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Designing and Operating Infrastructure for
Nonstationary Flood Risk Management
Columbia Water Center
Thanks
water.columbia.edu
Nonstationarity
0.0
2.5
5.0
7.5
1900 1950 2000
Date
River Stage [m]
Río Paraguay at Asunción
Data: DINAC Paraguay
4
6
8
1900 1950 2000 2050
Water Year
Ann−Max River Stage [m]
MLE Estimates
Observed Data
Lienar Trend; N=40
Linear Trend; N=20
Linear Trend; All Years
Figure 1:
Nonstationarity
0.0
2.5
5.0
7.5
1900 1950 2000
Date
River Stage [m]
Río Paraguay at Asunción
Data: DINAC Paraguay
4
6
8
1900 1950 2000 2050
Water Year
Ann−Max River Stage [m]
MLE Estimates
Observed Data
Lienar Trend; N=40
Linear Trend; N=20
Linear Trend; All Years
Figure 1:
Flood Frequency Analysis
Today
Flood Frequency Analysis
Today
Generating Streamflow Sequences
P=π(−π)
(−π)π.
T= π
µ(t) = µ+β(t−t) St=
µ+β(t−t) St=
σ(t)∝µ(t)
log Q(t)µ(t), σ(t)∼ N (µ(t), σ(t)).
Fitting Synthetic Streamflow Sequences
N
pT=Q(t)≥QT
stan
pT(t)
Variance Decomposition
=+
=E(pT−ˆ
pT)
= (E[ˆ
pT]−pT)
=V[ˆ
pT]
Variance Decomposition
=+
=E(pT−ˆ
pT)
= (E[ˆ
pT]−pT)
=V[ˆ
pT]
Stationary* Process
Figure 2: N=,M=
Stationary* Process, Stationary Model
Figure 3:
M,N
Trend Process
Figure 4: N=,M=
Trend Process, Stationary Model
Figure 5:
M,N
Trend Process, Trend Model
N M
N M
Discussion & Future Work
M
M
References i
Journal Of Statistical Software
Journal of Machine
Learning Research
Water Resources Research
10.1029/2001WR000495
Application of Frequency and Risk in
Water Resources
10.1007/978-94-009-3955-4_23
Journal of Water Resources Planning and Management
10.1061/(ASCE)0733-9496(1997)123:2(125)
