Transcript Weather and Climate Hazards in Hawaii and Taiwan

Weather and Climate Hazards
in Hawaii and Taiwan
Pao-Shin Chu
Department of Meteorology
University of Hawaii
Honolulu, Hawaii, USA
Presented at the Department of Atmospheric
Sciences, National Central University
6/14/2011
• An international workshop on natural
disasters and mitigation to be held in
Honolulu, Hawaii in March (?) 2012
• To be funded by the National Science
Council through its LA Office
• Heavy rainfall/flooding events, drought
• Hurricanes
• Wildland Fires
• Tornadoes, hails, winter storms, heat waves, cold
surges
• Earth Quakes/Tsunamis, volcanoes, landslides
Long-term rainfall variations in Hawaii (HRI)
Chu, P.-S., and H. Chen, 2005: Interannual and interdecadal variations in
the Hawaiian Islands. Journal of Climate, 18, 4796-4813.
• The HRI exhibits both a clear signal of
interannual and interdecadal variations.
• Rainfall is particularly low when El Niῆo occurred
in the presence of positive PDO.
• The band of anomalous surface westerlies to the
north of Hawaii, and the deep sinking motion
and the anomalously vertically integrated
moisture flux divergence over Hawaii are all
unfavorable for rainfall.
• In the past, heavy rainfall events have
resulted in major damage to properties, public
infrastructure, agriculture, transportation, and
tourism in Hawaii.
• The 1987 New Year’s Eve flood on Oahu
(a flood warning was NOT issued by the
NWS until flooding had already commenced,
affected densely populated urban areas)
• 24-hr totals as high as 37 inches (>925 mm)
on the Island of Hawaii in early Nov 2000
($88 million damage).
• 12-hr values were 10 inches and rainfall rate was 5
inches per hour in upper Manoa Valley of Oahu in late
October 2004 (Halloween flood) ($80 million damage
for UH).
• For 43 days between February and early April in 2006
(March Madness) Hawaii was battered by rain (Dam
wall broke on Kauai and 7 people died)
• Heavy rainfall and flood on Maui and Hawaii in
December 2007
• Hilo flooding (early Feb 2008), Oahu flooding
(December 2010)
March 2006 flooding on Oahu
(March Madness?)
Three different methods are commonly
used to define extreme rainfall events
• Daily precipitation with amounts above 2 (4)
inches is defined as a heavy (very heavy) event
- Karl et al. BAMS, 1996; Groisman et al., Climatic Change,
1999
• Daily precipitation values associated with the
90th (99th) percentile of the distribution as a
heavy (very heavy) event – Groisman et al., BAMS,
2001
• Annual maximum daily precipitation values
associated with 1-yr (20-yr) return periods as a
heavy (very heavy) event – Kunkel et al., J. Climate,
1999; Groisman et al., BAMS, 2001; Zwiers and Kharin, J.
Kunkel found that events that have a
recurrence interval of 1-yr or longer have a
high correlation with flooding in some U.S.
regions.
An n-yr event is often referred to as an
event having a 1/n chance of occurring in
a single year.
Objectives
To understand the frequency, intensity, locations,
and patterns of heavy rainfall events in Hawaii
To provide updated risk-event maps which may
benefit local partners (FEMA, state and county
civil defense, NOAA, DLNR, BWS) who are
concerned with floods and the relevant policymaking
Generalized Extreme Value (GEV) distribution
11/ 
f ( x) 
1   (x   ) 
1


 
exp{[1 
 ( x   ) 1/ 
 (x   )
] }, 1 
 0,


Here there are three parameters: a location (or shift) parameter
parameter  , and a shape parameter
.


 ( x   ) 1/ 
F ( x)  exp{[1 
] },

, a scale
How to determine values of the
distribution parameters?
• The method of maximum likelihood (ML) seeks to find
values that maximize the likelihood function. However, it
is not necessarily the best for finite sample sizes.
• The method of L-moments is chosen because this
method is computationally simpler than the method of
ML and because L-moment estimators have better
sampling properties than the method of ML with small
samples (more robust). Hosking & Wallis, 1997; Zwiers
& Kharin, 1998
As  approaches zero, the GEV is
reduced to the two-parameter
Gumbel distribution.
1
R ( x) 
.
[1  F ( x)]
where  is the average sampling frequency
(usually as 1 yr-1). The return period R(x)
associated with a quantile x is interpreted to be the
average time between occurrence of events of that
magnitude or greater.
Heavy rainfall/flood
Heavy rainfall: daily rainfall > 2 inches
Very heavy rainfall: daily rainfall >4 inches (NCDC)
Chu, P.-S., X. Zhao, Y. Ruan, and M. Grubbs, 2009:
Extreme rainfall events in the Hawaiian Islands.
J. Appl. Meteor. Climatol., 48, 502-516.
• For estimating the statistics of return periods, the
3-parameter GEV distribution is fit using the
method of L-moments.
• Spatial patterns of heavy and very heavy rainfall
events across the islands are mapped
separately based on 3 methods.
• Among all islands, the patterns on the island of
Hawaii is most distinguishable, with a sharp
gradient from east to west. For other islands,
extreme events tend to occur locally on the
windward slopes.
Hawaii’s costliest natural disasters (Source: Hawaii Civil Defense, 2004)
1. Hurricane Iniki
9/11/1992 $2.6B, 4 dead
2. Hurricane Iwa
11/23/1982 $307M, 3 dead
3. Big Island flood 11/1/2000 $88.2M
4. Floods
1/6-14/1980 $42.5M
5. New Year’s flood 12/31/1987 $35M
6. Tsunami
5/22/1960 $26.5M, 61 dead
7. Tsunami
4/1/1946 $26M, 159 dead
8. Kilauea lava flow 1990
$21M
9. Floods
3/19-23/1991 $10 to 15M
10. Oahu flood
11/7/1996 $11M
*Damage is not adjusted for the current value.
A rough damage estimate of $80 million from the October 30, 2004 flooding in UHManoa would make it the fourth-costliest natural disasters in Hawaii history. Damage
from March 2006 flood with a dam wall broke leading to 7 deaths??? Drought
damage is not accounted for.
Hurricane Iniki in 1992: Destructive winds, torrential rain, and
storm surges
Lihue, Kauai
during Hurricane Iniki
Destruction on Kauai from Iniki
Some applications of Bayesian analysis
for tropical cyclone research
•
Change-point analysis for extreme events
Zhao and Chu, 2010, J. Climate (Typhoons over WNP)
Zhao and Chu, 2006, J. Climate (Hurricanes over ENP)
Chu and Zhao, 2004, J. Climate (Hurricanes over CNP)
•
Tropical cyclone prediction Poisson regression model
Chu and Zhao, 2007,J. Climate (CNP)
Lu, Chu, and Chen, 2010, Wea. Forecasting (Taiwan)
Chu et al., 2010, J. Climate (Taiwan)
•
Clustering of typhoon tracks in the WNP
Chu et al., 2010, Regional typhoon activity as revealed by track
patterns and climate change, in Hurricanes and Climate Change,
Elsner et al., Eds., Springer
Why Bayesian inference?
• A rigorous way to make probability statements
about the parameters of interest. Probability is
the mathematical language of uncertainty.
• An ability to update these statements as new
information is received.
• Recognition that parameters are changing over time
rather than forever fixed.
• An efficient way to provide a coherent and
rational framework for reducing
uncertainties by incorporating diverse
information sources (e.g., subjective
beliefs, historical records, model
simulations). An example: annual rates of
US hurricanes (Elsner and Bossak, 2002)
• Uncertainty modeling and learning from
data (Berliner, 2003)
Bayes’ theorem
θ : parameter
Classical statistics: θ a constant
Bayesian inference: θ a random quantity, P(θ|y)
y: data
P(y|θ): likelihood function
π(θ): prior probability distribution
P (θ | y ) 
P ( y | θ ) ( θ )
 P ( y | θ ) ( θ ) d θ
θ
Change-point analysis for tropical
cyclones
• Given the Poisson intensity parameter (i.e., the
mean seasonal TC rates), the probability mass
function (PMF) of h tropical cyclones occurring
in T years is
h
(T )
P(h |  , T )  exp( T )
h!
• where h  0,1,2,... and   0 , T  0 . The λ is
regarded as a random variable, not a
constant.
• Gamma density is known as a conjugate prior
and posterior for λ. A functional choice for λ is
a gamma distribution
T 'h '  h '1
f ( | h ', T ') 
exp(T ')
(h ')
• where λ>0, h´ >0, T´>0. h´ and T´ are prior
parameters.
A hierarchical Bayesian tropical
cyclone model
h'
T'
i
hi
adapted from Elsner and Jagger (2004)
i  1,2,...,n
Hypothesis model for change-point analysis
(Consider 3 hypo.)
H0
H1
H2
(1) Hypothesis H 0 : “A no change of the rate” of the
typhoon series:
hi ~ Poisson (hi | 0 , T ) , i  1,2,..., n .
0 ~ gamma(h0 ' , T0 ' ) where the prior knowledge of
parameters h0 ' and T0 ' is given. T = 1.
(2)
Hypothesis
series:
H1 :
the
“A single change of the rate” of the typhoon
hi ~ Poisson (hi | 11 , T ) ,
when
hi ~ Poisson (hi | 12 , T ) , when
  2,3,..., n , and
i  1,2,...,  1
i   ,..., n
11 ~ gamma(h11' , T11' )
12 ~ gamma(h12' ,T12' )
where the prior knowledge of the parameters h11' , T11' , h12' , T12' is
given. There are two epochs in this model and  is defined as
the first year of the second epoch, or the change-point.
Bayesian inference under each hypothesis
(1) Bayesian inference under
hypothesis
H0
There is only one parameter under this hypothesis.
Since gamma is the conjugate prior for Poisson, the
conditional posterior density function for is:
0
0
n
0 | h, H 0 ~ gamma(h0 '  hi , T0 ' n)
i 1
(2)(2)
Bayesian
inference
Bayesian
inferenceunder
underH H hypothesis
hypothesis
1
1
Under
Underthis
thishypothesis,
hypothesis,there
thereare
are33parameters,
parameters, ,,
 . .
andand
1111
12
12
 1 1
H) hypothesis
(2)
Bayesian
inference
under

|
h
,

,
H
~
gamma
(
h
'

h
,
T
'



1
11 | 11h, , H 1 ~1 gamma (h11 '11 hi , Ti 11 11'  1)
1
i 1
i 1

Under this hypothesis,
there
are
3
parameters,
n
n
.
12 | h, ,and
H 1 ~ gamma
( h12 '  hi , T12 ' n    1)
12 | h, , H 1 ~ gamma (h12 ' i hi , T12 ' n1  1)
i 
11 | h, , H 1 ~ gamma
( h11 '  hi , T11 '  1)
11
i 1
 1
 1 h

P ( | h, H 1 , 11 , 12 ) e( 1)(   ) (n 11 
) hi
11 12
P ( | h, H 1 , 1211| h, ,12, H
)
( 1112h)i ,i T1 12 ' n    1)
1 ~e gamma ( h12 '
( 1)( 11 12 )
i
i 1
i 12
 1
P ( | h, H 1 , 11 , 12 )  e
( 1)( 11  12 )
11  h
i
(
)
i 1
•An abrupt shift in the typhoon counts near
Taiwan occurs in 2000 based on the
Bayesian change-point analysis, and this
change is consistent with a northward shift
of the typhoon tracks over the WNP-EA
region.
Tu, Chou, and Chu, 2009: Abrupt shift of typhoon activity
in the vicinity of Taiwan and its association with the
Western North Pacific-East Asian climate change.
J. Climate, 22, 3617-3628.