This document presents a framework for defining time-dependent hydraulic boundary conditions to analyze climate variability and coastal flooding extremes. The framework considers four sites: southern California, Kwajalein Atoll, Guam, and Hawaii. It accounts for total water level components including mean sea level, astronomical tides, non-tidal residuals, and run-up. Predictors are defined at annual, monthly, intraseasonal and daily timescales. Challenges include multi-decadal climate change effects and influence of processes like El Niño and tropical cyclones at different timescales. The framework uses statistical and process-based models to generate synthetic hydraulic boundary condition time series to enable coastal flood risk assessments under future climate change.

1. Fernando J. Mendez1, D. Anderson2 , P. Ruggiero2, A. Rueda1, J. A.A. Antolinez1,
L. Cagigal1, C. Storlazzi3, P. Barnard3
Defining time-dependent hydraulic boundary
conditions for the analysis of the climate variability of
extremes of coastal flooding
1Universidad de Cantabria, Spain
2Oregon State University, Corvallis, OR, USA.
3USGS, USA

2. 1
2
3
4
Site 1 – Southern California area between Dana Point and Mexican Border (e.g., Naval Base San
Diego – NBSD)
Site 2 – Republic of Marshall Islands, Kwajalein, Roi-Namur (i.e. Kwajalein Missile Range – KMR)
Site 3 – Guam, Apra Harbor area (i.e., Naval Base Guam)
Site 4 – Hawaii, Island of Oahu, Kaneohe Bay (i.e., Marine Corps Base Hawaii –MCBH)

3. Four ingredients of Total Water Level
TWL = MSL + ηA + ηNTR + R
mean sea
level
astronomical
tide
non-tidal
residual
Run-up

4. - joint probabilities of compound events
- tailor-made predictors at annual, monthly, intramonthly and daily scale
- non-linear relationships between predictors and predictands
- climate-based multivariate extreme value model
- chronology of events
- hybrid downscaling of thousands of synthetic events
- climate change projections in a feasible way
- influence of tropical cyclones
Challenges
- Multi-Decadal and Inter-annual Scale: Global SLR / ENSO
- Annual and Intra-annual Scale: seasonality, Madden-Julian Oscillation, Kelvin waves
- Daily Event Scale: tropical cyclones, distant swells and local wind seas
Which processes affect Pacific Ocean dynamics? … and at what timescales?

5. Xm
Xa
Monthly Predictor
XMJO
ETd
TCd
DWT
Hydraulic Boundary Cond.
Annual Predictor
Intraseasonal Pred.
Hs0 Tp0 Dir0
Hs1 Tp1 Dir1
Hs2 Tp2 Dir2
ηNTR
Hs0 Tp0 Dir0
ηNTR
MMSL
Regional Predictor
Extratropical Cyclones
Tropical Cyclones
Daily Weather Types
ηA
Methodological Framework of TESLAFlood(*)
(*) Time-varying Emulator for Short- and Long-term Analysis of coastal flooding
Hybrid Downscaling
Selection
Dynamic
Downs.(XBeach)
Meta-model
Maps / Statistics

6. longitude
A
S
O
N
D
Philosophy: a dynamic
predictor, capturing
changes in both time
and space…
Hovmoller Diagrams
How to simulate
large-scale ENSO
variability?
Annual Predictor Xa

7. Principle Component Analysis + Clustering = Select # of Representative “years”
(X1,t
a
,...,XnPCa
,t
a
) AWTt
Î{1,...,nAWT
}

8. Xm
Xa
Monthly Predictor
XMJO
ETd
TCd
DWT
Hydraulic Boundary Cond.
Annual Predictor
Intraseasonal Pred.
Hs0 Tp0 Dir0
Hs1 Tp1 Dir1
Hs2 Tp2 Dir2
ηNTR
Hs0 Tp0 Dir0
ηNTR
MMSL
Regional Predictor
Extratropical Cyclones
Tropical Cyclones
Daily Weather Types
ηA
Regression Model for MMSL
MMSL(t)= a0
+a1
X1
a
(t)+a2
X2
a
(t)+a3
X3
a
(t)+ b0
+b1
X1
a
(t)+b2
X2
a
(t)+b3
X3
a
(t)( )cos(
2pt
365
)+..
Hybrid Downscaling
Selection
Dynamic
Downs.(XBeach)
Meta-model
Maps / Statistics

9. Y0
Multi-modal wave spectra
Camus et al 2014 OD
Perez et al 2014 OD
Rueda et al 2017 JGR
Hegermiller et al 2017 JPO
HN,TN,DirNH
HE,TE,DirE
HSEA,TSEA,DirSEA
Daily Predictor DWT

10. Daily Weather Types
DWTi
,{i =1,...,nDWT
}
Based on Rueda et al 2017 JGR
Prob

11. ETd Hs0 Tp0 Dir0
Hs1 Tp1 Dir1
Hs2 Tp2 Dir2
ηNTR
Joint Distribution Hs-Tp-Dir
Rueda et al 2017 JGR
- Multivariate climate based extreme value model

12. Monte Carlo Simulation of daily multimodal spectra
1000 YEARS OF DAILY SIMULATION
Rueda et al 2017 JGR
HN,TN,DirNH
HE,TE,DirE
HSEA,TSEA,DirSEA

13. Xm
Xa
Monthly Predictor
XMJO
ETd
TCd
DWT
Hydraulic Boundary Cond.
Annual Predictor
Intraseasonal Pred.
Hs0 Tp0 Dir0
Hs1 Tp1 Dir1
Hs2 Tp2 Dir2
ηNTR
Hs0 Tp0 Dir0
ηNTR
MMSL
Regional Predictor
Extratropical Cyclones
Tropical Cyclones
Daily Weather Types
ηA
Hybrid Downscaling
Selection
Dynamic
Downs.(XBeach)
Meta-model
Maps / Statistics
Chronology Model
ENSO, seasonality and MJO together!

14. Kwajalein is affected by ExtraTropical (ET) and Tropical Cyclones (TC)

15. Pr(DWTt
= i DWTt-1
,...,DWTt-e
,Xt
a
,Xt
m
,Xt
MJO
)=
=
exp(ai
+bi
Xt
+ g ij
DWTt- j
d
j=1
e
å )
exp(ak
+ bk
Xt
+ g kj
DWTt- j
d
j=1
e
å )k=1
nDWT
å
;"i =1,...,nDWT
Xt
=(X1,t
a
,X2,t
a
,X3,t
a
,cos
2pt
Ta
,sin
2pt
Ta
,X1,t
MJO
,X2,t
MJO
)
Chronology Model: Climate-based Autoregressive Logistic Model
Guanche et al (2013) ClimDyn
Antolinez et al (2016) JGR
Annual
Cycle
MJO
ENSO
ET3 ET3 ET6 ET6 ET6 Cat2 ET1 ET13 ET2 Cat4 ET7 ET7…
Categorical time series of DWTs for Extratropical Cyclones (ET) and Tropical Cyclones affecting Kwajalein (Cati)
Cat0 Cat1 Cat2 Cat3 Cat4 Cat5 100 simula ons
ET1
ET2
ET36
ETt
d
Î{1,...,nET
}
TCt
d
Î{C0
,...,C5
}
DWTt
=(ETt
d
ÈTCt
d
)Î{1,...,nDWT
}

16. Dealing with Tropical Cyclones
Historical TC tracks (IBTracs)
Proposed model
r=4º
Parameters that define a TC
- pmin, Minimum Pressure
- V, forward velocity
- δ, azimut
- γ, angle of entrance
Historical TC tracks with the proposed model

17. Dealing with Tropical Cyclones
Historical TC tracks + Synthetic Tracks (Nakajo et al 2014) Synthetic Tracks + MDA Selection Algorithm (Camus et al,2011)
N=100 N=300Historical Synthetic
(N=10959 from 1 Million Worldwide)

18. Intra-daily simulations: hydrograph approach
ET2 ET2 ET6 ET6 ET6
Response function: 𝑇𝑊𝐿 = 𝛼𝐻𝑠
0.5
𝑇𝑝 + 𝑆𝑆
ET6 ET8 ET8 ET8
TWL
Modelling triangles:
𝑡 𝐴
Hs
Tp
ss
θ
TWL
𝑡 𝐵
∆𝑡
𝑇𝑊𝐿 𝑚𝑎𝑥2
𝑇𝑊𝐿 𝑚𝑎𝑥2
𝑇𝑊𝐿 𝑚𝑎𝑥1 𝑇𝑊𝐿 𝑚𝑎𝑥3
𝜇1
𝜇2
𝜇3
𝐷𝑊𝑇 = 𝐻𝑠
(𝑘)
, 𝑇𝑝
(𝑘)
, 𝜃
(𝑘)
, 𝑆𝑆, 𝜏, 𝜇
ET2 ET2 ET6 ET6 ET6 ET6 ET8 ET8 ET8
𝜏1 𝜏2 𝜏3
Timing until TWLmax
Average TWL during hydrograph

19. “Dynamic Annual
Weather Type” informed
by ocean processes
Operating in the
“continuum”
Daily Weather Type
depends on covariates at
multiple timescales
Tropical Cyclone
Probabilities depend on
all processes
Hs for SEA, NH and SH (days)
Sea State Type, I (days)
Daily Weather Type, DWT (days)
Annual Weather Type, AWT (years)
… …
Ci-1 Ci Ci+1
Realization of a “climate, C” (N years)
Astronomical tide, AT (1 year)
Astronomical Tide Type, ATT (days)
SS (days)
Monthly Mean Sea Level, MMSL (months)
Simulated Tropical Cyclones
Framework is built… Next
steps are to actually simulate
TESLAFlood
Time-varying Emulator for Short- and Long-term Analysis of coastal flooding

20. Fernando J. Mendez1, Dylan Anderson2 , Peter Ruggiero2,
Ana Rueda1, Jose A.A. Antolinez1, Laura Cagigal1, Curt
Storlazzi3, Patrick Barnard3
Defining time-dependent hydraulic boundary
conditions for the analysis of the climate
variability of extremes of coastal flooding
1Universidad de Cantabria, Spain
2Oregon State University, Corvallis, OR, USA.
3USGS, USA
Acknowledgments. US Department of Defense, Project SERDP Number RC-2644
(Advancing Best Practices for the Analysis of the Vulnerability of Military Installations
in the Pacific Basin to Coastal Flooding Under a Changing Climate) PI: John J. Marra,
NOAA NESDIS NCEI.
GOW2 data base has been kindly provided by IHCantabria