Download Precipitation Regional Extreme Mapping as a Tool for Ungauged

Assessment of Climate Change Impact by
Regional Storm Frequency Mapping for Upper
Yangtze River Basin
Prof. Jeanne Huang and Yu Li
College of Environmental Science and Engineering
Nankai University, Tianjin, China
Email: [email protected]
Outline
• Introduction and Issues
• Methodology
– Regional Frequency Mapping
– Climate Change Assessment
• Results and Analysis
• Conclusions
Introduction – Study Area
The Upper Yangtze River
Basin (UYRB) is the area
above the Three Gorges
Dam, extending 4512 km
in length and with an area
of about 106 km2.
The large scale reservoirs in UYRB (Including
constructed, under-construction and planed )
1. In the upper Yangtze River basin, more than 100 cascaded large
scale reservoirs will be constructed
2. The large scale reservoirs regulate flows and change the flow
regime substantially
Issues
1. The change of flow extremes may hugely affect the safety of the
hydraulic projects
2. The plan and design of hydraulic projects need the information
about the flows
3. There are many evidences of climate change and it may change
the precipitation extremes and consequently, change the flow
extremes
4. The large scale reservoirs regulate flows and change the flow
regime substantially
5. As the development of various hydrological models, precipitation
data is a reliable source for obtaining flows, especially for the
extreme events
Research Needs
Therefore, there are urgent needs for
1) regional frequency mapping
2) The assessment of climate change on precipitation extremes in
this region
Data
Precipitation data
(1966-2009, 44 years)
are obtained from 207
stations located in and
around the upper
Yangtze River basin
These data were
provided by China
Meteorological Data
Sharing Service System
(CMDSSS)
Methodology
• Regional Frequency Mapping
– Regional Analysis by L-Moments
– Extreme Mapping
• Climate Change Assessment
Regional Analysis
1. Identification for Homogenous regions
a.
Using L-Moments to calculate skewness and kurtosis for all the sites
b.
Testing for discordance for all the sites and identifying the
discordance sites
c.
Testing for regional heterogeneity
2. Identifying the appropriate distributions for characterizing
extremes and for evaluating quantiles
a.
Testing goodness of fit for various distributions
Storm Zoning by Jiaqi Wang based on Data
before 1990’s
Wang(2002) divided China into
three regions based on the
characteristics of topography,
mean annual daily maximum
precipitation and seasonal
variations.
Region I is strongly influenced
by the monsoon climate and has
the highest average annual
precipitation among the three
regions.
Region II has an arid/semi-arid
climate and Region III is located
in Qinghai-Tibetan Plateau,
which is the highest Plateau in
the world with an average
altitude exceeding 4000m.
The zoning need to be verified if it
can be used for Regional Analysis
L-Moments
The L-Moments method is proposed for parameter estimation of the frequency
analysis of extreme values (Hosking and Wallis, 2005).
Probability-weighted moments (PWMs) offers a description of the shape of a
probability by L-skewness and L-kurtosis are defined as
(1)
Where βr is the rth-order PWM, r = 0,1,2,…and F(x) is the cumulative distribution
function of x. The rth-order L-Moment λr is related to the rth PWM through
(2)
The first four L-moments in terms of PWMs are defined by
(3)
(4)
(5)
(6)
The L-moments ratios are given by
(1)
(2)
(3)
(4)
Where λ is a measure of central tendency, τ is a measure of scale and dispersion
(called L-CV), τ3 is a measure of skewness, and τ4 is a measure of kurtosis (Hosking
and Wallis, 2005).
Skewness
Higher Skewness means that lower
values have more occurrences
Kurtosis
Higher Kurtosis means that the
values closed to mean have more
occurrences
Discordancy measure test
The discordancy measure test is used to screen out the data from unusual sites and to
check whether the data are appropriate (as measured by the ‘discordance’) for
applying the regional frequency analysis.
Let ui= (τi, τ3i, τ4i)T be the vector of L-CV, L-skewness, L-kurtosis for site i, the group
average vector and the matrix of sums of squares and cross products are given by
(1)
(2)
Where N is the number of sites
Then the discordancy measure for site I is defined by
(3)
Discordant Test (Di)
Results of discordant test for 207 sites
Region
Sites used Discordant sites
Average discordancy measure
Di
Region I
107
1
0.69
Region II
28
1
0.89
Region III
66
4
0.80
If Di of a site exceeds 3, the site can be considered discordant in
a region with 11 or more sites (Hosking and Wallis, 2005).
Regional heterogeneity test, H
The heterogeneity measure H is used to verify whether the proposed sites make up a
spatially homogeneous region.
The regional average L-CV is obtained by the following formula
(1)
Where τ(i) and ni are the L-CV and sample length for site i, and N is the number of
sites in a region.
V, a measure of L-CV, is defined as
(2)
The heterogeneity measure H is calculated by
(3)
Where μV and σV are the mean and standard deviation of simulated V by using flexible
four-parameter kappa distribution and 500 generated equivalent regional data to
calculate V.
The region can be declared acceptably homogeneous if heterogeneity (H)< 1, possibly
heterogeneous if 1≤ H <2, and definitely heterogeneous if H ≥ 2 (Hosking and Wallis,
2005).
Homogeneous Test (H1)
Results of heterogeneity test for the three regions
Region
Heterogeneity measure H1
Region I
0.62
Region II
0.37
Region III
0.35
The homogeneous measure H is used to verify whether the
proposed sites make up a spatially homogeneous region. This
check is based on observed and simulated data.
A region can be declared acceptably homogeneous if
heterogeneity (H)< 1 (Hosking and Wallis, 2005).
Goodness-of -fit test
The critical value Z demonstrates how well the simulated L-skewness and L-kurtosis
of a given distribution matches the regional average L-skewness and L-kurtosis
calculated by the observed data.
The bias B4 and standard deviation σ4 of L-kurtosis from simulated data are defined as
(1)
(2)
Where τ4(i) is the regional average L-kurtosis and obtained by the ith-order simulated
region, and Nsim is the number of simulated regional data.
For a given distribution, Zdist is obtained by
(3)
A given distribution can be declared a good fit if |Zdist|≤ 1.64 (Hosking and Wallis,
2005).
Goodness of Fit Test
Results of Goodness-of -fit test
Regions
GLO
GEV GNO GPA
PE3
Region I
2.09
0.53
1.11
1.61
0.70
Region II
2.05
1.72
1.21
1.79
0.50
Region III
3.03
2.61
2.19
1.61
1.57
Acceptable distributions are all those satisfying |Z|≤ 1.64 whereas
the best distribution is the minimum value. These findings
demonstrate that the PE3 is acceptable in all three regions while the
GLO is the least acceptable. The best distributions were GEV for
Region I and PE3 for Regions II and III.
Goodness of Fit Test
Results of goodness-of-fit test
Region
|Z|≤ 1.64
Best fit
Region I
0.53
GEV
Region II
0.50
PE3
Region III
1.57
PE3
The critical value Z demonstrates how well the simulated Lskewness and L-kurtosis of a given distribution matches the
regional average L-skewness and L-kurtosis calculated by the
observed data.
Mapping
1. Extreme Mapping
a.
Mapping for Mean Annual Maximum
b.
Mapping for Standard Deviation
c.
Deriving the Factors by Selected Distribution
d.
Quintiles for individual Sites
2. Testing for Accuracy
a.
RMSE
b.
BIAS
Mean Annual Daily Maximum
Region I has mean annual daily maximum
Standard Deviation
Region I also has high standard deviation
Extreme Factors KT of Various Quantiles for
Selected Distribution
Regions
Return Period（years）
2
5
10
25
50
100
Region I
（GEV）
-0.016
0.719
1.305
2.044
2.592
3.317
Region II
（PE3）
-0.022
0.833
1.293
1.794
2.123
2.423
Region III
（PE3）
-0.026
0.831
1.295
1.800
2.134
2.438
𝑥𝑇 = 𝜇𝑥 + 𝐾𝑇 𝜎𝑥
Testing for Accuracy for Ungauged Area
1) Select a gauge from the 207 stations and was removed from the map,
2) The values (mean and standard deviation) of the removed station are
estimated using linear interpolation from nearby stations using Kriging;
3) The calculated values (mean and standard deviation) are compared to
the values of the removed gauge.
4) For comparison purposes, two evaluation indices including the root
mean square error (RMSE) and mean bias (BIAS) were applied to test
the accuracy of the estimated quantiles for each region.
5) The above procedure was done one by one for each site of the 207 sites
Testing for Accuracy for Ungauged Area
RMSE =
1
𝑁
1
BIAS =
𝑁
𝑁
(𝑥𝑖 − 𝑦𝑖 )2
𝑖=1
𝑁
(𝑥𝑖 − 𝑦𝑖 )
𝑖=1
Regions
RMSE(mm)
BIAS(%)
Region I
11.86
1.62
Region II
2.66
2.07
Region III
0.58
0.08
Assessment of climate change
To better understand whether trends exist in
extreme rainfall, the data were separated into
four sub-periods, namely 1966-1976, 1977-1987,
1988-1998, and 1999-2009. The changing trends
of the mean of annual rainfall rates between
each of the adjacent sub-periods adjacent were
analyzed, utilizing a two-tailed Student’s t-test
Climate Change Assessment
1. Decadal Trends in Annual Daily Maximum
a.
Student t-test for Mean Annual Daily Maximum
b.
Student t-test for Standard Deviation
2. Comparison of first 22 years and second 22 years
a.
Student t-test for Mean Annual Daily Maximum
b.
Student t-test for Standard Deviation
The Difference of Mean Annual Maximum
(2nd 22 years – 1st 22 years)
The Difference of Standard Deviation
(2nd 22 years – 1st 22 years)
Confidence Level (t-p) for the comparison
(2nd 22 years – 1st 22 years)
The results of t-test and the means and standard deviations of annual rainfall extremes in the upper Yangtze River basin
Results of the Assessment
The results indicate there are no significant trends over time
observed in the upper Yangtze River basin. The trends were weak
and failed to demonstrate a statistically significant difference at
the 95% confidence level.
Relatively increasing tendency of the two indices can be found in
the upper portion of the Yangtze River basin. This indicated that
the higher occurrence probability of flooding and hazards in
upstream is affected by climate change.
Conclusions
• The zoning identified in 1990’s was verified by
the regional analysis procedure
• The best distribution for region I is GEV, not
the commonly used PE3 in China
• The extreme mapping can be applied to
ungauged area
• The extreme mapping can be easily used to
identify the existence of climate change
Thanks for your
attention.
Any Question?