Abstract

Several lake-effect-snow forecasts are compared to assess how the choice of microphysical parameterization affects quantitative precipitation forecasting (QPF). Eight different schemes, with different numbers of moments and categories of hydrometeors, are considered. Half of the schemes are in the steady regime (so named because the precipitation rates are nearly constant with time), and the remaining experiments are in the unsteady regime, which has a high temporal variation in precipitation. The steady-regime members have broader precipitation shields and 24-h accumulations that range from 43 to 50 mm. In the unsteady regime, the precipitation shields are narrower, leading to higher accumulations (ranging from 55 to 94 mm). These differences are the result of lower terminal velocities υt in the steady regime, which allows for relofting or suspension of hydrometeors (assuming the vertical velocity is sufficiently large) and, hence, a longer in-cloud residence time and stronger downstream transport. In the six-category experiments, low υt values in the steady regime occur in conjunction with a lower production of graupel, which is primarily due to less accretion of rain by snow. In the five-category experiments, differences are due to the way υt is functionally dependent on environmental temperature and the degree of riming, with the steady regime having a more conservative relation. The steady regime compares better to available observations, although both have notable forecast errors.

1. Introduction

One of the most challenging forecast problems in the Great Lakes region is the prediction of lake-effect snow (LES). Certain ingredients can be used to anticipate LES potential (e.g., Burrows 1991; Niziol 1987; Niziol et al. 1995), but quantitative precipitation forecasting (QPF) remains a formidable challenge (Ralph et al. 2005). Convection-allowing numerical forecasts may improve QPFs, but it is unclear to what extent QPF is dependent on parameterized processes. Herein, the sensitivity to microphysical parameterization is tested.

Lake-effect snow—snow that occurs downwind of large lakes during late autumn or early winter—is the result of subfreezing air moving over relatively warm water. Destabilization of the lower portion of the atmosphere may result in vigorous convection and localized banding near the lake shore. It can be categorized as 1) widespread wind-parallel bands or open-cell convection (Kelly 1982, 1984), 2) single alongshore bands (Ballentine 1982; Braham 1983; Hjelmfelt and Braham 1983; Hjelmfelt 1990), 3) single midlake bands (Peace and Sykes 1966; Passarelli and Braham 1981; Braham and Kelly 1982; Braham 1983; Hjelmfelt 1990; Niziol et al. 1995), and 4) mesoscale vortices (Forbes and Merritt 1984; Kelly 1986). Types 2 and 3 usually yield the heaviest accumulations (Hjelmfelt 1990).

Lake-effect-snow potential can be assessed using a set of ingredients including the temperature difference between the lake surface and 850 hPa (Holroyd 1971), wind shear and direction (Juisto and Kaplan 1972; Niziol 1987), the depth of the mixed layer (Byrd et al. 1991), the upwind relative humidity (Kristovich and Laird 1998), the height of the capping inversion (Rothrock 1969; Holroyd 1971), and whether there exists synoptic-scale forced ascent (Niziol et al. 1995). While these ingredients are helpful for determining the likelihood, timing, and structure of LES (assuming large-scale flow patterns are well forecast), only rough estimates of precipitation can be gleaned using this approach. Yet, LES represents a significant disruption in the local economy. Persistent bands may produce excessive snowfall (>100 cm) in a given location while nearby areas receive little or no snow (Niziol 1987; Burrows 1991), and heavy snow can combine with even moderate wind to produce whiteout conditions (Kristovich et al. 2000).

Recent years have seen a rise in the number of forecast offices performing numerical model forecasts with grid spacings capable of resolving some bands (2–5 km). These models may provide a valuable tool for improving QPFs, but surprisingly little work has been published on the subject. Publications in recent years include Ballentine et al. (1998), who perform a 5-km grid-spaced simulation of a single event. They note that band type is well forecast, but the QPF is poor, with no specific trend across the domain. In a comparative study of several numerical forecasts, Sousounis et al. (1999) state that the models were of little use for QPF because of strong model-to-model differences in parameterized processes. Lackmann (2001) and Scott and Sousounis (2001) also consider numerical forecasts of LES, but neither discuss QPF. Last, Shi et al. (2010) consider an LES simulation with 1-km grid spacing and show that reasonable QPFs can be attained.

The QPF is modified by the degree of crystal growth, aggregation, riming, and availability of supercooled liquid water (e.g., Braham 1983, 1990; Agee and Hart 1990; Chang and Braham 1991; Barthold and Kristovich 2011): processes handled by the microphysical parameterization scheme. Studies comparing QPF for cool-season precipitation in the western United States show that some schemes tend to overpredict precipitation as a result of too early a fallout of graupel while other schemes have more snow and, consequently, stronger downstream hydrometeor transport (Colle et al. 2005; Garvert et al. 2005; Richard et al. 2007; Lin and Colle 2009; Jankov et al. 2009; Liu et al. 2011). No similar study has been published with regard to LES, but a trend toward more graupel may lead to narrower, heavier bands that are closer to the shore while a trend toward more snow may lead to lighter accumulations that are more broadly distributed.

The aim of this study is to assess how the microphysical parameterization scheme affects QPF and why differences occur. This paper is organized as follows. A synopsis of the event is provided in section 2. The numerical sensitivity experiment results are discussed in section 3, and concluding remarks are made in section 4.

2. Case-study description

The event occurs between 10 and 12 December 2009 off Lake Erie. The observed composite reflectivity shows a complex evolution. At 0300 UTC 10 December, there are two regions of enhanced precipitation over or near Lake Erie (Fig. 1a). The stronger is northeast of the Buffalo, New York (BUF), radar and the second surrounds the Cleveland, Ohio (CLE), radar. (Radar locations are indicated in Fig. 1f.) Automated Surface Observing Station (ASOS) data report only light snow at either location at this time. By 0900 UTC, the band has weakened to the south and strengthened to the north, extending straight off the northeast corner of the lake and over the greater Buffalo area (Fig. 1b). Surface observations report heavy, blowing snow at this time. Over the next 6 h, the band over Buffalo moves about 30 km south while maintaining maximum reflectivities approaching 35 dBZ (Fig. 1c), with surface reports of heavy, blowing snow. The southern half of the band continues to produce only light snow. By 2100 UTC, the band has elongated, stretching from CLE to northeast of BUF (Fig. 1d). (The apparent discontinuity just off the Pennsylvania shore is an artifact of area radars overshooting the cloud top.) The band also has adopted a double-banded structure at this time. Weakening occurs over the next 6 h (Fig. 1e), and the band dissipates shortly afterward (not shown).

Fig. 1.

(a)–(e) Mosaics of Weather Surveillance Radar-1988 Doppler composite radar reflectivity and (f) 24-h liquid-equivalent accumulated precipitation starting at 1200 UTC 10 Dec 2009. These figures are provided by the NMQ project (Vasiloff et al. 2007). The markers in (f) show the locations of area radars and selected surface observing stations.

Fig. 1.

(a)–(e) Mosaics of Weather Surveillance Radar-1988 Doppler composite radar reflectivity and (f) 24-h liquid-equivalent accumulated precipitation starting at 1200 UTC 10 Dec 2009. These figures are provided by the NMQ project (Vasiloff et al. 2007). The markers in (f) show the locations of area radars and selected surface observing stations.

Although there are interesting meteorological features throughout the time shown in Figs. 1a–e, our attention is focused on the hydrologic day starting at 1200 UTC 10 December. It is during this 24-h period that the greatest precipitation falls and the most intense convection occurs [between 2000 and 2100 UTC 10 December (Fig. 1d)]. The 24-h accumulated liquid-equivalent precipitation, according to the National Mosaic Multisensor quantitative precipitation estimate (NMQ-QPE; Vasiloff et al. 2007), shows that the heaviest accumulations (ranging from 25.4 to 38 mm) are just south of BUF (Fig. 1f). A second maximum is northeast of CLE.

The Rapid Update Cycle (RUC; Benjamin 1989) analysis at 2000 UTC 10 December shows strong, southwesterly low-level flow, allowing for maximum airmass modification via sensible and latent heat flux over Lake Erie (Fig. 2a; Laird et al. 2003a,b; Laird and Kristovich 2004). Low-level relative humidity RH over the lake is between 90% and 95%, indicating that even shallow ascent is likely to produce clouds and precipitation. Temperature differences between the lake and 850 hPa are well above the 13-K threshold deemed favorable for LES (Holroyd 1971). The lake and 700-hPa temperature differences are even greater, exceeding 30 K (not shown), putting this event in the extreme-instability category (Niziol et al. 1995). At 850 hPa, a shortwave trough is over western New York (Fig. 2b). The associated vertical velocity patterns show ascent over the east side of the lake, with a maximum just south of BUF. The trough was present during the times of heaviest convection.

Fig. 2.

The 2000 UTC 10 Dec 2009 RUC analysis of (a) the difference between the lake-surface and 850-hPa temperatures (shaded) and 975–850-hPa layer-averaged relative humidity (contoured) and wind barbs, (b) 850-hPa heights (m; contoured) and vertical velocity (shaded), and (c) the temperature (solid) and dewpoint (dashed) profiles at BUF. Times are indicated as DD/HHZ, where DD is the day and HH is the hour (UTC). The “10/12Z” and “11/00Z” soundings are observed. The “10/20Z” sounding is from the RUC analysis. In this and all other figures showing wind barbs, one full barb is 5 m s−1.

Fig. 2.

The 2000 UTC 10 Dec 2009 RUC analysis of (a) the difference between the lake-surface and 850-hPa temperatures (shaded) and 975–850-hPa layer-averaged relative humidity (contoured) and wind barbs, (b) 850-hPa heights (m; contoured) and vertical velocity (shaded), and (c) the temperature (solid) and dewpoint (dashed) profiles at BUF. Times are indicated as DD/HHZ, where DD is the day and HH is the hour (UTC). The “10/12Z” and “11/00Z” soundings are observed. The “10/20Z” sounding is from the RUC analysis. In this and all other figures showing wind barbs, one full barb is 5 m s−1.

The nearest observed soundings are at BUF at 1200 UTC 10 December and 0000 UTC 11 December. These show the lowest 300 hPa cooled by about 6 K during this period (Fig. 2c). The 2000 UTC RUC sounding has temperatures in the dendrite growth zone (from −12° to −18°C) between 875 and 800 hPa. This layer coincides with the layer of maximum vertical velocity, according to the RUC analyses (not shown). All soundings have a capping stable layer at about 700 hPa and weak vertical wind shear. Only the 2000 UTC sounding has saturated conditions in the lower part of the atmosphere. Consideration of the observed radar reflectivity shows that at the other times the band was south of the sounding location.

3. Experiment design and results

a. Experiment design

Eight experiments are conducted using the Advanced Research version of the Weather Research and Forecasting model (ARW-WRF; Skamarock et al. 2005), version 3.2.1. The horizontal grid spacing is 4 km; there are 51 vertical levels and 200 grid points in the x and y directions. The grid spacing and number of vertical levels are similar to those used in high-resolution operational models run by the National Weather Service. There may be some dependence on the grid spacing, but this is not tested herein. All experiments use the “Noah” land surface model (Ek et al. 2003), Mellor–Yamada–Janjić boundary layer parameterization (Janjić 2002), and Dudhia longwave and shortwave radiation schemes (Dudhia 1989). No convective parameterization scheme is used. The initial conditions are given by the 12-km North American Mesoscale (NAM; Janjić et al. 2005) model analyses, and boundary conditions are updated using the associated NAM model forecasts every 3 h.

Both single- and double-moment as well as five- and six-category microphysical parameterization schemes are tested. These are the Goddard (GD; Tao et al. 2003), WRF single-moment six-category (WSM6; Hong et al. 2004), Thompson (TSON; Thompson et al. 2004); WRF double-moment six-category (WDM6; Lim and Hong 2010); Morrison (MORR; Morrison et al. 2005); Milbrandt–Yau (MY; Milbrandt and Yau 2005); Stony Brook University/Lin (SL; Lin and Colle 2011); and Ferrier (FR; Ferrier 1994; Skamarock et al. 2005) schemes. Key differences between the schemes are listed in Table 1.

Table 1.

A summary of experiments, their key attributes (υ is water vapor, c is cloud water, i is cloud ice, s is snow, r is rain, and g is graupel), and the area-integrated liquid-equivalent precipitation for a parallelogram surrounding the band (see Fig. 3c).

A summary of experiments, their key attributes (υ is water vapor, c is cloud water, i is cloud ice, s is snow, r is rain, and g is graupel), and the area-integrated liquid-equivalent precipitation for a parallelogram surrounding the band (see Fig. 3c).
A summary of experiments, their key attributes (υ is water vapor, c is cloud water, i is cloud ice, s is snow, r is rain, and g is graupel), and the area-integrated liquid-equivalent precipitation for a parallelogram surrounding the band (see Fig. 3c).

The forecasts are initialized at 0000 UTC 10 December 2009 and are integrated for 36 h. Because there are no hydrometeors in the initial conditions and to allow the experiments time to produce divergent results, the first 12 h of integration are not considered. Given the grid spacing and lead times considered, it is unreasonable to expect the forecasts to capture some of the microscale detail noted in the observations, such as the splitting of the band into two parallel bands at 2100 UTC, or the slight shifts in location between 0900 and 1500 UTC (Figs. 1b–d). One would expect the overall patterns and daily accumulation to be captured, however.

b. Forecast precipitation accumulations

Based on the precipitation rates, which are discussed in the next paragraph, the experiments are classified as belonging to a steady or unsteady regime. The 24-h liquid-equivalent precipitation accumulations in the steady regime have maxima that range from 29 to 50 mm (Figs. 3a,c,e,g), whereas maxima in the unsteady regime are between 52 and 94 mm (Figs. 3b,d,f,h). The axis of maximum precipitation is also differently placed. In the steady regime, it is between 10 and 30 km east of Lake Erie; in the unsteady regime, it is adjacent to the coast. Last, the precipitation shields in the steady regime are slightly broader than in the unsteady regime. This is particularly obvious between SL and FR (Figs. 3g,h). Note that the regimes are not partitioned by the number of moments or hydrometeor categories (Table 1).

Fig. 3.

The forecast (a)–(h) 24-h (starting at forecast hour 12) liquid-equivalent accumulated precipitation (local maxima are indicated) for each of the microphysics experiments labeled in each panel, and (i) hourly band-maximum precipitation.

Fig. 3.

The forecast (a)–(h) 24-h (starting at forecast hour 12) liquid-equivalent accumulated precipitation (local maxima are indicated) for each of the microphysics experiments labeled in each panel, and (i) hourly band-maximum precipitation.

A time sequence of the band-maximum precipitation—defined as the maximum within a parallelogram surrounding the band (e.g., Fig. 3c)—shows that unsteady-regime maxima are nonconstant, with multiple peaks and lulls (Fig. 3i). Experiments in the steady regime have near-constant hourly maxima. Thus, the nomenclature of steady and unsteady is used. To more efficiently address the cause for the different patterns, a comparison of WSM6 and GD at forecast hours 20–21 (fhr20 and fhr21), when differences between the schemes are the greatest, is performed. The WSM6 and GD schemes are both six-category and single-moment.

c. An explanation for the two regimes

Differences between the flow patterns cannot account for the different regimes. At fhr20, both GD and WSM6 have low-level flow that is nearly parallel to the long axis of the lake and a temperature difference between the lake and 850 hPa that ranges from 22 to 27 K (Figs. 4a,b). The RH is also similar, with values of greater than 70% over most of the lake and a local maximum near the New York–Pennsylvania border. Soundings at BUF show low-level cooling between 1200 UTC 10 December and 0000 UTC 11 December for both GD and WSM6 (Figs. 4c,d). The wind profiles are also similar, with each having very little directional shear. The low-level humidity is much less than in the observed and RUC-analyzed soundings (Fig. 2c). This is likely because the band in the forecasts is shunted south of its observed location (cf. Figs. 3 and 1d). The reason for this is unclear, but since all experiments are similar in this regard, the phenomenon is likely not a microphysics issue. Rather, it may be due to errors in the initial or boundary conditions or in one of the other physical parameterization schemes. Hence, it is investigated no further.

Fig. 4.

The (a),(b) forecast difference between the lake-surface and 850-hPa temperatures (shaded) and 975–850-hPa layer-averaged relative humidity (contoured) and wind vectors at 2000 UTC 10 Dec 2009 and (c),(d) forecast temperature (solid) and dewpoint (dashed) profiles at BUF for (left) GD and (right) WSM6.

Fig. 4.

The (a),(b) forecast difference between the lake-surface and 850-hPa temperatures (shaded) and 975–850-hPa layer-averaged relative humidity (contoured) and wind vectors at 2000 UTC 10 Dec 2009 and (c),(d) forecast temperature (solid) and dewpoint (dashed) profiles at BUF for (left) GD and (right) WSM6.

One might presume that members of the unsteady regime periodically produce greater quantities of precipitating hydrometeors, but this is not the case. The area-integrated precipitation within the parallelogram in Fig. 3c is calculated as a function of time (Fig. 5a). The curves are similar for all experiments, as are the 24-h area-integrated accumulations (Table 1), suggesting that similar quantities of hydrometeors are produced regardless of the regime. The total precipitation mixing ratio qpr, which is the sum of the mixing ratios of snow, rain, and graupel (qs, qr, and qg), integrated over the whole depth of the atmosphere, also refutes the above hypothesis. At fhr20, GD has higher qpr along most of the band (although the maxima are comparable (Figs. 5b,c). Yet, Figs. 5a–c hold some important clues. In Fig. 5a, the unsteady regime members (excepting FR) have local maxima at fhr21. The corresponding maxima in the steady regime occur at fhr22. This may be the result of the steady regime allowing for longer hydrometeor residence times. In GD, the qpr maximum is farther downstream, toward the northeast end of the band, whereas in WSM6 it is more toward the center of the band (Figs. 5b,c), suggesting less downstream transport in WSM6.

Fig. 5.

The forecast (a) hourly area-integrated precipitation for the area shown by the parallelogram in Fig. 3c, (b) GD and (c) WSM6 fhr20 vertically integrated qpr (maximum values are indicated), and (d) GD and (e) WSM6 vertical cross sections of qpr (shaded) and vertical velocity (cm s−1; contoured) along the line labeled SW–NE [see (b) and (c) for its location]. Vertical velocity maxima are indicated with white numerals in (d) and (e).

Fig. 5.

The forecast (a) hourly area-integrated precipitation for the area shown by the parallelogram in Fig. 3c, (b) GD and (c) WSM6 fhr20 vertically integrated qpr (maximum values are indicated), and (d) GD and (e) WSM6 vertical cross sections of qpr (shaded) and vertical velocity (cm s−1; contoured) along the line labeled SW–NE [see (b) and (c) for its location]. Vertical velocity maxima are indicated with white numerals in (d) and (e).

Vertical cross sections of qpr and vertical velocity w parallel to and through the snowband provide even more clues. In GD, the qpr maximum is above the w maximum (Fig. 5d). This offset suggests that the hydrometeor terminal velocity is less than the upward ascent, leading to upward advection of hydrometeors, a longer in-cloud residence time, and allowing for enhanced downstream transport. The opposite appears to be true in regions of lower vertical velocity: at about 225 km, where there is a relative w minimum, the high qpr is able to penetrate to the surface. In WSM6, the qpr maximum is at or below the w maximum and lessens toward the northeast. In this case, it appears that falling hydrometeors are able to descend through the updraft and exit the cloud farther upstream.

By using hydrometeor trajectories, one can directly assess whether the steady regime has longer residence times and more downwind drift. For each experiment, 97 trajectories are calculated whose origins are given by the gray dots in Fig. 6. All trajectories are started at fhr20 and at 850 hPa and are traced until they hit the ground. For each trajectory, the terminal velocity υt of the dominant hydrometeor type at each location along the trajectory path is used. Hydrometeors are allowed to be transported both horizontally and vertically. The ambient wind and mixing ratios are updated every 60 s. All steady-regime experiments have strong downstream transport, a comparatively broad distribution of hydrometeors, and an average residence time of 39 min (Figs. 6a,c,e,g). All of the unsteady-regime members have a long and narrow distribution with comparatively small downstream transport and an average residence time of 17 min (Figs. 6b,d,f,h). The 1-h accumulated precipitation starting at fh20 has patterns that are consistent with the trajectories, with the steady-regime members having broader shields and lower maxima than the unsteady-regime members (Fig. 6).

Fig. 6.

The 1-h liquid-equivalent accumulated precipitation starting at fhr20 (shaded) and the start (gray dots) and end (black dots) points of hydrometeor trajectories for each of the experiments labeled in each panel. The average residence time for the trajectories is given in the lower right of each panel.

Fig. 6.

The 1-h liquid-equivalent accumulated precipitation starting at fhr20 (shaded) and the start (gray dots) and end (black dots) points of hydrometeor trajectories for each of the experiments labeled in each panel. The average residence time for the trajectories is given in the lower right of each panel.

d. Vertical velocity and hydrometeor mixing-ratio distributions

A likely contributor to enhanced downstream drift is the vertical velocity w. In Figs. 5d and 5e, individual maxima in GD are larger than their apparent counterparts in WSM6. However, these are instantaneous values that change rapidly in time and space. A better comparison is obtained by considering time and spatial averages along line “SW–NE” for the entire 24-h period starting at 1200 UTC 10 December. The bands do change from a single, alongshore form to a multibanded structure during this time (not shown), but the strongest convective elements are positioned along line SW–NE throughout the entire period. All experiments have a w maximum near 850 hPa (Fig. 7a). There is no trend for the steady-regime experiments to have higher w. The line-averaged w at fhr20 and fhr24 is also plotted (Figs. 7e,i). At fhr20, there is more spread in the maximum w, but there is no partitioning by regime. At fhr24, the differences between the regimes is minimal and the precipitation rates decrease (Fig. 3i). As expected, the line-averaged w is much smaller, near 0 m s−1.

Fig. 7.

Spatially averaged (along line SW–NE in Figs. 5b,c) vertical profiles of (a),(e),(i) w, (b),(f),(j) qpr, (c),(g),(k) qs, and (d),(h),(l) qg for a temporal average between (top) fhr12 and fhr36, (middle) fhr20, and (bottom) fhr24. The line styles corresponding to each experiment are indicated in (b).

Fig. 7.

Spatially averaged (along line SW–NE in Figs. 5b,c) vertical profiles of (a),(e),(i) w, (b),(f),(j) qpr, (c),(g),(k) qs, and (d),(h),(l) qg for a temporal average between (top) fhr12 and fhr36, (middle) fhr20, and (bottom) fhr24. The line styles corresponding to each experiment are indicated in (b).

The temporally and spatially averaged qpr show a distinct regime separation, with the steady-regime experiments having their maxima at about 775 hPa and the unsteady-regime experiments having their maxima between 850 and 800 hPa (Fig. 7b). A similar distinction occurs at fhr20 (Fig. 7f). Partitioning qpr by its component parts qs and qg (qr is negligible for all experiments) shows that graupel accounts for between 30 and 50% of the total qpr while the steady-regime experiments have little to no qg for both the temporally averaged profiles and at fhr20 (Figs. 7c,d,g,h). At fhr24, there is still a difference between the height of the qpr maxima in the two regimes, which is unexpected since there is no clear regime separation at this time and almost all precipitate is snow (Figs. 7j–l). We note, however, that WSM6, WDM6, and MY all assume a snow density of 500 kg m−3 while GD, TSON, and MORR assume it is 400 kg m−3. There are other minor differences in assumptions used to determine the snow υt that allow for faster fallout in the unsteady regime.

One subtlety worth noting in Fig. 7b is the difference in the qpr-maximum height for the unsteady-regime experiments. All but MY have their qpr maxima at about 850 hPa, whereas in MY it is at 800 hPa. This is a likely consequence of size sorting by the MY scheme. In single-moment schemes, all graupel falls with a uniform υt, whereas schemes that predict the number concentration of graupel allow larger particles (i.e., those with larger mean diameters) to have higher υt, leaving smaller particles lofted at higher altitudes. Consideration of vertical profiles of mean diameter shows that larger diameters are, indeed, found at lower altitudes (not shown). The same phenomenon does not occur in MORR. Snow, which is the dominant hydrometeor form for this scheme, has very little diversity in fall speed. So one would expect MORR to have hydrometeor transport and precipitation patterns that are similar to those of the other steady-regime experiments (cf. Figs. 6a,c,e).

e. Graupel in the six-category schemes

The effects of differences in qg content are determined by forcing all graupel to have the same υt as that for snow in WSM6, WDM6, and MY. The resulting 1-h liquid-equivalent precipitation accumulations starting at fhr20 are similar to the steady regime, having smaller maxima and broader shields (cf. Figs. 6a,c,e and 8a,b,c) implicating the higher qg content in some schemes as the primary cause for the different regimes.

Fig. 8.

The 1-h liquid-equivalent accumulated precipitation for the modified terminal-velocity experiments starting at fhr20. Experiments are indicated in each panel.

Fig. 8.

The 1-h liquid-equivalent accumulated precipitation for the modified terminal-velocity experiments starting at fhr20. Experiments are indicated in each panel.

An understanding for the enhanced graupel production in the unsteady regime is achieved by considering the graupel tendency as a function of its dominant control parameters: hydrometeor mixing ratios and temperature. (For these experiments, the water vapor mixing ratio is set to ice saturation and the pressure is set to 850 hPa.) Let us first consider as a function of temperature only. For this, both schemes are given initial cloud and hydrometeor mixing ratios from WSM6 at fhr20 (see Fig. 9a for values) and the schemes are integrated for one time step (12 s). Given the range of temperatures shown, the WSM6 scheme has a higher than GD. The as a function of qs, qr, and cloud and ice mixing ratios (qc and qi) is also lower in GD than in WSM6 for the ranges considered (Figs. 9b–e). The functional dependence on qg is nearly identical in both schemes (not shown).

Fig. 9.

The graupel tendency as a function of (a) temperature and (b)–(e) hydrometeor mixing ratio for the WSM6 (solid) and GD (dashed) schemes. The constants used for each comparison are provided at the tops of the panels.

Fig. 9.

The graupel tendency as a function of (a) temperature and (b)–(e) hydrometeor mixing ratio for the WSM6 (solid) and GD (dashed) schemes. The constants used for each comparison are provided at the tops of the panels.

To determine why GD has lower , the is partitioned according to the processes that act on it. The results, along with the initial temperature, pressure, and mixing ratios used in the calculation, are provided in Table 2. According to these calculations, the primary reason GD has lower is that Pracs is an order of magnitude less than in WSM6.1

Table 2.

The graupel tendency (g kg−1 s−1) and budget for the WSM6, GD, and modified GD microphysical parameterization schemes, assuming a pressure of 850 hPa, temperature of 264 K, qs and qg of 1 g kg−1, qr of 2.5 × 10−6 g kg−1, qc of 0.3 g kg−1, and qi of 0.1 g kg−1.

The graupel tendency  (g kg−1 s−1) and budget for the WSM6, GD, and modified GD microphysical parameterization schemes, assuming a pressure of 850 hPa, temperature of 264 K, qs and qg of 1 g kg−1, qr of 2.5 × 10−6 g kg−1, qc of 0.3 g kg−1, and qi of 0.1 g kg−1.
The graupel tendency  (g kg−1 s−1) and budget for the WSM6, GD, and modified GD microphysical parameterization schemes, assuming a pressure of 850 hPa, temperature of 264 K, qs and qg of 1 g kg−1, qr of 2.5 × 10−6 g kg−1, qc of 0.3 g kg−1, and qi of 0.1 g kg−1.

The equation for Pracs in GD and WSM6 is based on Lin et al. [1983; see their Eq. (27)], and can be approximated by

 
formula

where n0s is the intercept parameter for snow and Δυt is the difference between terminal velocities of different hydrometeor species (see below). In GD, n0s is 1.6 × 107 m−4. In WSM6, n0s is temperature dependent so that it is larger for colder temperatures. Its n0s values in the lowest 300 hPa above ground range from 2 × 106 to 6 × 106 m−4. The higher n0s in GD implies a high concentration of small hydrometeors, which may be appropriate in stratiform precipitation but is not likely to be representative in convective winter weather. Indeed, measurements of n0s from LES in western Michigan range from 0.4 × 106 to 8.75 × 106 m−4 (Braham 1990). The remaining six-category schemes use n0s values that are similar to that in WSM6. Changing n0s in GD so that it is the same as in WSM6 increases Pracs somewhat, but there is still an order-of-magnitude difference between the two (not shown).

The term Δυt in GD is given by υtrυts, where the subscripts r and s denote rain and snow. In WSM6 (and WDM6), it is expressed as

 
formula

(from Hong et al. 2004). If Δυt from WSM6 is substituted into GD, the resulting budget has an order-of-magnitude increase in Pracs, making it more comparable to WSM6 (Table 2). The term Psacr also increases substantially, but this term is not significant in the overall budget. Because the interactions between hydrometeor species are nonlinear, simply adjusting the equation for Δυt so that it is identical to that from another scheme may yield unreasonable distributions of hydrometeor mixing ratios after several time steps; hence, no full forecasts with an altered Δυt are attempted.

Consideration of how the other six-category schemes compute Pracs shows that they, too, use different approaches. The TSON and MORR schemes use a Δυt that is based on that from Reisner et al. [1998, their Eq. (A.48)]:

 
formula

TSON also assumes a collection efficiency that is less than 1, which further reduces Pracs in comparison with the other schemes. The MY scheme uses the Murakami (1990) version:

 
formula

The best choice of Δυt for LES is unclear.

f. Riming in the five-category schemes

The SL and FR schemes presume Δυt is a function of the riming intensity RI—a parameter that quantifies the amount of riming on a frozen hydrometeor. This allows for a more realistic spectrum of fall speeds. The RI at 850 hPa and fhr20 is shown in Figs. 10a and 10b. Since each scheme uses a different scale, the ranges that represent low, moderate, and heavy riming are indicated. Contrary to what one may expect, SL has considerably more riming than FR. This is true throughout the cloud layer. Therefore, the differences in trajectory patterns (Figs. 6g,h) are not due to heavier riming, as in the six-category schemes, but to the way υt is dependent on RI.

Fig. 10.

The (a),(b) 850-hPa riming intensity RI at fhr20 and (c),(d) terminal velocity υt (m s−1) as a function of temperature T and RI. For the (left) SL scheme, a qs of 0.25 g kg−1, and a pressure of 850 hPa are used. For the (right) FR scheme, a qs of 0.25 g kg−1, a qc 0.05 g kg−1, a pressure of 850 hPa, and a water vapor mixing ratio that is saturated with respect to ice are used.

Fig. 10.

The (a),(b) 850-hPa riming intensity RI at fhr20 and (c),(d) terminal velocity υt (m s−1) as a function of temperature T and RI. For the (left) SL scheme, a qs of 0.25 g kg−1, and a pressure of 850 hPa are used. For the (right) FR scheme, a qs of 0.25 g kg−1, a qc 0.05 g kg−1, a pressure of 850 hPa, and a water vapor mixing ratio that is saturated with respect to ice are used.

In SL, both RI and temperature T are used to determine the power-law relation for υt, which is based on Heymsfield and Donner (1990) and Locatelli and Hobbs (1974). The mean fall velocity is then calculated over the whole size spectrum (B. Colle, Stony Brook University, 2012, personal communication). Consideration of υt as a function of RI and T shows that the T dependence is very small while the RI dependence is strong (Fig. 10c). In FR, υt is given by s, where f (∝ expT lnRI) is a tuning function and υs is the mass-weighted snow terminal velocity that is based on that from Böhm (1989). The FR υt as a function of T and RI has a very strong dependence on RI for RI < 2 but otherwise is nearly independent of it (Fig. 10d). For RI > 2, υt is strongly dependent on T. The stepwise pattern in Fig. 10d is the result of the scheme using lookup tables rather than making direct computations. The reader is referred to Skamarock et al. (2005) and Lin et al. (2011) for more details on the relations between υt and RI/T. According to Figs. 10c and 10d, only for T < 262 K and RI > 0.75 in SL will the SL scheme have higher υt. This condition is never met in these experiments.

g. Comparison with observations

Comparison of Figs. 1f and 3a–h suggests that the steady regime more closely matches the estimated precipitation. Yet, there are limitations to a direct comparison of Figs. 1f and 3. First, the radar observations show a clear north-to-south wobbling of the band between 0900 and 2100 UTC (Figs. 1b–d), which could account for the relatively diffuse precipitation pattern. No such wobbling occurred in any of the experiments (not shown). Second, the radar-based estimate in Fig. 1f cannot account for relofting of hydrometeors or the generation of hydrometeors below the lowest elevation scan. Even though the QPEs are corrected using ground truth observations, if the observations are substantially different from the radar first guess then they are discarded [J. Zhang, National Oceanic and Atmospheric Administration (NOAA)/National Severe Storms Laboratory, 2011, personal communication]. To have a more direct comparison, a model-derived QPE is calculated. This is done by presuming that all hydrometeors along the 0.5° elevation angle at all radar locations (Fig. 1f) fall directly to the ground. The model data are output every 5 min for this task, and the precipitation rate is assumed to be constant over this time period. The 5-min accumulations are then summed over the 24-h period starting at 1200 UTC 10 December 2009.

The model-derived QPE in GD agrees well with the NMQ estimate (cf. Figs. 11a and 1f). It has two maxima, one near BUF and a lesser maximum to the southwest. The maxima near BUF are comparable in either estimate (15.95 vs 26 mm). The WSM6 estimate does not agree well with NMQ (Fig. 11b). Its accumulations are much lighter, and precipitation is more evenly distributed along the band. In this experiment, the bulk of the hydrometeor content is below the lowest elevation scans, and therefore the model-derived estimate is dramatically less than the actual forecast precipitation (Fig. 3b).

Fig. 11.

The model-derived 24-h quantitative liquid-equivalent precipitation estimate for (left) GD and (right) WSM6. Locations of ASOS stations used for point comparisons are indicated.

Fig. 11.

The model-derived 24-h quantitative liquid-equivalent precipitation estimate for (left) GD and (right) WSM6. Locations of ASOS stations used for point comparisons are indicated.

Comparisons of the model forecast (actual forecast rather than the model-derived QPE in Fig. 11) with observed accumulations at the two ASOS stations that are within the band—Dunkirk, New York, and Erie, Pennsylvania (KDKK and KERI, respectively; see Fig. 1f for locations)—show that at KDKK all schemes underpredict the amount of precipitation by between 7 and 21 mm, with the unsteady-regime members having closer agreement to the observation (Table 3). At KERI, all of the schemes overpredict the precipitation by between 5 and 34 mm, with the steady-regime members having the better agreement. Other data sources, such as the Community Collaborative Rain, Hail, and Snow network (Cifelli et al. 2005) and the Hydrometeorological Automated Data System (Kim et al. 2006), were considered for verification, but none of these had active stations in the region of precipitation of greater than 38 mm in the unsteady regime. Therefore, although the steady regime appears to have the better agreement, one cannot state this result definitively.

Table 3.

Observed and forecast 24-h liquid-equivalent precipitation accumulations (mm) at ASOS rain gauges (see Fig. 1f for locations).

Observed and forecast 24-h liquid-equivalent precipitation accumulations (mm) at ASOS rain gauges (see Fig. 1f for locations).
Observed and forecast 24-h liquid-equivalent precipitation accumulations (mm) at ASOS rain gauges (see Fig. 1f for locations).

4. Conclusions

Eight forecasts of a lake-effect-snow event were performed to assess how the quantitative precipitation forecast is altered as the microphysical parameterization scheme is changed. The experiments include both five- and six-category and single- and double-moment schemes. The 24-h accumulated precipitation and hourly band-maximum precipitation indicate the presence of two forecast regimes: steady and unsteady. The steady regime is characterized by relatively broad precipitation shields, lower and farther-inland/downstream maxima, and near-uniform hourly maxima. The unsteady regime has narrower precipitation shields, higher maxima that are farther upstream, and erratic hourly maxima.

The differences in the precipitation patterns are due to stronger relofting or suspension of hydrometeors in the steady-regime experiments. This leads to longer in-cloud residence times, stronger downstream transport, and a more diffuse precipitation pattern. In the unsteady regime, hydrometeors are able to descend through the vertical velocity maximum, there is less downstream drift, and, consequently, the precipitation is concentrated over a smaller area. The relofting of hydrometeors only occurs at those times at which w is sufficiently large.

The root cause for the differences observed in this study is the different assumptions used in each microphysical parameterization scheme. In the six-category schemes, the unsteady-regime experiments have a much higher graupel content than in the steady regime. Accretion of snow by rain (Pracs) is the primary means by which graupel is produced in the unsteady regime. In the steady-regime, Pracs is an order of magnitude smaller, leading to a near-negligible graupel production. Deeper investigation shows that each scheme uses a different formula for Pracs. It is unclear what expression best approximates conditions in LES storms. In the five-category schemes, the riming intensity was compared. In these experiments, the different precipitation patterns are due to the way in which terminal velocity is dependent on RI and temperature, with the steady-regime experiment having a more conservative relation. Again, lack of observational details of the degree of riming and fall speeds typical of LES precludes one from determining the most suitable approach.

Confirmation that one regime is superior to the other was hampered by the quality and density of available observations. The steady-regime experiments compare better to radar-based quantitative precipitation estimates, but the comparison is not direct given known biases. Rain gauge comparisons show no trend, but there were only two active gauges in the heaviest portion of the band. One may expect that previous observational studies of LES would shed some light on whether graupel and riming are common for LES, which would give some credence to one regime over the other. Braham (1983) states that riming (or graupel) is “quite common” for early-season LES, which seems to indicate the unsteady regime may be closer to the truth. This claim was not supported with observational evidence, however, and we could find no other reference noting the degree of riming during LES. The best route for understanding accretion in LES may be to first establish how predominant graupel is during LES storms and to measure typical fall speeds. Observational data collected with dual-polarized radars, vertically pointing radars, or other in situ instruments would be helpful to this end.

Acknowledgments

Special thanks are given to B. Colle, D. Kristovich, T. Mansell, G. Thompson, J. Zhang, and anonymous reviewers. Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA17RJ1227, U. S. Department of Commerce, and the National Research Council. This study was made possible in part because of the data made available by the governmental agencies, commercial firms, and educational institutions that participate in MesoWest.

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Footnotes

1

The reader may have noticed that the input qr for Table 2 is on the order of 10−6 while Pracs is on the order of 10−3 in WSM6. In both WSM6 and GD, the magnitude of Pracs is not limited by the magnitude of qr but rather by the magnitude of qs. The companion term Psacr accounts for the depletion of rain.