A Deficiency In the GrellDévényi Cumulus Parameterization
Department Seminar
Nick P. Bassill
December 12th, 2012
Outline
• Introduction/Motivation
• Description of Problem
• Global “Case Study”
• Conclusions
Introduction
• Current NWP models require parameterizations to
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accurately simulate most meteorological phenomena
Parameterization definition: “The representation, in a
dynamic model, of physical effects in terms of admittedly
oversimplified parameters, rather than realistically
requiring such effects to be consequences of the
dynamics of the system.”*
One class of parameterizations (cumulus
parameterizations) are required to represent the
cumulative effects of cumulus clouds, particularly when
using a model with a horizontal resolution greater than a
few kilometers
This includes virtually every global model, every climate
model, and many mesoscale models
*http://amsglossary.allenpress.com/glossary/search?id=parameterization1
Motivation
• There exist many available forms of cumulus
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parameterization (CP)
Frequently, certain parameterizations work well in some
weather regimes and not in others
Many studies exist which examine parameterization
differences, but these generally (1) use short forecast
time-scales, (2) are of the case study variety, and (3)
study weather over land
Broadly speaking, my research largely attempts to do
the opposite of these studies, by examining many
lengthy (5 day) simulations over the tropical Atlantic
Collectively, the CPs studied in this talk have been used
in hundreds of AMS publications
Two Literature Examples
• Mukhopadhyay et al. (2010) use a nested WRF
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simulation to simulate precipitation patterns in
the Indian Monsoon
- They studied the impact of varying CPs on six
4-month simulations of the Indian Monsoon
Wehner (2012) examine the occurrence of
heavy rainfall among different NARCCAP models
- NARCCAP models are regional, downscaled
20+ year simulations used to more accurately
simulate the potential effects of climate change
Mukhopadhyay et al. (2010)
Left: The contribution to the total
seasonal rainfall (%) as a function of
rain rate for JJAS
Mukhopadhyay et al. (2010): “This
shows that the GD systematically
overestimates the lighter rain rate
and underestimates the moderate
rain rate throughout the season”
Wehner (2012)
“Fig. 3 A performance portrait plot showing the models’ percentage error relative to the UW
gridded observations in the seasonal mean precipitation, the average seasonal daily maximum
precipitation rate and the 20 year return values of seasonal maximum daily precipitation rates in
the simulations forced by the NCEP reanalysis. Results are shown for each of the four seasons and
are averaged separately over the eastern and western portions of the contiguous US as defined in
the text. The seasons are arranged as quadrants in each box as shown in the legend. Units are
percent.”
Wehner (2012) Continued
• “The most striking features of Fig. 3 are the
large errors exhibited by the WRFG model in the
extreme precipitation rate. This discrepancy is
puzzling as the mean precipitation rate error is
relatively low … The ensemble mean exhibits
lower than average model error in the mean
precipitation but the large WRFG error adversely
effects the mean model’s error in extreme
precipitation.”
Description of Parameterizations
• Kain-Fritsch (KF): Mass-flux scheme triggered when CAPE
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is present and upward vertical motion at LCL exists.
Betts-Miller-Janjic (BMJ): Adjustment scheme which seeks
to relax unstable soundings toward predetermined
reference profiles.
Grell-Dévényi (G3): 144 member ensemble of mass-flux
schemes, consisting of many different triggers (moisture
convergence, CAPE removal, upward vertical motion, etc.)
and parameters (entrainment rates, precipitation
efficiency, etc.). For a given grid point, all members are
averaged and output is sent back to the model.
First Dataset
• 76 5-day “real-time” ensembles were created during the 2009 Atlantic
hurricane season (one every two days) using the WRF model, with 10
members comprised of a variety of differing parameterizations
• This presentation will focus on the Grell-Dévényi (Grell and Dévényi,
2002) cumulus parameterization in comparison to two others
WRF-ARW 3.0
Domain 1: 90 km
Domain 2: 30 km
Mean 120 Hour
Precipitation
120 Hour
Total (mm)
Mean
STD
KF
31.71
4.57
BMJ
28.62
4.57
G3
28.34
4.43
KF
BMJ
• All three CPs display similar
characteristics over 120 hours
• However, an analysis of the
final 3 hours demonstrates
something different
• The mean of the standard
deviation of 3 hour
precipitation over all cases is
.11 mm, .11 mm, and .06 mm
for the KF, BMJ, and G3 CPs
G3
Further Examination
• While the KF and BMJ CPs have similar
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tendencies, the G3 CP seems to perform
differently, particularly at shorter intervals
Specifically, the G3 produces more (less) light
(heavy) precipitation than the other CPs
Another way to examine this is to study
cumulative distribution functions (CDFs) of 3
hour rainfall totals
The following two plots show the evolution of
these CPs’ CDFs with time
Model Hour 12
Hour 72
Colors: KF, BMJ, G3
Hour 24
Hour 96
Hour 48
Hour 120
KF
Colors: 12 H, 24 H, 48H, 72 H, 96 H, 120 H
BMJ
G3
CDF
Conclusions
KF
• Early on, the G3 CP is more
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likely to produce heavy
precipitation than the other
CPs
After about 24 hours, the
opposite is true
For all CPs, stability isn’t
reached until approximately
72+ hours
For the G3 CP, available
moisture is a probable
cause of these changes
Right: Mean difference in
600 hPa relative humidity
between forecast hour 72
and forecast hour 6
BMJ
G3
Hypothesis
• The ensembling technique the G3 CP employs
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negatively impacts forecasts
The extreme drying in regions where rainfall is
produced is a sign of an overactive
parameterization
The G3 CP is overactive in these regions
because of the likelihood that some members
will produce precipitation
Since the G3 CP averages all members, if some
produce precipitation and others do not, a likely
result will be that there will be more total areas
where rain is falling, but that rainfall will be
lighter (which is what was observed earlier)
+
(
) / 2 = ??
• What happens when half the members predict a
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thunderstorm, and half do not?
The result is weaker updrafts, and less intense
precipitation
Problems arise in moderately unstable, moist,
weakly forced environments
Examples are air-mass thunderstorm regimes,
tropical areas, ITCZ regions, and warm SST
regions
EOF Analysis
• To demonstrate this phenomenon, an EOF
analysis is performed
• EOF analyses are designed to determine
dominant modes of variability
• Profiles of vertical motion are examined at
forecast hour 120 for all simulations at all
grid points within the ITCZ (defined as the
latitude band 7°-15° N)
KF (72%)
BMJ (59%)
G3 (59%)
This plot shows the leading EOF regressed
onto the first principal component for each
CP (red), as well as the mean vertical
motion (black). The % is the amount of
variance the first EOF explains
EOF Analysis Continued
• The profile of upward vertical motion associated with
precipitation for the G3 CP is significantly muted relative
to the other CPs
• This is consistent with observations of lighter rainfall
• Given earlier hypotheses, if the ensemble size of the G3
CP were dramatically reduced, it is reasonable to assume
that the observed convection differences will be lessened
compared with the other CPs
• This is tested by recreating the G3 CP simulations in two
ways
(1) by reducing the G3 CP to an ensemble comprised
only of members using a vertical motion closure
(2) by reducing the G3 CP to an ensemble comprised
only of members using a moisture convergence closure
G3: Omega Threshold (75%)
G3: Moisture Convergence (72%)
G3: Original
(59%)
Cumulatively, these EOF analyses suggest that
(1) the original G3 CP produces convection
characterized by less intense upward vertical
motion, and (2) the ensemble nature of the G3
CP is a likely cause of this discrepancy
Second Dataset: Global Case Study
• In order to more fully examine the potential G3
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CP deficiencies (and any global circulation
effects), a series of global WRF simulations are
conducted
Using the G3 CP and KF CP (for comparison
purposes) simulations are created for the period
January 1st-February 19th and July 1st-August
24th (2005)
Simulation details:
– 80 km grid spacing at equator
– SSTs updated once daily
– Initialized using FNL data (which is also used for
comparison purposes)
– The first week is omitted for comparison purposes
R
Precipitation Rate
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Upon first glance,
rainfall patterns look
approximately similar
between either CP
K
F
G
3
G
3
K
F
- On closer inspection, the
G3 CP produces slightly
more precipitation in
subtropical high regions
- The G3 CP produces less
precipitation in regions
commonly characterized
by high rain rates and
over land
• A comparison of
R
K
F
G
3
G
3
K
F
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smoothed outgoing
longwave radiation
(OLR) suggests
that there is more
convection over
tropical regions
with the G3
This is
counterintuitive,
given the
previously analyzed
weaker convection
produced by the G3
CP
KF
G3
G3-KF
Standard
deviation
of OLR
KF
G3
G3-KF
Standard
deviation
of OLR
Preliminary Observations
• Both CPs produce roughly similar rainfall
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distributions and totals
They arrive at these totals in different ways
The G3 CP produces widespread weak
convection while the KF CP produces less
frequent, yet more intense convection over
tropical and subtropical regions
The remainder of this presentation will examine
the potential affect these differences have on
the global circulation
KF
G3
G3-KF
Temporally
and zonally
averaged
meridional
wind
Dotted lines
indicate the
mean
position of
the ITCZ as
determined
by the axis of
greatest
rainfall
Real
KF
Temporally
averaged
250 hPa
zonal wind
G3
KF Real
G3 Real
The G3 CP
appears to have
an equatorial
displacement of
the mean zonal jet
in the winter
hemisphere
Zoomed-in Northern Winter
Real
KF
G3
One location in which the KF CP
and the G3 CP perform very
differently is in the northeastern
Pacific Ocean
Further Observations
• The G3 CP produces a weaker mean Hadley Cell than the
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KF CP
The primary impact seems to be in the winter hemisphere
Simmons et al (1983) demonstrated a significant
relationship between tropical forcing and downstream
extratropical impacts (below)
KF
G3
G3-KF
342-354 K
thickness
(hPa)
Conclusions
• The ensembling technique of the Grell-Dévényi CP
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causes unrealistic depictions of convection (and
attendant precipitation)
For larger domains (and longer simulation lengths) this
unrealistic convection potentially causes undesirable
downstream consequences
These problems were likely not found due to the short
time scale many parameterization studies use (Grell and
Dévényi (2002) used a series of 12 hour simulations
when developing their CP)
The results shown here corroborate and explain many
earlier findings relating to the G3 CP
The CP differences also suggest the potential utility in
using malfunctioning parameterizations to learn more
about atmospheric phenomena
References
• Grell, G. A., and D. Dévényi, 2002: A generalized approach to
parameterizing convection combining ensemble and data
assimilation techniques. Geophys. Res. Lett., 29, 1693,
doi:10.1029/2002GL015311.
• Mukhopadhyay, P., S. Taraphdar, B. N. Goswami, K. Krishnakumar,
2010: Indian Summer Monsoon Precipitation Climatology in a
High-Resolution Regional Climate Model: Impacts of Convective
Parameterization on Systematic Biases. Wea. Forecasting, 25,
369–387.
• Simmons, A. J., J. M. Wallace, G. W. Branstator, 1983: Barotropic
Wave Propagation and Instability, and Atmospheric
Teleconnection Patterns. J. Atmos. Sci., 40, 1363–1392.
• Wehner, M., 2012: Very extreme seasonal precipitation in the
NARCCAP ensemble: model performance and projections.
Climate Dyn., 22, doi: 10.1007/s00382-012-1393-1
January 7th-February 19th
July 7th-August 24th
Observations Continued
• A reduced ability to produce intense convection
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in the G3 CP, particularly near the maritime
continent, appears to negatively impact
downstream forecast locations (even where the
G3 CP is not active)
This is analyzed by taking the difference of
isentropic trajectories on the 348 K surface
(driven by the KF-G3 observed wind), beginning
at the initial time through forecast hour 168
Red
trajectories
initial
north of
the equator
Blue
trajectories
initiate
south of
the equator
Temporally
averaged
sea level
pressure
Large sea level
pressure differences
exist in the same
northeastern Pacific
Ocean region for
northern winter
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- Similarly, storm track
differences in the
southern winter G3 CP
simulation
Note to Michael: I don’t plan on
including this slide, but here is the
completed histogram.
On the y-axis is number of studies and
the x-axis is maximum length of
parameterization comparison in studies
that are not climate studies
Given the CDFs I showed earlier, you can
see that parameterization stabilization
isn’t reached until about 72 hours,
making shorter comparisons suspect
Stop Here
Grell Example Continued
• A forecast (initialized 00 UTC 19 August) of
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Hurricane Bill (2009) is shown for comparison
During the time shown, Bill was a powerful
hurricane over the central Atlantic Ocean
The top panel will show the standard Grell-3
cumulus parameterization
The bottom panel will show the Grell-3 using
only moisture convergence as a closure
Real-Time Data Generation Overview
Dynamical Core is WRF-ARW 3.0
Two Days Between Each Initialization (From GFS 00Z Forecast)
76 Cases
From Early
June Through
October For
2009
Initialization Time
Spread Of 120 Hour Forecasts