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Designing and Operating Infrastructure for Nonstationary Flood Risk Management

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Climate exhibits organized low-frequency and regime-like variability at multiple time scales, causing the risk associated with climate extremes such as floods and droughts to vary in time. Despite broad recognition of this nonstationarity, there has been little theoretical development of ideas for the design and operation of infrastructure considering the regime structure of such changes and their potential predictability. We use paleo streamflow reconstructions to illustrate an approach to the design and operation of infrastructure to address nonstationary flood and drought risk. Specifically, we consider the tradeoff between flood control and conservation storage, and develop design and operation principles for allocating these storage volumes considering both a M-year project planning period and a $n$-year historical sampling record. As N increases, the potential uncertainty in probabilistic estimates of the return periods associated with the T-year extreme event decreases. As the duration M of the future operation period decreases, the uncertainty associated with the occurrence of the T-year event also increases. Finally, given the quasi-periodic nature of the system it may be possible to offer probabilistic predictions of the conditions in the M-year future period, especially if M is small. In the context of such predictions, one can consider that a M-year prediction may have lower bias, but higher variance, than would be associated with using a stationary estimate from the preceding N years. This bias-variance trade-off, and the potential for considering risk management for multiple values of M, provides an interesting system design challenge. We use wavelet-based simulation models in a Bayesian framework to estimate these biases and uncertainty distributions and devise a risk-optimized decision rule for the allocation of flood and conservation storage. The associated theoretical development also provides a methodology for the sizing of storage for new infrastructure under nonstationarity, and an examination of risk adaptation measures which consider both short term and long term options simultaneously.
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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(tt) St=  
µ+β(tt) 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(pTˆ
pT)
 = (E[ˆ
pT]pT)
 =V[ˆ
pT]
Variance Decomposition
       
 =+ 

 =E(pTˆ
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  
          
      
  
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References i
         
Journal Of Statistical Software
          
      Journal of Machine
Learning Research
           
     Water Resources Research  
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         
   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)
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james.doss-gollin@columbia.edu
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