Regional climate of hazardous convective weather through high-resolution dynamical downscaling

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: [email protected]

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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