Regional climate of hazardous convective weather through high-resolution dynamical downscaling
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Regional climate of hazardous convective weatherthrough high-resolution dynamical downscaling
Robert J. Trapp • Eric D. Robinson •
Michael E. Baldwin • Noah S. Diffenbaugh •
Benjamin R. J. Schwedler
Received: 15 January 2010 / Accepted: 10 April 2010
� Springer-Verlag 2010
Abstract We explore the use of high-resolution dynami-
cal downscaling as a means to simulate the regional cli-
matology and variability of hazardous convective-scale
weather. Our basic approach differs from a traditional
regional climate model application in that it involves a
sequence of daily integrations. We use the weather research
and forecasting (WRF) model, with global reanalysis data
as initial and boundary conditions. Horizontal grid lengths
of 4.25 km allow for explicit representation of deep con-
vective storms and hence a compilation of their occurrence
statistics over a large portion of the conterminous United
States. The resultant 10-year sequence of WRF model
integrations yields precipitation that, despite its positive
bias, has a diurnal cycle consistent with observations, and
otherwise has a realistic geographical distribution. Simi-
larly, the occurrence frequency of short-duration, poten-
tially flooding rainfall compares well to analyses of hourly
rain gauge data. Finally, the climatological distribution of
hazardous-thunderstorm occurrence is shown to be repre-
sented with some degree of skill through a model proxy
that relates rotating convective updraft cores to the pres-
ence of hail, damaging surface winds, and tornadoes. The
results suggest that the proxy occurrences, when coupled
with information on the larger-scale atmosphere, could
provide guidance on the reliability of trends in the observed
occurrences.
Keywords Severe thunderstorm � Heavy rainfall �Dynamical downscaling � Reanalysis �Weather research and forecasting model
1 Introduction
The regional climatology, temporal variability, and long-
term trends of hazardous, local-scale phenomena such as
tornadoes, hail, and damaging thunderstorm winds have
been difficult to determine reliably, owing to the often-
subjective nature of their observations (e.g., Diffenbaugh
et al. 2008). This is one of the leading reasons why climate
change assessments to date have avoided definitive con-
clusions about how anthropogenic global warming (AGW)
will, or perhaps already has affected these phenomena
(e.g., Intergovernmental Panel on Climate Change 2007;
US Global Change Research Program 2009).
The use of climate models toward this end is possible,
despite the small scale of convective precipitating storms
(CPSs) relative to the grid lengths of such models. Recent
applications have exploited the established relation
between local convective-storm formation and organiza-
tion, and the larger-scale or environmental vertical distri-
butions of temperature, humidity, and horizontal wind
(e.g., Weisman and Klemp 1982). Hereinafter, quantifica-
tions of these atmospheric conditions are referred to as
environmental controls, and include the vertical shear of
horizontal wind over the lower half of the troposphere, and
convective available potential energy (CAPE). The spatial
analysis of the product of these parameters computed from
global reanalysis data has been shown to bear ‘‘a strong
R. J. Trapp (&) � E. D. Robinson � M. E. Baldwin �B. R. J. Schwedler
Department of Earth and Atmospheric Sciences,
Purdue Climate Change Research Center, Purdue University,
550 Stadium Mall Drive, West Lafayette, IN 47906, USA
e-mail: jtrapp@purdue.edu
N. S. Diffenbaugh
Department of Environmental Earth System Science,
Woods Institute for the Environment Stanford University,
473 Via Ortega, Stanford, CA 94305, USA
123
Clim Dyn
DOI 10.1007/s00382-010-0826-y
resemblance’’ to the distribution of significant severe
thunderstorm1 observations (Brooks et al. 2003b). A simi-
lar analysis derived from regional climate model (RCM)
simulations has been used to argue that the number of days
supportive of severe-thunderstorm formation over the
United States will likely increase in response to elevated
greenhouse forcing (Trapp et al. 2007a). The modeling
studies of Del Genio et al. (2007), Trapp et al. (2009), and
Van Klooster and Roebber (2009), lend support to this
argument.
Such ‘‘implicit’’ modeling approaches are not without
limitations however. For example, environmental CAPE
and vertical wind shear alone provide little information
about how and whether deep convective clouds initially
form (i.e., the convection initiation), which is fundamental
to conclusions about changes in the frequency of storms
themselves. Furthermore, environmental parameters fail to
predict storm morphology unambiguously and thus the
likelihood of specific convective phenomena (Gallus et al.
2008).
Climate modeling that permits explicit representation
of convective storms would remove these and other limi-
tations. One ‘‘explicit’’ modeling approach was intro-
duced by Trapp et al. (2007b) through the simulation of
historical extreme convective-storm events using a non-
hydrostatic model. Global reanalysis data provided the
initial and boundary conditions for their 36-h integrations
over nested domains. Although this particular application
could be characterized more as regional forecasting than
as regional climate modeling, it did show that global
reanalysis could be dynamically downscaled to produce
the correct organizational mode of convective precipita-
tion, in the correct general geographic location, and
within a few hours of the correct time. In addition, tor-
nado proxies computed from the model-simulated winds
were shown to compare well in relative numbers to those
of tornado observations on many of the days considered.
Of course, the successful simulation of a few specific
events does not guarantee successful simulation of all
convective-storm events (as confirmed by the collective
experiences of high-resolution modelers; e.g., see Weis-
man et al. 2008; Kain et al. 2006), thus motivating this
next phase of our research.
Indeed, with the approach of Trapp et al. (2007b) as a
blueprint for the methodology followed herein, we consider
non-hydrostatic model integrations for multiple seasons,
over a single, large, convective-storm-permitting domain.
Work with GCM-driven simulations is underway to
investigate postulated changes in convective storminess
under AGW scenarios. The focus here, however, is on the
use of reanalysis-driven simulations to explore the ability
of high-resolution dynamical downscaling to generate the
regional climatology of hazardous convective-scale
weather. In addition to providing an evaluation of the
downscaling technique, reanalysis-driven simulations
allow us to consider occurrences of phenomena not well
observed, including historical trends in convective weather.
Such trends are difficult to assess currently, owing to the
nature of the hazard observations: they are largely derived
from eyewitness observations/damage, which are con-
volved with population growth, changes in reporting pro-
cedures, and organized programs that have made trend
detection difficult (see Diffenbaugh et al. 2008).
The modeling approach is described in Sect. 2, and its
application over a 10-year period in the United States is
given in Sect. 3. Resultant trends in downscaled convective
hazard occurrences are also revealed in Sect. 3. A sum-
mary and discussion are offered in Sect. 4.
2 Model and methods
We dynamically downscale the National Centers for
Environmental Predictions (NCEP)-National Center for
Atmospheric Research (NCAR) Reanalysis (R1) (Kalnay
et al. 1996) data using the non-hydrostatic, ‘‘advanced
research’’ core of the weather research and forecasting
(WRF) model (Skamarock et al. 2008). The computational
domain has a horizontal gridpoint spacing of 4.25 km, and
encompasses much of the continental United States (see
Fig. 1). This single domain can be considered convective-
storm permitting (e.g., Weisman et al. 1997), and therefore
allows us to consider CPS statistics anywhere within the
domain. Our experimentation has not shown a need for a
larger, coarser-grid domain that intermediates the 2.5� R1
data and the WRF domain (see Trapp et al. 2007b), yet a
five grid-cell buffer at the lateral edges of the domain is
employed. Parameterizations of physical processes
(Table 1) and other aspects of the model set-up are based
on the experimental, high-resolution, WRF-model predic-
tions of convective weather in the United States (e.g.,
Weisman et al. 2008; Kain et al. 2006).
Our procedure is to integrate the model over a 24-h
period (12 UTC day 1 to 12 UTC day 2), re-initialize the
model with the R1 data (see Table 1) and then integrate/re-
initialize over each subsequent 24-h period during April–
June, 1991–2000. These months represent the time of
highest frequency of hazardous convective weather (e.g.,
Brooks et al. 2003a; Doswell et al. 2005), and although the
10-year length is arbitrary, it is sufficiently long to generate
a reasonable sample of CPSs and also to admit some inter-
annual variability.
1 We use the term ‘‘thunderstorm’’ to indicate a deep convective
cloud that has a time scale of hours and a length scale of tens of
kilometers. The existence of lightning is not necessarily implied.
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
Our decision to limit the individual integrations to 24 h is
guided in part by the documented ability of the WRF model
to develop the mesoscale portion of the atmospheric kinetic
energy spectrum out of the larger scales resolved in the
initial conditions (i.e., model spin-up) within the first 6–8 h
of the integration (see Skamarock 2004). Thus, a 1200 UTC
(local morning) initialization should still allow for simula-
tion of the typical initiation and evolution of CPSs within a
diurnal heating cycle. (This will in fact be demonstrated
below.) A beneficial consequence of this procedure is a
greatly diminished segment of the integration period lost to
spin up, and thus a much more efficient use of computa-
tional resources. Moreover, this early morning period is
outside of the time when convective hazards are most fre-
quent (e.g., Kelly et al. 1978, 1985), thus minimizing the
effect of spin-up on our occurrence statistics.
April May June
WR
F M
od
elO
bse
rvat
ion
s
0.1 0.3 0.5
a b c
d e f
mm/hr
Fig. 1 Mean daily precipitation rate (mm h-1) for the months of
April, May, and June from a–c the WRF model integrations, and (d–f)the 0.25� resolution US daily precipitation analysis produced by
NOAA/CPC. Daily precipitation rates are averaged over the respec-
tive months and the years 1996–2000
Table 1 WRF model physics
parameterization schemes,
relevant model parameters, and
details on initial/boundary
condition data
WSM6, Hong and Lim (2006);
Dudhia, Dudhia (1989); RRTM,
Rapid Radiative Transfer Model
(Mlawer et al. 1997; Iacono
et al. 2000); Noah, Chen and
Dudhia (2001); MYJ, Mellor-
Yamada-Janjic, Mellor and
Yamada (1982)
Parameterization
Microphysics WSM6
Radiation (SW/LW) Dudhia/RRTM
Land surface model Noah
Planetary boundary layer MYJ
Model parameters
Time step 25 s
Vertical (Eta) levels 35
Initial/boundary conditions
Temperature, specific humidity, geopotential height,
horizontal winds, surface pressure
17 isobaric levels, surface level; 6-h intervals
Soil temperature, soil moisture 0–10, 10–200, 300 cm; 6-h intervals
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
We recognize that the daily re-initialization limits an
equilibration of the surface physics (soil moisture and
temperature), which is particularly desirable in long-term
regional climate modeling (e.g., Giorgi and Mearns 1999).
However, the benefit of re-initialization is that it prevents
error growth in the form of a succession of convective-
scale interactions and feedbacks that, consistent with
Lorenz’s (1969) theoretical prediction, can erroneously
saturate the solution at these scales of greatest interest.
Moreover, a well-equilibrated land surface and attendant
mesoscale heterogeneity (e.g., Pielke et al. 1991; Weaver
and Avissar 2001) may be of lesser importance during the
months of interest here (April, May and June), in which
significant CPSs tend to have strong links to synoptic-scale
processes (e.g., Doswell and Bosart 2001). Experiments
with longer (continuous) integration times and thus less
frequent re-initializations are planned to examine potential
contributions of long-memory processes to the climate
statistics of hazardous convective weather.
3 Results
We begin with daily rainfall. This is not necessarily a con-
vective weather hazard per se, but does have far-reaching
socio-economic importance, and is known to be a difficult
variable to model accurately, especially when generated in
convective clouds (e.g., Duffy and Govindasamy 2003;
Walker and Diffenbaugh 2009). The observational dataset
produced by National Oceanic and Atmospheric Adminis-
tration (NOAA)/Climate Prediction Center (CPC) at 0.25�resolution (http://www.cpc.ncep.noaa.gov/products/precip/
realtime/retro.shtml) reveals a monthly evolution in the
areal extent and magnitude of mean daily rainfall, and this is
similarly shown in the modeled precipitation (Fig. 1).
Although there is an obvious difference in the precipitation
magnitudes, we do find some parity in the geographical
distributions of the observed and modeled precipitation.
Interpolating the WRF output to the native grid of the
precipitation observations allows for a quantification of this
comparison. We find a consistent positive bias (or mean
error) in the WRF precipitation rate, which is a primary
contributor to the root mean square errors (RMSE) listed in
Table 2. This agrees with Weisman et al. (2008), who have
documented a tendency of the WRF model to under- (over-)
predict the amount of stratiform (convective) precipitation.
The errors also tend to grow by month within the warm
season. As discussed below, this is likely attributable to the
seasonal progression in the scale of the predominant CPS
forcing.
The modeled precipitation displayed in Fig. 1a–c
appears to initiate and persist in a manner consistent with
the diurnal cycle of solar heating. This is demonstrated
using frequency diagrams of simulated and observed
hourly precipitation ([0.1 mm) averaged over the latitu-
dinal zone of 33�–48�N; the frequency diagrams, also
known as diurnal cycle composites, are constructed fol-
lowing the procedure outlined by Ahijevych et al. (2005),
who produced the observational analyses (Fig. 2d–j; see
http://locust.mmm.ucar.edu/episodes/Hovmoller/index.html).
Of the months simulated, June has the strongest diurnal
cycle and hence is featured in Fig. 2. In the longitudinal
span of 95�–80�W, we see a high frequency of observed
precipitation occurrence between the afternoon and even-
ing hours of *1800 UTC to *0100 UTC. Despite its 1200
UTC initialization, the model likewise generates precipi-
tation in high frequency over this geographic area and time
period, although with a slight lag. It is obvious that the
simulated convective precipitation occurs more frequently,
consistent again with biases documented by Weisman et al.
(2008). As inferred from longitude-time sections of rainfall
(zonal Hovmoller diagrams; e.g., see Fig. 2 of Carbone
et al. 2002), the frequency diagrams suggest time-pro-
gressive areas of precipitation originating *105�W in the
late afternoon. These are manifestations of mesoscale
convective systems that initiate in the High Plains of the
United States late during the day and then propagate
eastward overnight through the Great Plains (e.g., Carbone
et al. 2002). In the observations, these CPSs generally
decay by 1200 UTC except near 95�W; a similar evolution
can be deduced in the simulated precipitation. Thus, haz-
ardous convective weather naturally occurring during
(local) morning hours in association with nocturnal meso-
scale convective systems will not be represented in our
simulations. Although the precipitation occurring during
this morning gap would add to biases in daily precipitation,
it should not be too critical for the primary purposes of this
modeling application, since tornadoes, hail, and damaging
straight-line winds are most frequent in the late afternoon
hours (e.g., Kelly et al. 1978, 1985).
Heavy rainfall is connected to the hazard of flooding of
course, and a rough guideline for the potential for flash
flooding is rainfall exceeding 25 mm (*1 in.) per hour for
several hours (Doswell et al. 1996). This guideline has
objective support from the recent work of Hitchens et al.
(2010), who found that extreme sub-diurnal precipitation
events determined using statistical methods from extreme
Table 2 Error statistics in WRF precipitation rate (mm h-1) com-
puted using the 0.25� resolution US daily precipitation analysis pro-
duced by NOAA/CPC
Month Bias RMSE
April 0.045 0.086
May 0.054 0.096
June 0.052 0.121
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
value theory are usually comprised of individual hours of
rainfall [25 mm. We thus adopt this 25-mm threshold in
our analyses, as did Brooks and Stensrud (2000) previ-
ously, and quantify the mean frequency of such hourly
rainfall at individual gridpoints.
The monthly geographical progression of the WRF-
simulated heavy-rainfall occurrence is compared in Fig. 3
to hourly rain gauge data analyzed by Brooks and Stensrud
(2000). The modeled heavy-rainfall distributions span the
same geographical area as those observed, but with some
differences in locations of maxima. The average occur-
rence frequencies represented in the modeled maxima can
be as much as twice those in the observed maxima. When
evaluating these details, however, it should be kept in mind
that the observational analysis is based on rain gauges that
have a non-uniform, *50 km separation distance, and is
derived from data over a much longer time period (1948–
1993). Given these differences, our conclusion is that the
simulated monthly distributions of heavy-rainfall occur-
rence also compare favorably with the observed distribu-
tions, although this is unavoidably subjective as was the
conclusions on daily precipitation rate.
Relatively accurate determination of the regional cli-
matology of precipitation is possible using direct and
remotely sensed observations. As mentioned previously,
this is not the case with the severe thunderstorm-generated
phenomena of hail, damaging winds, and tornadoes,
therefore motivating the following analysis. We begin with
the fact that supercell thunderstorms, which are a mode of
highly organized deep convection, are nearly always
associated with reports of one or more of these hazardous
phenomena during their typical several-hour lifecycle (e.g.,
Bunkers et al. 2006). Particularly in the middle tropo-
sphere, supercells are characterized by a high degree of
spatial correlation between primary cores of vertical wind
(an updraft) and vertical rotation (a mesocyclone); both
have diameters of roughly 5–10 km. Figure 4a shows an
example of a supercell that occurred in one of our simu-
lations. This feature, which is represented (though only
nominally resolved) by the 4.25-km gridpoint spacing, is
identified by a local maximum in simulated radar reflec-
tivity factor2 (Z), and by its rotating updraft core. The latter
can be quantified by updraft helicity (UH):
UH ¼Zzt¼5 km
z0¼ 2 km
w fdz; ð1Þ
where w is the vertical component of velocity, f is the vertical
component of vorticity, and the vertical integration is over
the 2–5 km layer above ground level (Kain et al. 2008).
-100 -90 -80
12
12
00
00
-100 -90 -80
12
12
00
00
604 20 5236605236204
a
b
c
d
e
f
g
h
i
j
Fig. 2 Diurnally averaged frequency of a–e observed and f–jsimulated hourly precipitation ([0.1 mm), averaged over the latitu-
dinal zone of 33�–48�N, for each June over the years 1996–2000. The
diagrams are produced following the procedure outlined by Ahijevych
et al. (2005), who generated the observational analyses (see http://
locust.mmm.ucar.edu/episodes/Hovmoller/index.html). Abscissa val-
ues are longitude (degrees), as indicated by solid vertical lines.
Ordinate values are time (UTC), and dashed horizontal lines indicate
1200 UTC 2 See Kain et al. (2008) for details on how Z is computed.
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
Supercells are not the only convective storms that possess
rotating updraft cores, however. Consider Fig. 4b, which
reveals a developing quasi-linear convective system. This
CPS morphology is: also well organized; frequently causes
wind damage and occasionally, tornadoes (Gallus et al.
2008; Trapp et al. 2005); and is known to possess multiple
rotating updraft cores, albeit not as intense and vertically
deep as those in supercells (Weisman and Trapp 2003).
Thus, we explore a proxy for severe thunderstorm
occurrence in the downscaled fields, given the existence of
April
May
June
d
e
f
occurrrence frequency of 25mm/1 hr rainfall
a
b
c
Fig. 3 Mean occurrence frequency of hourly rainfall [25 mm, a–c from the reanalysis-driven WRF model integrations (1991–2000), and d–ffrom hourly rain gauge data analyzed by Brooks and Stensrud (2000) (1948–1993), for the months of April, May, and June
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
a rotating updraft core. Our occurrence proxy requires
gridpoint values of UH C 40 m2 s-2 (see Kain et al. 2008)
and Z [ 50 dBZ, which indicates convective precipitation.
These thresholds are based on a quantitative comparison
with observed reports of hail, severe convective winds, and
tornadoes (e.g., NCDC 2009). Comparisons are enabled by
assigning each report to the nearest WRF gridpoint (a
‘‘nearest-neighbor’’ interpolation), and then summing these
within coarsened grid cells of 38.25-km length. This coarse
grid length is approximately half that used in severe-
weather climatologies (Brooks et al. 2003a), and partially
compensates for known errors in report location (and time).
Occurrences of the model proxy are likewise coarsened.
Figure 5a–c depicts a monthly geographical progression
of simulated severe-thunderstorm frequency that is con-
sistent with the observed northward migration of severe
convective weather during these months. The maximum in
simulated severe-weather frequency generally envelops the
observed maximum (Fig. 5d, e). However, there is a ten-
dency for the model simulations to over-predict the report
frequencies during the months of May and June in the
Northern Great Plains (NGP), and then under-predict the
report frequencies during June in the eastern US. Indeed,
an evaluation of the RMSE between the simulated and
observed occurrences reveals a monthly increase in such
error within the warm season (Fig. 6). We attribute this in
part to the seasonal variation in the predominant CPS
forcing, from well-defined (and R1-resolved) synoptic-
scale weather systems down to weaker synoptic-scale
systems and also mesoscale systems that are not resolved in
the R1 data. Some of the discrepancies can also be attrib-
uted to the use of a constant UH–Z pair for the entire
period, which we did for the sake of consistency: Fig. 6
indicates that the UH–Z proxy has a monthly dependence,
with different pairs of these variables giving lower RMSE
values. We will continue to explore ways of improving this
severe-weather proxy; one possibility is suggested below.
Though helpful at a basic level, measures such as RMSE
can be misleading due to the sporadic nature of convective
weather occurrence and its fine-scale variations. For
example, a simulated occurrence maximum that is dis-
placed one grid cell from the observed maximum would be
Z UHa
b
Fig. 4 Example of a a supercell
thunderstorm and b quasi-linear
convective system included in
our set of simulations, as shown
by fields of simulated radar
reflectivity factor (Z), and by
markers where updraft helicity
(UH) locally exceeds 40 m2 s-2
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
penalized with a large error, even though subjectively such
a small displacement would be considered acceptable and
reasonably accurate. Borrowing from the forecast verifi-
cation community, we employ the concept of ‘‘fuzzy
verification,’’ which relaxes the requirement of exact spa-
tial matches but still rewards proximity between the simu-
lations and verifying data (Ebert 2008). Our approach is to
map the modeled and observed severe weather occurrence
to increasingly coarse grids, and then compute a scale-
normalized similarity,
SNSn ¼ 1� RMSEn
RMSEn;ref
; ð2Þ
where n quantifies the coarseness of the grid relative to
native WRF grid, Oi,j and Mi,j are the observational and
modeled data at gridpoints (i, j), and thus
RMSEn ¼1
NxNy
XNx
i¼1
XNy
j¼1
On;i;j �Mn;i;j
� �224
35
1=2
; ð3Þ
and
RMSEn;ref ¼1
NxNy
XNx
i¼1
XNy
j¼1
O2n;i;j þ
XNx
i¼1
XNy
j¼1
M2n;i;j
!" #1=2
:
ð4Þ
Equation 2 is patterned after the fractions skill score
(FSS; see Roberts and Lean 2008), and like FSS, SNS
increases asymptotically as n and the corresponding grid
length (n 9 4.25 km) are increased over *2 orders of
magnitude (Fig. 7). SNS also has a dependence on month,
mean occurrrence frequency
JuneMayApril
Ob
serv
atio
ns
WR
F M
od
el
a b c
d e f
Fig. 5 Mean occurrence frequency of severe convective weather (hail, severe wind, and tornado) over the period 1991–2000, a–c from reported
occurrences, and d–f derived from the reanalysis-driven WRF model integrations, for the months of April, May, and June
70-50 70-40 70-30 60-50 60-40 60-30 50-50 50-40 50-30 40-50 40-40 40-30
Fig. 6 Evaluation of the RMSE between the simulated and observed
occurrences of severe convective weather for a range of UH–Z pairs,
as a function of month: April (blue), May (red), and June (green). The
UH–Z pair of 40–50 defines the proxy used in Fig. 5
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
with the modeled occurrences in May having the lowest
error, and in essence, the most skill. The apparent
discrepancy between SNS and the RSME evaluation in
Fig. 6 is due to the higher numbers of occurrences in May
relative to April (and June), which would contribute to a
higher SNS (see Eqs. 2–4). Noting from Eq. 2 that
SNS = 1.0 would represent perfect ‘‘skill,’’ an important
implication of Fig. 7 is that, although necessarily run at
several-kilometer scales, our current model simulations of
severe convective-weather climatology do not become
skillful in a strict sense until evaluated at several-hundred-
kilometer scales. This conclusion will need to be revisited
once a longer time series becomes available, and hence
when the modeled climatological distribution is more
robust.
We conclude this section with a consideration of
temporal trends in the downscaled convective hazards.
Figure 7 prompts us to evaluate these over relatively large
geographical regions, and accordingly we use the US
regions defined in Trapp et al. (2009), hereinafter the
southeast (SE; 75–95�W, 25–37.5�N), northeast (NE; 67.5–
80�W, 37.5–47.5�N), Midwest (MW; 80–95�W, 37.5–
50�N), southern Great Plains (SGP; 95–105�W, 25–40�N),
and NGP (95–105�W, 40–50�N). Time series are con-
structed of annual occurrences within each region, over the
3-month season.
Although the relatively short length of these time series
does not permit advanced statistical analysis, it is apparent
that the observed severe weather occurrences have positive
trends over each region (Fig. 8a–e). Relative to the
observations, the time series of model proxy occurrences in
the SE, MW, SGP, and NE regions have shallow positive
slopes, while that in the NGP region has a negative slope
(Fig. 8b). The agreement in sign of the trend over four of
the five regions suggests that the trends are due at least in
part to the natural environment rather than to entirely non-
physical factors (such as population growth, etc.). We also
raise the possibility that the modeled trends—including
that over the NGP region—could actually be closer to the
(unknown) true state of the natural environment, owing to
their consistency with the reanalysis-based environmental
controls. Support for this possibility comes from regionally
and seasonally averaged calculations of the product
CAPE 9 S06, where S06 is the magnitude of the vector
difference between the horizontal wind at 6 km AGL and
the wind at 10 m AGL (Fig. 8b) (Brooks et al. 2003b;
Trapp et al. 2007a). Linear (Pearson) correlations between
the time series of this environmental control and that of the
proxy occurrences range from 0.77 over the SE region to
0.44 over the MW region (see Fig. 8b), which owing to the
short length of the series are somewhat crude estimates of
moderate-to-strong relationships.
As an aside, rather good correspondence can be found
between the model and observations over some of the
individual years. In 1998, for example, the SE, NE, and
MW regions each exhibit sharp peaks (and the SGP region,
a sharp dip) in the environmental control, proxy occur-
rences, and observed storm occurrences. Of course, 1998
was a year of a significant El Nino event (Bell et al. 1999),
and excessive rainfall in the SE and MW has been attri-
buted to that event; drought in the SGP has been attributed
to the El Nino event and to other internal forcing (Hong
and Kalnay 2002).
It is important to note that, taken alone, the environ-
mental controls still suffer from the weaknesses described
in Sect. 1, and indeed, Fig. 8 indicates the regional and
temporal dependency of the convective-scale response to
the large-scale forcing. Yet, it is plausible that the model
occurrences, coupled with analysis of this and other envi-
ronmental controls can provide some guidance on the
reliability of the trends in the observed occurrences, and
furthermore could be used to reconstruct such trends, given
a longer time series. Our future improvements to the model
proxy will be made with this in mind.
4 Summary and discussion
Motivated by the established uncertainty in the observational
dataset of tornadoes, hail, and damaging thunderstorm
winds, we have explored herein the use of high-resolution
dynamical downscaling as a means to simulate the regional
climatology and variability in convective-scale hazardous
Sca
le-N
orm
aliz
ed S
imila
rity
Grid Scale
Fig. 7 Scale-normalized similarity (see text) of severe convective
weather occurrence as a function of grid coarseness n 9 4.25 km, for
the months of April (blue), May (red), and June (green)
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
weather. The basic approach involved a 10-year sequence of
daily integrations of the WRF model. R1 global reanalysis
data served as initial and boundary conditions. Since the
study focused on convective weather in the United States, the
integrations were limited to the warm-season months of
April–June, over the years 1991–2000. Horizontal grid
lengths of 4.25 km allowed for explicit representation of
deep convective storms, and their occurrence statistics were
compiled over a large portion of the conterminous United
States.
The 10-year sequence of WRF-model integrations
yielded precipitation with a diurnal cycle consistent with
observations, and otherwise with a realistic geographical
distribution. Similarly, the occurrence frequency of short-
Occ
urr
ence
s
Env
iro
nm
enta
l Co
ntr
ol
southeast
northeast
midwest
southern Great Plains
northern Great Plains
a
b
c
d
e
f
g
h
i
j
0.76
0.42
0.49
0.60
0.60
Fig. 8 Time series of
regionally and seasonally
compiled a–e observed severe
convective storm occurrences,
and f–j modeled severe
convective storm occurrences
(blue line) and an environmental
control (CAPE 9 S06; greenline; see text) over the
southeast, northeast, Midwest,
southern Great Plains and
northern Great Plains regions. In
a–e, the dashed red line is the
linear least squares fit to the
time series of observed
occurrences, and in f–j, the
dashed blue line is the linear
least squares fit to the time
series of modeled occurrences.
Also indicated in f–j are the
linear correlations between the
modeled occurrences and
environmental control
R. J. Trapp et al.: Regional climate of hazardous convective weather
123
duration, potentially flooding rainfall, defined here as an
accumulation that exceeds 25 mm in 1 h, compared well to
analyses of hourly rain gauge data. A positive bias in such
heavy precipitation as well as in mean daily precipitation
was revealed, however.
To identify other severe convective storms in the WRF
integrations, a model proxy was developed: model-
resolved rotating convective updraft cores were assumed to
indicate the presence of hail, damaging surface winds, and/
or tornadoes. We showed that the model proxy occurrence
represents the climatological distribution of hazardous
thunderstorms with some skill. Moreover, we suggested
that the proxies, when coupled with information on the
larger-scale environment, could provide guidance on the
reliability of trends in the observed occurrences, and in fact
could be used to reconstruct such trends, given a longer
time series. Our future improvements to the model proxy
will be made with this in mind.
This study lends further support to the idea that the
atmospheric state is sufficiently represented in relatively
coarse data (equivalent to *100 km grid lengths) such that
dynamical downscaling of these data can yield climate
statistics of convective-scale phenomena. Although model
resolution is not a panacea, it is not too surprising that
explicit representation of the convective-scale processes is
an integral part of the downscaling technique. In our future
work, we will extend our reanalysis-based downscaling to
other convectively active months, over more years. This
will allow us to explore the influences of natural and
anthropogenic processes on hazardous convective-weather
occurrence. Additional experiments with longer integration
times and less frequent re-initializations will be used to
examine the potential contributions to hazardous CPS
forcing through feedbacks associated with long-memory
processes. Finally, ongoing GCM-driven simulations are
underway to investigate model-resolved convective
storminess under AGW scenarios.
Acknowledgments This research was supported in part by NSF
ATM-0756624 (RT, MB, ND, and ER), DOE DE-FG02-08ER64649
(ND), and benefitted from computing resources provided through the
NCAR Accelerated Scientific Discovery program and by the Purdue
University Rosen Center for Advanced Computing. Dr. David
Ahijevych at NCAR provided helpful information regarding the
Hovmoller diagrams. Comments made by the two anonymous
reviewers helped us clarify and improve our discussion. This is
PCCRC Paper #0920.
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