Extremes Weather Potential Weather and Climate Impact ...

Modeling the Potential for
Extreme Convective Weather
Weather and Climate Impact Assessment Program
Matt Pocernich*, Barbara Brown*,
Eric Gilleland* and Harold Brooks +
*National Center for Atmospheric Research, Boulder, USA
+ NOAA, Norman, Oklahoma, USA
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The problem is …
There is a desire to make inferences about
severe storm activity under climate change.
But…
Severe convective storms are not directly
predicted or indicated by climate models nor reanalysis
data.
Historical records rely on human observations
Limited temporal and spatial coverage
Determining changes in the frequency and
intensity of these events is problematic.
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CAPE, shear and severe
storms
Work by Brooks, Lee and Craven (2003)
links CAPE and shear to discriminating
convective events
CAPE = convective available potential
energy; Shear = changes in vertical
velocity with height
The influence of both variables can be
captured by modeling CAPE * Shear
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Limitations of CAPE*Shear in
discriminating storm types.
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Discrimination plot and
empirical distribution
functions for match
proximity soundings by
storm type. Data from
Craven and Brooks,
2002.

Limitations of CAPE*Shear in
discriminating storm types.
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Discrimination plot and
empirical distribution
functions for match
proximity soundings by
storm type. Data from
Craven and Brooks,
2002.
Median values
indicate reasonable
spread

NCEP/NCAR Reanalysis Data
(Kalnay 1996)
Resolution ~1.9x1.9 degree lat lon, 27
levels (Approx 17,000 gridpoints).
Every 6 hours from June 1, 1957- Dec
31, 1999 with global coverage.
Values of CAPE and shear were
calculated using the re-analysis data at
each grid point.
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Other approaches
Satellite based analysis for Tropics
(Zipser, BAMS 2006)
Observation based (Europe, US)
Model CAPE based on radiosonde data.
(Derubertis, 2006)
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What is new…
Global dataset
Modeling extreme values
Address issues of multiple comparisons
Use spatial statistics techniques
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Mean Annual 95 th percentile CAPE
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Mean annual 95 th percentile
shear
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Mean Annual 95 th Percentile
CAPE*Shear
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20 year return level for CAPE *
shear estimated with GEV (Gilleland, 2006)
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Compare with satellite derived
data Zipser (BAMS, 2006)
/scratch/pocernic/josh2/
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Minimum brightness
temperatures
Max height of 40dBZ
echo
Lightning flash rate

Controlling for multiple
comparisons
Simplest: Bonferroni
Sets significance level at α/N.
Very restrictive. (Our N = 17,800)
Livezey and Chen (1983)
Tests field significance rather than individual tests
Number of p-values less than α compared with the expected
number from a binomial distribution.
Does not take into account strength of p-value.
False Discovery Rate (FDR) – Ventura et al (2004)
Controls number of falsely rejected Ho compare with the
number of rejected.
Wilks (2006) demonstrated use of FDR to measure global
significance.
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Hypothesis tests and the FDR
TRUTH Decision
Accept Ho Reject Ho
Ho n Ho -n FP n FP
Ha n FN n Ha -n FN
Col Totals n accept n reject
FDR Rule:
Reject all Ho when
⎧ i ⎫
= ⎨ ≤ ⎬
⎩ ⎭
k max i: p() i q
i= 0,..., n n
Row
Totals
n Ho
n Ho True
n Ho False
n total
Where q = FDR and p-values are ordered
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Typical local
significance level α =
n FP/n Ho
FDR = α global and
equals E(n FP/n reject)
Provides upper bound
for determining
significant p-values.

Other attributes of the FDR
method.
Much less restrictive than the
Bonferroni.
More powerful when the number of true
Ha is small
Robust to spatial correlation which is a
common feature of climate and weather
data.
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Trends of Annual 95 th
percentile CAPE
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Trends in CAPE, 1973 – 1997
Derubertis, 2006
Spring
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Summer

Trends in Annual 95 th
percentile Shear
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Trends in CAPE * Shear
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Conclusions
CAPE*shear has utility in identifying
convective events, but limited utility is
discriminating between storm types.
Trends in the CAPE values calculated from
soundings generally concur with those from
the reanalysis data.
Regions of high storms identified by other
methods concur with CAPE*shear values
calculated using reanalysis data.
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Future work
Compare results with those of climate
model data.
Address differences in spatial resolution
between climate models and reanalysis.
Develop methods for applying GEV in a
spatial context to improve robustness.
Communicate these findings.
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Trend in extremes using GEV
distribution
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References
Brooks, H.E, J. L., and J. Craven, 2003: The spatial distribution of severe
thunderstorm and tornado environments from global reanalysis data.
ATMOSPHERIC RESEARCH, 67-8, 73–94.
Benjamini , Y. and Y. Hochberg, 1995: Controlling the false discovery rate: A practical
and powerful approach to multiple testing. J. Roy. Stat. Soc. 57B, 289-300.
Craven, J., and H. E. Brooks, 2006: Baseline climatology of sounding derived
parameters associated with deep, moist convection. Nat. Wea. Digest, in
press.
Marsh, P. T., H. E. Brooks, and David J. Karoly (2007). Assesment Of The Severe
Weather Environment In North America Simulated By A Global Climate
Model. Accepted Atmospheric Science Letters
Ventura, V., C.J. Paciorek, and J.S. Risbey, 2004: Controlling the proportion of falsely
rejected hypotheses when conducting multiple tests with climatological data.
J. Climate, 17, 4343-4356.
Wilks, D.S. 2006: On “Field Significance” and the False Discovery Rate. J. of Applied
Meteorology and Climatology, 45, p 1181 – 1189.
Zipser, E. J., Daniel J. Cecil, Chuntao Liu, Stephen W. Nesbitt, and David P. Yorty,
2006: Where are the most intense thunderstorms on earth? (87), 8 Bulletin
of the American Meteorological Society page 1057–1071.
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FDR rule (Benjamini and Hochberg, 1995)
Reject all Ho when
⎧ i ⎫
⎨ ⎬
⎩ ⎭
k = max i: p() i ≤q
i= 0,..., n n
Where q = FDR and p-values are
ordered
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Illustration of false discovery
rate. (Venturi et al, 2004)
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