dynamic flood risk conditional on climate variation: a new direction for managing hydrologic hazards...
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Dynamic Flood Risk Conditional on Climate Variation:
A New Direction for Managing Hydrologic Hazards in the 21st Century?
Upmanu LallDept. of Earth & Environmental Engineering
& Intl. Research Institute For Climate Prediction
Columbia University
Co-authors: G. Pizarro, S. Arumugam and S. Jain
Climate Variability vs. Change Variability:
Structured Inter-annual and Longer Variations that arise as a consequence of internal feedback processes in the climate system, with large spatial scales of organization – ENSO, PDO, ….
Change: Secular changes due to anthropogenic causes – Global Warming
and related effects
Dynamic vs Static Flood Risk Seasonal Flood Forecasts /Warning – Insurance/ Preparedness Diagnosing Historical Record and Improving Regional Flood
Frequency Estimates using Climate Information with non-overlapping periods of record
Outline
Context through Sacramento Floods Nature of Nonstationarity:
Washington Example Cane-Zebiak Model Inferences
Prediction in the US West E[Annual Max Flood] for the upcoming year Reconstruction of Past floods
Local Likelihood Method for Quantile Forecasts
19th century : Personal Levees, Rebuild to higher than last biggest
20th century : Dams, Levees, bypass, Heavily Federally Subsidized
21st century : ??
American River at Fair Oaks - Ann. Max. Flood
020,00040,00060,00080,000
100,000120,000140,000160,000180,000
1900 1920 1940 1960 1980 2000
Year
An
n M
ax
Flo
w
100 yr flood estimated from 21 & 51 yr moving windows
100 Yr Quantile of 4 Rivers Index of annual flow from a 700-1961 Tree Ring Reconstruction (Meko et al., 1998) using a 51 year moving window and the Log Normal Distibution
Identifying Variability & co-variation with climate indices
Moving Window Analyses Mean, Variance, T-year flood “Arrival Rate” – Non-homogeneous Poisson Process
Correlations and Nonparametric Regression Spectrum (Frequency Domain)
Multivariate Spectrum Composites of Climate Fields for High/Low
Flood Years
Historical Record for the Blacksmith Fork river (1914-96)Historical Record for the Blacksmith Fork river (1914-96)
1920 1930 1940 1950 1960 1970 1980 1990
200
600
1000
1400
(a)
year
Flo
od (
cfs)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(b)
Frequency (/yr)
Sca
led
Spe
ctru
m
1920 1930 1940 1950 1960 1970 1980 1990
160
170
180
190
200
210
220
230
240
(c)
year
Day
of
Wat
er y
r
160 170 180 190 200 210 220 230 240
200
600
1000
1400
(d)
Day of Water yr
Flo
od (
cfs)
BFR Flood w/10yr smooth Spectrum
Annual Max: Day of Water year Flood magnitude vs. timing
Jain & Lall, 2000
Blacksmith Fork, Hyrum, UT
Analyses of Flood Statistics using a 30 year Moving Window
From Jain and Lall (2000)
100 yr flood (LN)
Var(log(Q))Mean(log(Q))
Flood mean given DJF NINO3 and PDO
NINO3 PDO
Flood Variance given DJFNINO3 and PDO
NINO3PDO
Derived using weighted local regression with 30 neighbors
Correlations:
Log(Q) vs DJF NINO3 -0.34 vs DJF PDO -0.32
Jain & Lall, 2000
1920 1940 1960 1980 2000
year
5000
10000
20000
40000
Ann
ual M
axim
um F
lood
(cf
s)
30-year smooth
1920 1940 1960 1980 2000
year
-0.2
0.0
0.2
0.4
0.6
0.8
NIN
O3
Inde
x
-1.5
-1.0
-0.5
0.0
0.5
1.0
PD
O I
ndex
Similkameen River near Nighthawk, Washington, 1911-98
NINO3 NINO3|PDO
PDO PDO|NINO3
Flood -0.39 -0.27 -0.44 -0.33
Correlations
Jain & Lall, 2001
1920 1940 1960 1980 2000
Year
020
4060
8010
0
Per
cen
t p
rob
abili
ty o
f ex
ceed
ance
10%
33%
67%
90%
Floods
as a
Non-homogeneous Poisson Process:
Prob. Of Exceedance of flood (t) =
“rate of arrival” (t)
= “rate of Poisson Process of exceedances”
Kernel Estimate using a 30 year moving window
Jain & Lall, 2001
Probability distribution of the number of anomalous exceedances of the flood series based on a quantile threshold. (a) <10%, (b) <33%, (c) >67%, (d) >90%. Quantiles are computed using a 30-year time window, and exceedances of each quantile are computed for the next 30 years on record.
Wavelet Analysis of 1000 year sample of annual maximum NINO3 from a 110,000 year integration of the Cane-Zebiak Model with stationary forcing ( Clement and Cane, 1999)
Probability distribution of the number of anomalous exceedances of the 90th percentile of the ZC model NINO3 series, for two successive n year periods using block or random sampling, where n is: (a) 50 years, (b) 200 years. - based on 1,000 years of control run data
Ann. Max. Flood Seasonality in the West
3133
1
3
333 3
33
33
3
43
44
444
1111
14
3
31
11111
14
1344444
44444444
4
44
44
422
4
11131
1
2
1
11111
1
13
31 11
22
2211
2 3
222 22 122 22222 12
2 2222 22 12 22 1222222
2 12 12222 12 24 11Pizarro & Lall, 2002
Predictors Considered (All Jan-Apr)
First 2 PCs of the average SST and first 2 PCs of the Jan-Apr change of the Pacific SST over
Lat (5S,60N) and Long(60E, 60W)
NINO3 Average and Change
PDO Average and Change
Projection Pursuit Regression
Goal: Fit the multivariate model
y = f(x) + e f(x) is approximated by univariate nonparameteric functions
applied to linear combinations of x For a single response:
Sj(.) = Univariate Regression = Supersmoother Weighted unexplained variance reduction across all response
variables used to choose # of basis functions Cross-validation (Randomly drop 10% of data 100 times) used
to choose predictors
From Friedman & Stuetzle, 1981
εSαyM
j
Tjj
10 xα
PPR Implementation Normalize Log(Flow) Data at each site in cluster
Try several PPR models varying the number of basis functions (M …. 1), and Predictor Combinations.
Choose m <=M basis functions as breakpoint of unexplained variance vs M for each predictor set
Choose Predictor Combination using cross validated average error variance reduction across all sites in cluster
From Cross-validation runs estimate: Unexplained variance per station Hindcasts/Forecasts for each station Approx. Confidence interval per station
(6b) Local Likelihood
0
10000
20000
30000
40000
50000
60000
1930 1940 1950 1960 1970 1980 1990 2000
Year
Qu
anti
les
(Cfs
)
p=0.1 Unconditionalp=0.5 Unconditionalp=0.9 UnconditionalObserved flowsp=0.1 Conditionalp=0.5 Conditionalp=0.9 Conditional
Local Likelihood: Annual Conditional Flood Forecasts
Arumugam and Lall, 2003Conditional pdf with parameters (Xt). )( ttQf X
)()( ttt XX )θ(X
m
kktkjkt xx
10 )()( X
m
kktxkjxkt
1)(0)( X
otherwise 0
1|| if 1
)21()(
kkjum
kkjutjw X
khkjxktx
kju
n
tj
jttttQftjwttCV
1)ˆ ;(log()()ˆ,ˆ( )(X-θXXh)(X-θ
Summary Connections to key modes of low frequency climate variability provide
a mechanism for new directions in managing flood risk with a season or longer lead time.
Even with stationary underlying dynamics, finite sample statistics of a nonlinear dynamical system can be nonstationary. Thus, a dynamic risk framework may be more useful even in this case.
A pathway for the reconstruction of missing values of prior history of annual floods is indicated. This provides a new direction for regional flood risk estimation
Translating a dynamic risk framework into management options is feasible, but will require institutional reform.