Typhoon Season in Taiwan PaoShin Chu Hanpei Zhang Kristine Tofte Department of Atmospheric Sciences University of Hawaii and Huiling Chang and TL Chen Central Weather Bureau Presented at the NCUs Department of Atmospheric Sciences 3282017 ID: 794826
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Slide1
Trends in Return Levels of Rainfall Extremes during the
Typhoon Season in Taiwan
Pao-Shin Chu,
Hanpei
Zhang, Kristine
Tofte
Department of Atmospheric Sciences, University of Hawaii
and
Huiling
Chang and T.L. Chen
Central Weather Bureau
Presented at the NCU’s Department of Atmospheric Sciences, 3/28/2017
Slide2Three
different methods are commonly used to define extreme rainfall eventsDaily 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
90
th
(
99
th
) 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. Climate, 1998
Slide3Values are mean annual number of days
with daily precipitation above 50.8 mm (heavy) and 101.6 mm (very heavy) – Groisman
, Knight, Karl 2001
Slide4Values are maximum daily precipitation (mm) associated with
90th (heavy) and 99th (very heavy) percentiles
of Jan and
July
precipitation
Slide5Values are maximum daily precipitation (mm) associated with
1- (heavy
) and
20-yr
(
very heavy
)
return periods
.
Slide6What is the
return period?The return period, also known as recurrence interval, is interpreted to be the average time between occurrence of events of that magnitude or greater. It is commonly used for engineering design (e.g., urban drainage, flood control), risk analysis, environmental regulation, and flood insurance
policy (flood hazard areas).
For example, a 100-yr rain storm has a 1% chance of being exceeded in any one year. However, there is no guarantee that a 100-yr event will occur within a 100-yr period. The probability of the 100-yr event occurring in a century is 0.634.
Slide7Extreme Value Analysis
Extreme value analysis (EVA) refers to the use of extreme value theory for analyzing data where interest is in rare, or low probability, events (e.g., annual maximum 24-hr precipitation)
The R package in2extRemes from UCAR provides a graphical user interface (GUI) or windows to functions from a
ismev
package, along with some additional functionality of its own.
Slide8Generalized
Extreme Value (GEV) distribution
]
1-1/
]
-1/
},
1
+
>
0
Here there are three parameters: a location (or shift) parameter
, a scale parameter
, and a shape parameter
.
1}.
CDF
Quantile function
Slide9For a
stationary GEV, a cumulative distribution function given by (1)
where
μ
,
σ
and
ξ
are the
location, scale, and shape parameter, respectively.
Estimates of the extreme quantiles, known as the
return level
z
p
, corresponding to the
return period (τ) where p is the probability of occurrence
(2)
(3)
Slide10Chu et al., 2009
Slide11For the
non-stationary GEV, (4)
The
return level
z
p
becomes
(5)
It is now obvious that the
location
and
scale
parameters and the
return level
zp are also a function of time.
Slide12A positive slope of the location parameter (µ
1 >0) will result in an increase in the return level, and vice versa. For a positive trend in the scale parameter (σ1 >0), the trend of return level will increase as p decreases, or return period τ increases. The opposite is true for a negative trend in the scale parameter.
Slide13Station ID
Station Name
Data
GEV
GEV
466900
Danshui
+
+
+
466910
Anbu
+466920Taipei+466930Zhuzihu +466940Keelung +466950Pengjia Islet+
+
466990
Hualien
+ (*)
+
+
467080
Ilan
+
+
467350
Penghu+++467410Tainan++
+
467440
Kaohsiung
+
+
+
467490
Taichung
+
+
+
467530Alishan++467540Dawu+++467550Yushan++ + 467590Hengchun+ (*)++467610Chenggong 467620Lanyu+ (*) ++467650Riyuetan+++467660Taitung+++
* 10% significance level
Slide14When a positive trend in the location parameter is embedded with a positive trend of the scale parameter, then the trends of 20- and 100-yr return level will be steeper than that of the 2-yr return level (e.g., Taichung).
Slide15Zp
(return level) is exceeded by the annual maximum in any particular year with probability p.
Slide16Slide17Slide18Slide19Slide20Perspective
Index
Definition
Unit
Intensity
SDII
Average precipitation intensity in wet days
mm/day
Frequency
R25
Annual total number of days with precipitation
≥
25.4 mm
days
Magnitude
R5dAnnual maximum consecutive 5-day precipitation amountmmMagnitudeR95pFraction of annual total precipitation due to events exceeding the 1961-90 95th percentile%DroughtCDDAnnual maximum number of consecutive dry daysdays Climate Change Indices (WMO) for a standard comparison R50≥ 50 mmSDII, R50 (R25 for Hawaii), R5d, CDD
Slide21Nonparametric Mann-Kendall test and Sen’s method
Mann-Kendall test assumes that the time series dataset obeys the model:For data pair xj and xk, where j>k, the sign is calculated:
The
test
statistic
S
is calculated:
If
n>10, the normal approximation statistics Y, which is based on S will be calculated. Positive (negative) S or Y means positive (negative) trend; the significance of the trend is estimated based on the Y value using the table of the standard normal distribution cumulative probabilities.
Slide22Nonparametric Mann-Kendall test and Sen’s method
When using Sen’s method to estimate the slope of the trend, assume that f(t) in
can be represented by:
where
Q
is the slope to be estimated and
B
is a constant. The slopes of all data pairs are calculated using where j>k. The median of all these slopes of data pairs is the Sen’s estimator of slope. Mann-Kendall method tests whether the trend is increasing or decreasing and estimates the significance of the trend. Sen’s method quantifies the slope of this trend.
Missing values are allowed in these two methods, and the data need not conform to any particular
parametric
distribution. Besides, the
Sen’s
method is
robust against skewed distributions and outliers.
Slide23JASO, 1950-2010
Chu, Chen, Lin, 2014: Atm. Sci. Lett.
Slide24A distinct dry-wet condition
during the typhoon season since 1950
Changes in plain stations are more
consistent
among the 3 precipitation-related indices (SDII,
R50, R5d)
but not so
for stations in the CMR.
Slide25Rainfall
intensity
Slide26Heavy rainfall days
Slide27Slide28Slide29Slide30Slide31Slide32Slide33Summary for Part II
A non-stationary GEV model is recently developed to examine trends in return levels for annual maximum 1-day precipitation amounts since 1960.The return-level threshold values are also found to change with time. For example, a rare storm with daily rainfall of 300 mm (20-yr return period) in 1960 has become a less rare event (4 to 5 yr return period) in 2009 on the Big Island.
•
An investigation of changes in return levels for the annual maximum 24-hr rainfall as induced by typhoons during the typhoon season (JASO) in Taiwan using a novel non-stationary GEV model
• Upward trends of return levels in extreme rainfall are noted for a majority of stations since 1958
•
The
return-level threshold values are
found
to change
with
time considerably.
For example, a
rare storm with daily rainfall of
390
mm (20-yr return period) in Taichung in 1958 has become a rather common storm event (~13-yr return period) in 2013. Heavy rainfall events have become more frequent over the last 56 years.• El Niño events favor high extreme rainfall in the following typhoon season for northern and eastern Taiwan, while low extreme rainfall is expected for the CMR and western Taiwan.
Slide34Impact of this study
In the engineering design (e.g., urban drainage) and environmental regulations, return-period rainfall amounts are assumed to be constant at a given threshold level (e.g., 357 mm for a 100-yr return period). Because climate is changing, this assumption of
stationary precipitation climatology should be revisited.
Need to modify existing facilities and safety preparation (e.g., reservoirs, dams, high-impact structures) as heavy rainfall and flooding are common in a warming climate
Slide35Chu et al., 2017: Trends in return levels of precipitation extremes during the typhoon season in Taiwan. In Prep.
Chen, Y.R., and P.-S. Chu, 2014: Trends in precipitation extremes and return levels in the Hawaiian Islands under a changing climate. Int. J. Climatol., 34, 3913-3925.Chu, P.-S., D.J. Chen, and P.-L. Lin, 2014: Trends in precipitation extremes during the typhoon season in Taiwan over the last 60 years. Atmos. Sci. Lett., 15, 37-43.Chu, P.-S., X. Zhao, Y. Ruan, and M. Grubbs, 2009: Extreme rainfall events in the Hawaiian Islands. J. Appl. Meteorol.
Climatol
., 48, 502-516.
Slide36Thank you!