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The Dependence of QPF on the Choice of Boundary- and Surface-Layer
Parameterization for a Lake-Effect Snowstorm
ROBERT CONRICK
Research Experience for Undergraduates Program, National Weather Center, Norman, Oklahoma, and Indiana
University, Bloomington, Indiana
HEATHER DAWN REEVES
NOAA/OAR/National Severe Storms Laboratory, and Cooperative Institute for Mesoscale Meteorological
Studies, University of Oklahoma, Norman, Oklahoma
SHIYUAN ZHONG
Michigan State University, Lansing, Michigan
(Manuscript received 31 October 2014, in final form 2 March 2015)
ABSTRACT
Six forecasts of a lake-effect-snow event off Lake Erie were conducted using the Weather Research and
Forecasting Model to determine how the quantitative precipitation forecast (QPF) was affected when the
boundary- and surface-layer parameterization schemes were changed. These forecasts showed strong variability, with differences in liquid-equivalent precipitation maxima in excess of 20 mm over a 6-h period. The
quasi-normal scale elimination (QNSE) schemes produced the highest accumulations, and the Mellor–
Yamada–Nakanishi–Niino (MYNN) schemes produced the lowest. Differences in precipitation were primarily due to different sensible heat flux FH and moisture flux FQ off the lake, with lower FH and FQ in MYNN
leading to comparatively weak low-level instability and, consequently, reduced ascent and production of
hydrometeors. The different FH and FQ were found to have two causes. In QNSE, the higher FH and FQ were
due to the decision to use a Prandtl number PR of 0.72 (all other schemes use a PR of 1). In MYNN, the lower
FH and FQ were due to the manner in which the similarity stability function for heat ch is functionally dependent on the temperature gradient between the surface and the lowest model layer. It is not known what
assumptions are more accurate for environments that are typical for lake-effect snow, but comparisons with
available observations and Rapid-Update-Cycle analyses indicated that MYNN had the most accurate
results.
1. Introduction
Prediction of the amount and location of lake-effect
snow (LESN) is a challenge for operational forecasters.
These storms have significant impact not only because
they can produce copious amounts of snow but also
because the snowbands can be narrow [O(10–50 km)]
and are not resolved by some forecast systems. Recent
computing advances allow for real-time prediction at
grid spacings that are capable of resolving individual
Corresponding author address: Heather Dawn Reeves, DOC/
NOAA/OAR, National Severe Storms Laboratory, 120 David L.
Boren Blvd., Suite 2401, Norman, OK 73072-7319.
E-mail: [email protected]
DOI: 10.1175/JAMC-D-14-0291.1
Ó 2015 American Meteorological Society
bands (1–4 km), and therefore one might reasonably
expect a more precise quantitative precipitation forecast
(QPF) from these numerical modeling systems. The
extent to which LESN forecasts are sensitive to the parameterization schemes used in numerical weather
prediction (NWP) models is not completely understood,
however, and the choice of schemes may affect the accuracy of the QPF. In this paper, the manner in which
the QPF is dependent on the choice of boundary- and
surface-layer parameterization schemes is examined.
Lake-effect snow results from the destabilization of a
cold-air mass as it moves over warm water. It is characterized by intense, shallow convection and heavy, localized snowfall near the downwind side of the lake. The
bands may be multibanded or single-banded and/or may
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have embedded mesoscale vortices (Peace and Sykes
1966; Passarelli and Braham 1981; Braham and Kelly
1982; Ballentine 1982; Kelly 1982, 1984, 1986; Braham
1983; Hjelmfelt and Braham 1983; Forbes and Merritt
1984; Hjelmfelt 1990; Niziol et al. 1995). Single-banded
LESN storms usually have the greatest snowfall
(Hjelmfelt 1990).
An ingredient-based approach has been advocated for
forecasting LESN that measures various upwind indices
as well as synoptic patterns (Rothrock 1969; Holroyd
1971; Jiusto and Kaplan 1972; Niziol 1987; Byrd et al.
1991; Niziol et al. 1995; Kristovich and Laird 1998). This
method has been used in operational settings for several
years and works well for anticipating the potential for
banding and the type of bands, assuming that the largescale flows are well forecast. But precise guidance on the
intensity and/or location of individual bands cannot be
gleaned from this method.
Several forecast offices now perform numerical model
forecasts with grid spacings that are able to resolve
some bands (2–5 km) and, presumably, provide a more
accurate QPF. There are only a few papers that address
the QPF associated with LESN from numerical forecasts, but these provide evidence that QPF may
be strongly influenced by parameterized processes
(Ballentine et al. 1998; Sousounis et al. 1999). Systematic
evaluations of the degree of sensitivity and causes for
different forecasts have only recently begun to be explored. For example, a strong sensitivity to the choice of
microphysical parameterization has recently been found
that is the result of the overproduction of graupel by
some schemes (Shi et al. 2010; Theeuwes et al. 2010;
Reeves and Dawson 2013; McMillen and Steenburgh
2015). Theeuwes et al. (2010) also considered LESN
sensitivity to cumulus parameterization but found only
minimal effects on QPF. To the best of our knowledge,
no other parameterized process has hitherto been examined for LESN.
The cloud systems associated with LESN are typically
very shallow, topping off near or below 700 hPa, and
convection is usually fully contained within the boundary layer. Hence, it is reasonable to question whether
the QPF is sensitive to the choice of boundary- and
surface-layer parameterization. Several intercomparison studies of boundary- and surface-layer schemes have
been conducted by numerous investigators and for various phenomena such as tropical cyclones, orographic
precipitation, sea breezes, and quiescent conditions over
uniform terrain. It is well established that the predicted
environments can be significantly different when the
schemes used within NWP models are changed. There
is a growing body of literature that suggests that the
primary culprit for these differences is the varying
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sensible and latent heat fluxes at the surface produced by
the different surface-layer schemes, which affect the
low-level stability and wind fields (e.g., Braun and Tao
2000; Zhang and Zheng 2004; Srinivas et al. 2007; Zhong
et al. 2007; Han et al. 2008; Li and Pu 2008; Miao et al.
2008; Shin and Hong 2011). This may have important
implications for LESN—several investigators have
found that it is very sensitive to the different heat and
moisture fluxes that occur as the amount of ice cover
over the lakes increases (Cordeira and Laird 2008;
Gerbush et al. 2008; Vavrus et al. 2013; Wright et al.
2013). It is unknown whether the differences in sensible
and latent heat fluxes among various surface-layer
schemes are sufficient to radically affect the QPF, but
one might easily imagine that a strong sensitivity exists.
This is tested herein through a series of numerical-model
sensitivity experiments for a select LESN event. This
paper is organized as follows: A synopsis of the event
is provided in section 2. The full-physics numericalsensitivity-experiment results are discussed in section 3.
Concluding remarks are made in section 4.
2. Case-study description
The event is the same as that studied in Reeves and
Dawson (2013). It is a very intense LESN storm off Lake
Erie that occurs between 10 and 12 December 2009.
Attention is focused on the hydrologic day starting at
1200 UTC 10 December, during which most of the
precipitation falls. The stage-IV quantitative precipitation estimate (QPE; Lin and Mitchell 2005)
shows a precipitation band along the northeast shore of
Lake Erie (Fig. 1a). The 24-h maximum is 28 mm near
Dunkirk, New York (DKK), but accumulations in excess of 14 mm extend about 40 km inland. Within this
24-h period, the greatest precipitation falls during the
6-h period starting at 1800 UTC 10 December, during
which the pattern is consistent with single-banded LESN,
having an elongated zone of precipitation extending off
the northeast corner of Lake Erie (Fig. 1b). The maximum 6-h precipitation (13 mm) is over Genesee County,
but there is a second maximum of 12 mm near DKK.
A time sequence of observed composite radar reflectivity shows that the heaviest precipitation is over western
New York throughout the time period shown (Figs. 2a–e).
The intensity of the convection increases between 1200
and 1800 UTC (Figs. 2a,b) and reaches a maximum at
2200 UTC (Fig. 2c). Analyses in Reeves and Dawson
(2013) indicate that the episode of heaviest convection
occurs coincident with the passage of a midlevel shortwave trough (see their Fig. 2b). After 0000 UTC 11
December, the band moves slightly southward and the
reflectivities decrease (Figs. 2d,e). The Rapid-Update-Cycle
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FIG. 1. The (a) 24-h liquid-equivalent QPE started at 1200 UTC 10 Dec and (b) 6-h QPE started at 1800 UTC 10 Dec.
(RUC; Benjamin 1989) analyses of 10-m winds show
that this decrease coincides with a subtle, more westerly,
shift in the low-level wind direction over the lake. At
later times, the wind becomes more westerly and
multibanded LESN forms (not shown). A vertical cross
section taken parallel to the long axis of the band at the
time of maximum convection shows the strong enhancement of precipitation as the air moves over the Allegheny
Mountains of western New York (Fig. 2f). The RUCanalyzed equivalent potential temperature ue shows
that the convection is contained within an approximately
300-hPa-deep surface-based mixed layer, although some
cloud turrets extend above this layer. The ue analysis also
indicates that the most intense convection forms in a
layer of decreasing ue with height.
A glimpse into the dynamics that drives the heavy
precipitation is provided through consideration of the
synoptic-scale flow over the Great Lakes region at
2200 UTC according to the RUC analysis (Fig. 3a). As is
typical for LESN, the Great Lakes are in the cold sector
of a midlatitude cyclone. Subfreezing air is being advected over the lakes, and the low-level flow is from the
west-southwest. The difference between the lakesurface temperature and the temperature at 850 hPa is
shown in Fig. 3b. Differences over Lake Erie range from
21 to 25 K, which suggests that strong upward sensible
heat fluxes are occurring. The layer-average temperature between 975 and 850 hPa confirms this is true, indicating that a thermal ridge is present over the lake.
The low-level relative humidity is higher over the lake
than over the land, likely because of strong moisture
fluxes, although this cannot be confirmed with the
available RUC data.
The RUC-analyzed sounding at Buffalo, New York,
(BUF) at 2200 UTC shows that the temperature profile
is unstable with respect to the moist-adiabatic lapse rate
between 900 and 800 hPa (Fig. 3c). Above this is a stable
layer with decreased relative humidity. Within the moist
unstable layer, temperatures range from 2108
to 2188C, a span that includes the dendrite-growth zone.
The vertical velocity profile at this same time and location shows that the moist unstable layer coincides with
the layer of maximum ascent, having a maximum vertical velocity in excess of 1 m s21 (Fig. 3d). Hence, the
impressive snowfall rates appear to be largely due to two
factors: 1) sufficient surface heating that allows for a
moist unstable layer to develop and 2) the vertical
temperature profile in the layer of maximum ascent
coinciding with the dendrite-growth zone.
3. Experiment design and results
a. Experiment design
The Advanced Research Weather Research and
Forecasting (WRF-ARW; Skamarock et al. 2005)
Model, version 3.5, is used to test the sensitivity of QPF
to the choice of boundary- and surface-layer parameterization. All of the forecasts have a horizontal grid
spacing of 4 km and have 51 vertical levels. There are
200 grid points in both the north and south directions
(Fig. 4). The western edge of the domain is purposefully couched very close to the western edge of Lake
Erie. This is to insure that the flow upstream of Lake
Erie is not significantly different in the experiments,
thus allowing for a more accurate assessment of the
effects of changing heat and moisture fluxes over the
lake on the QPF. All experiments use the Noah land
surface model (Ek et al. 2003), Thompson microphysical parameterization (Thompson et al. 2004) and
Dudhia longwave and shortwave radiation schemes
(Dudhia 1989). No cumulus parameterization scheme
is utilized. The 12-km North American Mesoscale
(NAM; Janjic et al. 2005) model analyses are used to
initialize the experiments, and the boundary conditions are updated every 3 h from the associated NAM
model forecasts. The experiments are initialized at
0000 UTC 10 December 2009 and are integrated for
48 h with a 12-s time step.
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FIG. 2. The (a)–(e) observed radar reflectivity mosaics and RUC-analyzed 10-m wind barbs (in this figure and all others with wind barbs,
one full barb is 5 m s21), and (f) a vertical cross section [indicated by line AB in (c)] of the observed composite reflectivity (dBZ; shaded)
and RUC-analyzed equivalent potential temperature (K; contoured). In (f) and all other cross sections, the blue section in the terrain map
at the bottom indicates the region of the cross section that is over Lake Erie.
Six different control experiments are performed, each
with a different boundary- and surface-layer parameterization. These are the ‘‘BouLac’’ (Bougeault and
Lacarrere 1989), Mellor–Yamada–Janjic (MYJ; Janjic
2002), Mellor–Yamada–Nakanishi–Niino level 2.5
(MYNN; Nakanishi and Niino 2004), asymmetric convective model (ACM; Pleim 2007), quasi-normal scale
elimination (QNSE; Sukoriansky et al. 2006), and
Yonsei University (YSU; Hong et al. 2006) schemes. Table 1
summarizes all of the experiments. In the WRF-ARW,
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FIG. 4. The model domain and terrain (shaded). The red parallelogram indicates the area used in Fig. 5 and other similar figures.
the surface-layer scheme is specified independent of the
boundary-layer scheme. However, most boundary-layer
schemes are only compatible with their corresponding
surface-layer schemes. Therefore, each experiment in
this paper uses the surface-layer scheme that corresponds
to the indicated boundary-layer scheme, as recommended in the WRF-ARW documentation. In particular,
ACM uses the Pleim–Xiu (Pleim 2007) scheme, YSU
uses the Monin–Obukhov scheme, and BouLac, because
it does not have an associated surface-layer scheme, uses
the MYJ surface-layer scheme as recommended in the
WRF-ARW documentation (Skamarock et al. 2005). To
distinguish these experiments from other sensitivity
tests that are discussed later in this paper, we refer to the
above experiments collectively as the control (CNTL)
experiments, and individual experiments are referred to
as CNTL-MYJ, CNTL-MYNN, and so on.
b. Experiment results
1) DIFFERENCES IN PRECIPITATION
FIG. 3. The RUC-analyzed (a) 2-m temperature (K; shaded), sea
level pressure (hPa; contoured), and 10-m wind barbs; (b) difference
between lake-surface temperature and the 850-hPa temperature
(K; shaded), and the 975–850-hPa layer-averaged relative humidity
(%; solid contours) and temperature (K; dashed contours); and profiles
of (c) temperature (red) and dewpoint (blue) and (d) vertical velocity
at BUF. Both (c) and (d) use the pressure coordinates as indicated
to the left of (c). All analyses are at 2200 UTC 10 Dec.
We start with consideration of the hourly areaintegrated liquid-equivalent precipitation for the parallelogram shown in Fig. 4. This area completely encloses
the precipitation off Lake Erie for all experiments. Between forecast hour 0 (fhr0) and fhr24, the spread in the
solutions is very large—CNTL-QNSE has comparatively high precipitation rates whereas CNTL-MYNN
has rather low rates (Fig. 5a). At fhr21, the time of
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TABLE 1. A summary of all sets of experiments (expts) conducted in this paper.
Expt name
Description
Schemes tested
CNTL
CF
c
PR
MYJ
Schemes are run ‘‘as is’’ with no modification to the source code
The FH and FQ are modified to be the same in all expts
The ch are set to be the same in all expts
The PR is set to be 1 in all expts
The surface-layer parameterization is MYJ
ACM, BouLac, MYJ, MYNN, QNSE, and YSU
ACM, BouLac, MYJ, MYNN, QNSE, and YSU
MYJ and MYNN
QNSE
MYNN
greatest spread, the difference between the areaintegrated precipitation from CNTL-QNSE and
CNTL-MYNN is 1396 mm. The spread among the remaining experiments is comparatively small. After
fhr24, the wind shifts to a more northwesterly direction
and the amount of precipitation decreases in all experiments, leading to a decreased spread in the hourly
precipitation rates. One can consider the area-maximum
precipitation (defined as the maximum hourly precipitation at any grid point within the parallelogram
shown in Fig. 4) in the same way (Fig. 5b). Before fhr24,
CNTL-QNSE has the highest maxima and CNTLMYNN has the lowest. The spread among the remaining experiments is modest. After fhr24, the spread among
all experiments decreases.
A reasonable question to pose is whether the QPF
differences are due to the type of turbulence closure
(i.e., local or nonlocal). Apparently, this is not the case
as QNSE, MYJ, and MYNN are all local-closure
schemes and represent the full distribution of solutions
noted in Fig. 5. In the subsequent discussion, particular
attention is given to differences among these three experiments. Comparison between CNTL-MYJ, CNTLACM, CNTL-BouLac, and CNTL-YSU shows that, for
all analyses below, these forecasts produce similar results (not shown).
The 6-h accumulated liquid-equivalent precipitation
between fhr18 and fhr24 lends additional insight into the
differences in precipitation among CNTL-QNSE,
CNTL-MYJ, and CNTL-MYNN. All have an elongated band of precipitation along the west shore of Lake
Erie, with the heaviest accumulations over western New
York (Figs. 6a–c). CNTL-QNSE and CNTL-MYJ have
two maxima, one near DKK and the other either south
or west of BUF, whereas CNTL-MYNN has only one
localized maximum near BUF. Maxima in CNTLQNSE (CNTL-MYNN) are on the order of 10 mm
higher (lower) than those in CNTL-MYJ.
The positions of the bands in these forecasts compare
well to the stage-IV analysis, with CNTL-MYNN having
the best agreement in the areal extent of the band and
magnitude of individual maxima (cf. Figs. 1b, 6c).
However, all three have precipitation extending farther
to the southwest than in the stage-IV analysis. In this
regard, the stage-IV data product may not be reliable
because it uses radar data as a first guess of the precipitation estimate—overshooting of the cloud top at
distances far from the radar and the absence of rain
gauges over Lake Erie may lead to an underestimate of
precipitation in this area.
2) DIFFERENCES IN AIRMASS MODIFICATION
OVER THE LAKE
To understand better the cause for the different precipitation patterns, a trajectory analysis is undertaken.
Three trajectories are started at the lowest model level
at select points on the west side of Lake Erie at fhr18 and
are integrated for 6 h (Fig. 7a). Although the trajectories
are not identical, they are all oriented roughly west-toeast, with air parcels in each experiment spending a
similar amount of time over the lake. Along-trajectory
calculations of potential temperature u and water vapor
mixing ratio qvp show that the CNTL-QNSE (CNTLMYNN) trajectories experience more (less) warming
and moistening than CNTL-MYJ (Figs. 7b,c). By fhr20,
which is just prior to the formation of convection for
these trajectories (indicated by the rapid decrease in qvp
in Fig. 7c), the along-trajectory u is between 1 and 3 K
FIG. 5. The (a) area-integrated and (b) area-maximum liquidequivalent hourly precipitation rates for the CNTL experiments.
The area is given by the parallelogram in Fig. 4.
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FIG. 6. The 6-h accumulated liquid-equivalent precipitation starting at 1800 UTC 10 Dec (fhr18) for (a) CNTL-QNSE, (b) CNTL-MYJ,
and (c) CNTL-MYNN. Maxima are indicated in each panel. Line AB indicates the cross-sectional area shown in Fig. 8.
higher in CNTL-QNSE than in CNTL-MYJ and between 2 and 4 K lower in CNTL-MYNN than in CNTLMYJ. Similarly, the along-trajectory qvp at fhr20 is between 0.1 and 0.4 g kg21 higher in CNTL-QNSE and
between 0.3 and 0.5 g kg21 lower in CNTL-MYNN than
in CNTL-MYJ.
The greater heating and moistening in CNTL-QNSE
leads to a greater degree of low-level instability relative
to the other experiments, as demonstrated in Fig. 8,
which shows skew T–logp diagrams of temperature and
dewpoint averaged along the line of maximum ascent
(indicated in Fig. 6a) at fhr21. From the surface to about
800 hPa, the CNTL-QNSE profile is saturated and unstable with respect to the moist adiabatic lapse rate
(Fig. 8a). CNTL-MYJ is somewhat more stable (cf.
Figure 8d), and CNTL-MYNN is approximately moist
neutral (Fig. 8g). CNTL-MYNN also has a shallower
saturated layer and slightly colder temperatures. These
temperatures are more consistent with those observed at
BUF (Fig. 3c), but since Fig. 8 shows along-line averages
the comparison is not direct.
The relatively strong instability in CNTL-QNSE
manifests itself in stronger ascent, as demonstrated using along-band vertical velocity (Fig. 8b). The maximum
vertical velocity in CNTL-QNSE (1.9 m s21) is nearly 4
times that in CNTL-MYNN (0.52 m s21; Fig. 8h). The
maximum in CNTL-MYJ is about 1.5 m s21 (Fig. 8e).
Another perspective is provided in Figs. 8c,f,i, which
show vertical cross sections of along-band ue at fhr21. All
of the experiments have surface-based layers of decreasing ue with increasing height, but the gradient of ue
is largest in CNTL-QNSE (Fig. 8c). Accordingly, the
along-band precipitation mixing ratio qpr is between 0.6
and 1.2 g kg21 higher in CNTL-QNSE than in CNTLMYNN, as is demonstrated in Figs. 8c,i. Again, CNTLMYJ is midway between the other experiments (Fig. 8f).
Comparison of Figs. 2f and 8 indicates that CNTLMYNN has the closest agreement with the RUC analyses
and radar observations. CNTL-QNSE and CNTL-MYJ
are more unstable than the RUC analyses and have their
maximum reflectivity returns too far upstream. It is possible that the RUC analysis is not an accurate measure of
the overlake stability and that some of the intensity in the
band may be underestimated in the radar observations
because of overrunning of the cloud top by the radar
beam and beam broadening (as noted above). In addition,
the cross-sectional areas in Figs. 2f and 8 are slightly different because the axis of maximum convection is in a
FIG. 7. The fhr18–fhr24 (a) forward trajectories and alongtrajectory (b) potential temperature and (c) water vapor mixing
ratio for CNTL-QNSE, CNTL-MYJ, and CNTL-MYNN.
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FIG. 8. (a),(d),(g) Skew T–logp diagrams of temperature (red) and dewpoint (blue) and (b),(e),(h) vertical
profiles of vertical velocity averaged along line AB. (c),(f),(i) Vertical cross sections of equivalent potential
temperature (K; contoured) and precipitation (i.e., the sum of the mixing ratios for snow, rain, and graupel) mixing
ratio (g kg21; shaded). The location of AB is indicated in Fig. 6a. All panels use the pressure coordinates as indicated on the leftmost panels and are valid at fhr21.
slightly different location in the experiments relative to the
observations. All of the cross sections in Fig. 8 are aligned
with the axis of maximum convection, which happens to be
the same in all experiments at the time shown.
3) DIFFERENCES IN HEAT AND MOISTURE FLUXES
Variations in the net low-level heating and moistening
over Lake Erie are linked to varying surface heat flux FH
and moisture flux FQ as is demonstrated at fhr21 (Fig. 9).
CNTL-QNSE has FH that is, on average, 225 W m22
higher over Lake Erie than is that in CNTL-MYJ.
CNTL-MYNN has FH that is ;250 W m22 lower
(Figs. 9a–c). The CNTL-QNSE FQ (latent heat flux LH)
is also, on average, 8.3 3 1025 kg m22 s21 (209 W m22)
higher than in CNTL-MYJ while CNTL-MYNN is 7.9 3
1025 kg m22 s21 (197 W m22) lower (Figs. 9d–f). The FH
in CNTL-QNSE is large, approaching the typical incoming solar radiation over the Great Lakes during
winter, and far exceeds satellite measurements of the
average surface heat flux, according to Lofgren and Zhu
(2000). Their satellite-based measurements suggest that
typical values for FH and LH in December are about
50 and 54 W m22, respectively. These measurements,
however, are monthly averages and may underestimate
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FIG. 9. The surface (a)–(c) sensible heat and (d)–(f) moisture flux at fhr21 for the CNTL experiments. The mean over Lake Erie is
indicated at the top of each panel. The mean LH is included in (d)–(f).
values that are typical during LESN. Though still higher
than the observations from Lofgren and Zhu (2000),
CNTL-MYNN FH is more compatible with satellite
measurements and appears to be a more reasonable
estimate, although this conclusion cannot be confirmed
because cloud cover over the lake on this day blocks
satellites from measuring the lake temperatures.
A simple test of whether the different FH and FQ are
responsible for the differences noted above is performed
by forcing all surface-layer schemes to use the same
overwater values (550 W m22 and 1.65 3 1024 kg m22 s21,
respectively). These values are held constant throughout
the integration period. This FH is close to the overwater
mean at fhr21 in the CNTL-MYJ experiment (Fig. 9b).
The choice for FQ is smaller than that in CNTL-MYJ
because the MYNN scheme would not run with a higher
FQ. These experiments are referred to as the constantflux (CF) experiments.
A time sequence of the area-integrated and areamaximum precipitation rates for the CF experiments is
shown in Fig. 10. Experiment CF-QNSE (CF-MYNN)
has comparatively high (low) precipitation rates before
fhr24, but the spread in the CF experiments is considerably less than that in the CNTL experiments (cf.
Figs. 5, 10). At fhr21, the difference between CF-QNSE
and CF-MYNN is 332 mm (as compared with 1396 mm
for the CNTL experiments).
The improved agreement in the CF experiments is a
direct consequence of reduced overwater modification
of air parcels. This is demonstrated through a trajectory
analysis that is identical to that described for the CNTL
experiments [see section 3b(2)]. The paths of these
trajectories and the amount of time spent over the lake
are comparable to those from the CNTL experiments
FIG. 10. The (a) area-integrated and (b) area-maximum liquidequivalent hourly precipitation rates for the CF experiments. The
area is given by the parallelogram in Fig. 4.
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FIG. 11. The fhr18–fhr24 (a) forward trajectories and alongtrajectory (b) potential temperature and (c) water vapor mixing
ratio for CF-QNSE, CF-MYJ, and CF-MYNN.
(cf. Figs. 7a, 11a). However, CF-QNSE, CF-MYJ, and
CF-MYNN have quite similar along-trajectory changes
in u and qvp (Figs. 11b,c), whereas in the CNTL experiments varying degrees of heating and moistening were
observed among the experiments.
The low-level stability in the CF experiments has
much closer agreement among the experiments than in
the CNTL experiments. Vertical cross sections of ue
through the axis of maximum convection indicate that,
although there is a layer of decreasing ue with height, this
gradient is similar in all experiments (Fig. 12). This
condition leads to along-band maximum vertical velocities for the lowest 3 km for CF-QNSE, CF-MYJ, and
CF-MYNN of about 0.9 m s21. As a result, all of the
CF experiments have along-band qpr maxima of
;1.6 g kg21.
4) DIFFERENCES IN HEAT AND MOISTURE FLUX
CALCULATIONS
We now consider the equations used to compute FH
and FQ, which are both computed in the surface-layer
scheme. All schemes use a similar formulation that is
given by
FIG. 12. Vertical cross sections of precipitation mixing ratio
(g kg21; shaded) and ue (K; contoured) at fhr21 for (a) CF-QNSE,
(b) CF-MYJ, and (c) CF-MYNN along the line AB in Fig. 6.
cp ro u*k(ug 2 uo )
z
and
PR ln 2 ch
L
ro u*k(qyg 2 qyo )
z
,
FQ 5
PR ln 2 ch
L
FH 5
(1)
(2)
where cp is the specific heat at constant pressure; u* is
the friction velocity; k is the von Karmán constant; PR is
the Prandtl number; ro, uo, and qyo are the density, potential temperature, and water vapor mixing ratio on the
lowest model layer; ug and qyg are the potential temperature and water vapor mixing ratio at ground level;
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z is the lowest model-layer height; L is the Monin–
Obukhov length; and ch is the similarity stability function for heat. In both (1) and (2), the factors that are
calculated within the surface-layer parameterization are
L, ch, and u* (u* is a function of z, L, and ch).
One important difference among the schemes is the
way in which ch is computed. For unstable stratification,
QNSE and MYJ use the Paulson (1970) equation and
MYNN uses the Dyer–Hicks (Dyer and Hicks 1970)
formula. Although both formulas are based on observations taken over Australia during winter by Swinbank
(1964), the small differences in the formulations can
have nonnegligible differences for the stratification that
is possible during LESN. Let us consider ch as a function
of ug 2 uo. Assuming a ug of 280 K (similar to that in the
CNTL experiments), and a ug 2 uo ranging from 0 to
30 K, ch is plotted in Fig. 13a. Although 30 K is a high
value, even for LESN, it is used here as an upper limit.
When ug 2 uo is less than about 6 K, the Dyer–Hicks
version of ch is slightly higher than the Paulson version.
For ug 2 uo greater than 6 K, the Paulson version is
higher and differences in ch increase rapidly with increasing ug 2 uo. The same is true for colder lake-surface
temperatures as is demonstrated for a ug of 273 K (included in Fig. 13a). At fhr21, the ug 2 uo over Lake Erie
ranges from 4 to 17 K with a mean difference of 12.5 K,
suggesting that most of the area over Lake Erie is in a
regime in which the Paulson version yields higher ch.
Returning to (1) and (2), we can see that as ch increases,
the denominators decrease, leading to higher FH and FQ
[assuming ln(z/L) is small relative to the change in ch,
which is approximately true for the CNTL experiments].
An increase in ch also increases u*, which further increases FH and FQ. The ug 2 uo in the numerator of (1)
simultaneously increases, leading to even larger differences between the FH obtained from MYJ and MYNN.
To confirm that differences in ch are nonnegligible,
the MYJ and MYNN experiments are rerun using a
prescribed overwater value for ch (51) and are referred
to as MYJ-c and MYNN-c, respectively. These experiments are otherwise identical to their CNTL counterparts.
The area-integrated and area-maximum precipitation from
these experiments are in very good agreement with each
other (Figs. 13b,c). At fhr21, the difference between the
area-integrated precipitation for MYJ-c and MYNN-c is
103.5 mm whereas for the CNTL experiments it is 702 mm.
This exercise does not include the QNSE scheme because it
uses the same ch as MYJ and therefore the conclusions are
the same (not shown).
The above arguments do not account for the higher FH
in CNTL-QNSE relative to CNTL-MYJ because both
use the Paulson (1970) version for ch. Here, the distinction is in the choice of PR. The QNSE surface-layer
1187
FIG. 13. The (a) ch as a function of ug 2 uo for the MYJ (and
QNSE; red) and MYNN (blue) experiments and (b) areaintegrated and (c) area-maximum liquid-equivalent hourly precipitation rates for the c, PR, and MYJ experiments. The area is
given by the parallelogram in Fig. 4. In (a), the solid and dashed
lines indicate a ug of 280 and 273 K, respectively.
scheme uses a PR of 0.72 while all other surface-layer
schemes use a PR of 1. To confirm the sensitivity of QPF
to PR, the QNSE experiment is rerun using a PR of 1.
This is referred to as the QNSEPR experiment and is
otherwise identical to the CNTL-QNSE experiment.
The area-integrated and area-maximum precipitation
curves for QNSEPR are nearly identical to those in the
CNTL-MYJ experiment (Figs. 13b,c). The difference
between the area-integrated precipitation for QNSEPR
and the CNTL-MYJ experiment at fhr21 is 54 mm
whereas for the CNTL-QNSE and CNTL-MYJ experiments it is 794 mm.
One is also tempted to mix and match the boundaryand surface-layer parameterization schemes to determine
whether the QPF is altered. Most boundary-layer
schemes are only compatible with their surface-layer
counterparts, however. The one exception is the MYNN
boundary-layer scheme, which can be paired with either
the MYNN or MYJ surface-layer scheme. An experiment
using the MYNN boundary- and MYJ surface-layer
scheme was performed, and, indeed, the results are
nearly identical to the CNTL-MYJ experiment (indicated
as MYNN-MYJ in Figs. 13b,c), confirming that differences in the surface-layer parameterization are primarily
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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
responsible for the different precipitation amounts.
(MYNN can also be paired with the Monin–Obukhov
surface-layer scheme, but, because the YSU experiment—
which uses this scheme—yields results that are very
similar results to those of MYJ, such an experiment is
not performed herein.)
4. Conclusions
Six forecasts of a lake-effect snow event off Lake Erie
were performed to test the sensitivity of forecast precipitation to boundary- and surface-layer parameterization. The event was a particularly strong case of LESN
in which a maximum of 28 mm of liquid-equivalent
precipitation fell in a 24-h period. Observations and
RUC analyses of the event indicate that there were
strong sensible and latent heat fluxes from the lake that
caused a low-level layer of absolute instability to form.
The numerical model results show that the CNTLQNSE (CNTL-MYNN) scheme produces much higher
(lower) accumulations than do the other schemes considered. Over the 6-h period of maximum precipitation,
the liquid-equivalent QPF was ;20 mm higher in
CNTL-QNSE. Large differences in QPF existed
throughout the first 24 h of integration, however. As the
system weakened, the spread in QPF decreased.
An in-depth comparison was made of three of the
local-closure schemes (QNSE, MYJ, and MYNN) during the time of maximum precipitation. Trajectory
analyses show that each experiment was subject to a
different degree of heating and moistening as air parcels
traveled over Lake Erie. CNTL-QNSE experienced
more warming and moistening than did CNTL-MYJ,
whereas CNTL-MYNN had less warming and moistening. This led to significant differences in the low-level
stability, with CNTL-QNSE having stronger low-level
instability than the other experiments and consequently
higher vertical velocities and more precipitation. Although not shown, the other experiments (CNTL-ACM,
CNTL-BouLac, and CNTL-YSU) are in close agreement with CNTL-MYJ.
The degree of heating and moistening is correlated to
the magnitude of the surface heat and moisture fluxes
(FH and FQ) off Lake Erie. A set of sensitivity experiments was performed in which all surface-layer schemes
were forced to use the same overwater values of FH and
FQ to confirm their influence on QPF. The spread in
QPF for these experiments was comparatively small
throughout the integration period, a result of the similar
overwater modification of air parcels crossing Lake Erie
that occurred in these experiments.
To clarify why the schemes have different FH and FQ,
an analysis of the factors involved in the computation of
VOLUME 54
these quantities was undertaken. The MYNN scheme
was found to produce lower values for the similarity
stability function for heat ch than did MYJ for the same
vertical temperature gradient, thus leading to lower FH
and FQ. Forcing both schemes to use the same ch caused
them to have a nearly identical QPF. The QNSE scheme
uses a smaller Prandtl number than the other schemes.
Forcing QNSE to use the same PR as MYJ resulted in a
QPF that was nearly identical to that obtained from the
MYJ experiment.
Last, we note that comparison with observations and
the RUC analyses indicates that MYNN produced the
most accurate forecasts, but a lack of observations of
heat fluxes over the lake prevents a rigorous assessment
of which scheme is most accurate in this regard. Whether
such a result would occur for other events, particularly
those that are weaker or of a different type, is unknown.
Future research should be conducted to assess this
sensitivity.
Acknowledgments. Special thanks are given to
D. Turner. Funding was provided by the NOAA/Office
of Oceanic and Atmospheric Research under NOAA–
University of Oklahoma Cooperative Agreement
NA11OAR4320072, U.S. Department of Commerce
and the National Research Council.
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