become an intractable problem. In our method, we simplify the interactions by defining the habit mixing ratios in a general way, such that they do not refer to particles of a pure habit, but to the portion of the total snow mass that is in a particular habit, without regard to how the mass in each habit is distributed among single crystals, single-habit aggregates, or multihabit aggregates. In this framework, the many collection terms (collection of habit A by habit B) can be ignored. Thus, while the habit mixing ratios are separately predicted, the bulk approach to handling the snow field is retained for some properties and processes, to keep the complexity and computational cost manageable. For example, all snow at a grid point is still assumed to follow a single mass–diameter, velocity–diameter, and capacitance relationship. The key difference with the habit prediction approach is that, rather than using static snow parameters that are the same throughout the model simulation, we use dynamic values of the a and b parameters in the mass– and velocity–diameter power laws, determined (as described further below) from the locally predicted habit composition of snow. Other habit dependent aspects of the microphysical scheme could also be coupled to the predicted habits, such as the capacitance for depositional growth, or the habit-dependent size distribution behavior found by Woods et al. (2007). However, as a first step, this study limits the habit-dependent feedback to the mass– and velocity–diameter power laws for snow.
Because the production terms for snow are calculated for the snow species as a whole rather than separately for each habit, we require a single mass– and velocity–diameter power law at each grid point and time step, rather than seven different power laws. Therefore, the power-law coefficients (i.e., am, bm, aυ, bυ) used for the snow production terms at each grid point and time step are averages of the habit-specific values shown in Table 1, weighted by the local mass fractions of the predicted particle habits at each grid point:
where subscript i refers to the ith habit specified in Table 1. The product form of the averaging method for am arises because it made sense to have the habit-averaged power law be a linear combination of the component power laws on a log–log plot, where they appear as straight lines. A similar set of computations follows (6) and (7) to derive aυ and bυ for the velocity–diameter relationship.
b. Habit prediction results for the rainband offshore
The habit prediction method described above was applied to the wide cold-frontal rainband of 1–2 February 2001, using the same model arrangement described in sections 2 and 3. It is examined here at 0100 UTC 2 February when the band was still mostly offshore (analogous to the presentation in section 4b). In terms of surface precipitation, the habit prediction simulation of the rainband offshore (Fig. 10) was quite similar to the control run (Fig. 4) in position and intensity, as was the case for the single-habit sensitivity tests. Nevertheless, we examine the habit prediction results in the same vertical cross section seen in Fig. 6, to assess the ability of the model to predict the habits that were (or were not) observed by the Convair-580 aircraft.
Figure 11 shows the contribution to the total precipitation rate of each of the habits that grew in the new scheme. At heights above the −15°C level, cold-type particles were the dominant particle predicted and observed, while the presence of bullets, which naturally grow at temperatures below −40°C (Bailey and Hallett 2002), were also observed and predicted in much lower amounts. Dendrites, which require water-saturated conditions and temperatures near −15°C for growth, were not observed within the rainband from the aircraft data. The model also did not predict any radiating assemblages of dendrites or dendrites (and thus these habits are not shown in Fig. 11), a direct result of the updrafts not reaching water saturation within this key temperature zone.
At temperatures greater than −15°C, the aircraft analyses indicated that a variety of snow particles formed and included broad-branched particles, columns, and needles that formed below 5 km, as well as cold-type particles and bullets that fell into the lower regions from above (see Fig. 5). Figure 11b shows that above the 550-hPa level, cold-type particles grew as they fell (indicated by the substantial vertical gradient in precipitation rate there), whereas below that level, cold-type particles fell from above but did not grow (indicated by the lack of vertical gradient in precipitation rate there). Sectors, broad-branched particles, and columns are known to grow at both ice and water supersaturation at temperatures greater than −15°C, and since the model simulation had depositional growth occurring at these temperatures, the simulation produced those particle habits. Needles were observed in the lower regions of the rainband where water saturation existed. The simulation also predicted some needles, although in relatively small concentrations, and (unlike in the in situ observations) only on the periphery of the rainband (Fig. 11d). This suggests that, unlike in the observed case, the simulation produced water-subsaturated conditions in the lower portions of the rainband immediately beneath the strongest regions of snowfall where water vapor was readily used by growth of other particle types falling from above. Even though this discrepancy represents a failing of the model, it demonstrates that the habit prediction results, in conjunction with observations of snow habit types, provide further insight into why the error is occurring.
c. Habit-prediction results in the orographically influenced rainband
Shown in Fig. 12 are the precipitation rates for the different habits in the simulated rainband as it interacted with the Olympic Mountains. This cross section is at the same time and location as the sensitivity results shown in Fig. 8. As was the case when the rainband was offshore (Fig. 11), there are significant contributions from cold-type crystals (Fig. 12a), sectors/broad-branched (Fig. 12b), and columns (Fig. 12d). Above 600 hPa, most of the snow is of cold-type habit, and the precipitation rate is maximized within the frontally forced part of the rainband, which is still offshore (on the left side of Fig. 12a). Progressively warmer-type crystals (Figs. 12b–d) are less prevalent within the heart of the rainband (due to its upper-level forcing), and more prevalent within the upslope zone on the windward side of the Olympic Mountains. Needles (Fig. 12c) are particularly prominent in the upslope zone, where ascent is strong enough to produce the water saturation required for their formation. There was a minimal development of bullets aloft (not shown), similar to what was seen in the offshore cross section (Fig. 11). Dendrites and radiating assemblages of dendrites were again almost entirely inactive, with the exception of a narrow region on the far right-hand side of the cross section (not shown). Apparently, even with the enhancement of upward motion by the Olympic Mountains, the model still did not achieve water saturation in the dendritic growth temperature range.
It is also of interest to compare how the habit prediction result compared to the highly variable sensitivity tests that each used the mass and velocity properties of a single-habit type everywhere. The 1-h precipitation plan view from the habit prediction run (Fig. 13a), although generally similar to some of its counterparts from the single-habit sensitivity tests (Fig. 7), is not the same as any of them, confirming the benefit of representing different habits at different times and locations in the rainband. It produced heavier precipitation on the windward side of the Olympic Mountains than did the control run (Fig. 7a). The vertical cross section across the Olympic Mountains in the habit prediction run (Fig. 13b) also does not look the same as any of its counterparts from the sensitivity tests (Fig. 8). The RHi pattern aloft most closely resembles the cold-type (m and υ) run (Fig. 8b), since most of the snow in the habit prediction run was cold-type aloft. However, the precipitation rate pattern at and below the freezing level most closely resembles either of the “columns” runs (Fig. 8g or 8h), even though sectors/broad-branched, needles, and columns were present. These results serve to illustrate how the complex interactions within the microphysical scheme, and between the cloud microphysics and other physical and dynamical processes in the model, produce snow habit and precipitation distributions that would be difficult to anticipate without performing habit prediction.
Various mesoscale modeling efforts (McFarquhar and Black 2004; Cox 1988; Straka and Mansell 2005; Gilmore et al. 2004) have suggested that the variable characteristics of snow particles of different habits may significantly affect precipitation processes. The results of our sensitivity tests that examined the effects of setting the mass and velocity characteristics of snow particles to those of different snow particle habit types provide further supporting evidence that this is true.
Previous attempts have been made to account for varying snow particle habits in microphysical schemes. One approach has been to predict several different snow species (Straka and Mansell 2005; Lynn et al. 2005). However, in these schemes, the habit segregation is applied only to initial ice particles prior to aggregation. Aggregates of snow particles, which have been shown to dominate size spectra evolution in observed stratiform precipitation events (Houze et al. 1979; Lo and Passarelli 1982; Mitchell 1988; Ryan 2000; Field and Heymsfield 2003; Field et al. 2005), are still represented in these schemes by constant-density spheres. Thus, as soon as mass is transferred from the single-crystal ice categories to the snow aggregate category, which occurs on a fairly short time scale, no habit information is available to set habit-specific parameters, and the aggregate category is subject to the pitfalls of the constant-density sphere assumption found in the present study. Our approach to habit prediction attempts to retain information on the habit composition of snow independent of aggregation.
Another approach is that of Meyers et al. (1997), who diagnosed (rather than predicted) the habit of snow particles based on either current local temperature, or temperature at cloud top above a grid point. However, this approach did not account for the evolving growth history of the snow field in the different temperature/humidity zones through which it falls. Results from our experiments demonstrate the importance of accounting for the habit of snow particles that grow in one set of conditions and subsequently fall into lower regions where different conditions and habit growth exist.
As outlined in section 2, one of the key ways in which snow particle habit affects the microphysical scheme is through a change in the size distribution (for a given predicted snow mass), due to habit-dependent changes in the particle mass–diameter relationship. It should be noted that there are a variety of other approaches to improving the representation of particle size distributions in microphysical schemes, including changing the functional form from an exponential distribution to something that more closely matches observations, such as using a gamma distribution (Mitchell 1991) or using Field et al.’s (2005) distribution function (Thompson et al. 2006); predicting two moments (Meyers et al. 1997) or three moments (Milbrandt and Yau 2005) of the size distribution; or using an explicit (or “bin”) microphysical scheme (e.g., Hall 1980; Kogan 1991) instead of a bulk scheme. However, none of these approaches is mutually exclusive with the habit prediction approach described in this study. Habit prediction can be used in addition to, not instead of, these other approaches. Regardless of the level of sophistication used for the snow size distribution, mass–diameter and velocity–diameter relationships are still utilized, and a habit prediction approach that assigns habit-dependent values to the constants in these power laws moves the scheme closer to a realistic representation of the snow hydrometeor species.
In addition to the feedbacks of habit prediction within the scheme itself, habit prediction provides the useful side benefit of information on the habit composition of snow accumulating at the ground. Density of new snow is dependent on snow particle habit (Judson and Doesken 2000; Roebber et al. 2003) and is necessary for predicting snow depth from a model’s quantitative precipitation forecast. Both snow depth and density are important for the determination of vegetation covering in land surface models (Strack et al. 2004; Narapusetty and Mölders 2005), as well as for snow removal operations and winter recreational activities. Furthermore, the shear strength of new snow, which is also dependent on snow particle habit, as well as the density of new snow, are important parameters in avalanche science and modeling (e.g., Conway and Wilbour 1999). The probability of avalanche release increases when a dense layer of snow accumulates over a less dense layer, particularly when the shear strength of snow particles in the underlying layer is weaker. Snow habit prediction within a mesoscale model may enhance our ability to provide better forecasts in all of these realms. However, significant further work is required before these applications can become a reality.
In order for snow habit prediction to realize a fuller potential, additional work is necessary in both the modeling and observational realms. The habit prediction method could be enhanced by making use of additional habit-dependent parameters, such as the capacitance for depositional growth of snow particles, and the habit-dependent size distribution behavior found by Woods et al. (2007). Furthermore, the habit dependencies of these additional characteristics of snow particles, as well as the mass and velocity characteristics that were examined in the present study, need to be more firmly established with observations. In particular, more information is needed on the masses, velocities, and size distributions of aggregates of a wider variety of habit types, including both aggregates of single-habit types and of mixed habit types. Such information would provide guidance on the best way to calculate bulk properties when multiple habits are present in the model. Finally, it is reasonable to assume that the performance of the habit prediction scheme is resolution dependent, since at most temperatures, a different habit is produced depending on whether water saturation is reached or not, and it is likely that in many cases, a threshold grid spacing is required to produce the vertical velocities necessary to produce water saturation. We are currently experimenting with an orographic precipitation case from IMPROVE-2 to test this idea.
A mesoscale model simulation of the 1–2 February 2001 wide cold-frontal rainband that was observed in the Pacific Northwest during the IMPROVE-1 field study was used to test the sensitivity of the model-produced precipitation to varied representations of the characteristics of snow particles in a bulk microphysical scheme. Two approaches were used: the first was to examine the sensitivity of the model to universal changes in the snow particle characteristics (i.e., setting the mass and velocity versus diameter relationships for all snow to behave as dendrites, or needles, etc.). The second was to implement a snow habit prediction scheme, from which predicted habit composition of snow particles can be used to locally and dynamically change the mass and velocity characteristics of the snow particles. With both strategies, the model simulation was compared to in situ microphysical observations taken when the rainband was primarily offshore and microphysical processes were relatively simple and steady, and was also examined later when the band interacted with the Olympic Mountain barrier, producing a stronger and more complex microphysical response, but without observations for comparison.
Results of the sensitivity tests on the 1–2 February 2001 Pacific Northwest precipitation event demonstrated that alteration of the snowfall velocity does not substantially affect precipitation rate for widespread stratiform precipitation over a flat surface, but does significantly alter the distribution of orographically influenced precipitation. The assumption of snow particles as constant-density spheres results in a size distribution that is not representative of those obtained using any of the more realistic empirical mass–diameter relationships used in the sensitivity tests. The empirical mass–diameter relationships result in more and larger particles for the same mixing ratio (compared to the spherical assumption), which leads to increased depositional growth of snow, decreased humidity aloft, and decreased cloud water at mid- to low levels, all of which appeared to be an improvement compared to observations of the rainband when it was offshore. For the dendrites experiment, the empirical mass–diameter relationship worked in concert with the slower fall velocity to further redistribute precipitation toward the lee of the barrier when the rainband was interacting with orography. For all the habit types (except columns), the use of the empirical mass–diameter relationship resulted in heavier precipitation on the windward side of the mountain barrier, a result that will unfortunately not address the recurring finding in previous studies that the MM5 model overpredicts precipitation on the windward side of mountain barriers.
The habit prediction model was successful in producing habit types that were observed by aircraft in the 1–2 February 2001 rainband (and not producing those that were not) when the band was offshore. As with the single-habit sensitivity tests, the use of habit prediction did not significantly alter the surface precipitation rate in the relatively steady and widespread stratiform rainband offshore. However, it did increase the precipitation on the windward side of the Olympic Mountains when the rainband moved onshore and interacted with the orography (as also occurred with the sensitivity tests). When viewed three-dimensionally, the precipitation pattern in the habit prediction run resembled neither the control nor any of the sensitivity tests at all locations, demonstrating the merits of including habit prediction in the model.
Although applied here to only a single case, this study demonstrates the promise of the habit prediction approach to treating snow in bulk microphysical schemes. As the method matures, it should lead to new insights in snow microphysics, better quantitative precipitation forecasts, and new applications for forecasting of important properties of snowfall at the ground.
Thanks are due to Greg Thompson, Roy Rasmussen, Bill Hall, and Axel Siefert for fruitful discussions on cloud microphysical parameterization schemes. This research was supported by Grant ATM-0242592 from the National Science Foundation, Atmospheric Sciences Division.
Corresponding author address: Mark T. Stoelinga, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195. Email: email@example.com
Although the scheme does predict the number concentration of small ice particles (“cloud ice”), it is single moment in the cloud water, rain, snow, and graupel species.