A Delft3D model was implemented for the study of the hydrodynamics of San Quintin Bay. Calibration and validation have been successfully executed in previous research, but uncertainties propagated through simulation of future conditions are mostly unknown, and have not been tested in this region. Data Assimilation (DA) techniques play an important role, as their mathematical methods depict algorithms for combining dynamical system observations, implement computational models describing their evolution, and any relevant prior information. The aim of this study was to make a comparative analysis of calibration methods versus DA, as well as evaluate the long-term predictive capability of a model using sea surface height and current measurements taken within the bay. Delft3D-OpenDA is considered an effective a tool for delivering real-time forecasting via employment of the ensemble Kalman filter algorithm, and this automatic procedure is expected to obtain an improved model forecast. We anticipate an ensemble size of between 40 and 60 will provide the optimal and most accurately predicted water levels for San Quintin Bay by assimilating a single observation point located at the bay’s entry. New computational challenges will also be addressed, as well as means of reducing the computational costs of these implementations.

1. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Ensemble Filters to Reduce Uncertainties
in San Quintin Bays Hydrodynamic Forecast System
Mariangel Garcia
mgarcia@sciences.sdsu.edu
http://www.csrc.sdsu.edu/
Isabel Ramirez, CICESE (Baja Mexico)
Martin Verlaan, Delft University (The Netherlands)
Jose Castillo, San Diego State University
Computational Science Research Center
Joint Program with Claremont Graduate University
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 1 / 43

2. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Outline
• Motivation
• Hydrodynamic Model
• Data Assimilation
• SQ Bay
• New Challenges
• Significance of Study
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 2 / 43

3. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Motivation
Any data assimilation system consists of three components:
1 set of observations
2 a dynamical model
3 data assimilation scheme
The Main goal
Reduce the uncertainty in the entire system
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 3 / 43

4. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Data Assimilation Framework
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 4 / 43

5. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Data Assimilation Scheme
Question to be addressed
• What assimilation algorithms do we use?
• What models do we use?
• What type of observations do we assimilate?
• What are the observation errors?
• What are the model and analysis errors?
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 5 / 43

6. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Assimilation Approaches
Variational Approach
• Optimal Interpolation
• 3D Var
• 4D Var
Sequential Approach
• Kalman Filter Kalman, 1960
• EnsKF Evensen, 1994
• ELTKF Bishoop& Hunt, 2001
• EAKF Anderson, 2001
• Particular Filter Non Gaussian
• ESRKF Tippett, 2003
• Hybrid: OI EnsKF, SSEnsKF
12
1E. Kalnay (2003). Atmospheric Modeling, Data Assimilation, and Predictability.
Cambridge University Press. isbn: 9780521791793. url:
http://books.google.com/books?id=zx_BakP2I5gC.
2Geir Evensen (2006). Data Assimilation: The Ensemble Kalman Filter.
Secaucus, NJ, USA: Springer-Verlag New York, Inc. isbn: 354038300X.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 6 / 43

7. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Kalman Filtering
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 7 / 43

8. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Advection Example
3
3Mariangel Garcia, Guillermo Miranda and Barbara Bailey (2012). “Ensemble
Kalman Filter with the Advection Equation”. In: Jornadas de Investigacion
Matmatica. Universidad Central de Venezuela. Caracas, Venezuela.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 8 / 43

9. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
3D Navier Stoke Equations
4
4Hydraulics Delft (2011). User manual Delft3D-Flow. DELTARES.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 9 / 43

10. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
5
5Hydraulics Delft (2011). User manual Delft3D-Flow. DELTARES.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 10 / 43

11. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Source of Uncertainties
• Bathymetry
• Initial conditions
• BCs: surface atmospheric, coastal-estuary and open boundary
fluxes
• Parameterized processes
• Numerical errors: steep topographies and pressure gradient
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 11 / 43

12. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
DA Frameworks
678
6National Center for Atmospheric Research (NCAR). Data Assimilation Research
Testbed - DART. .
7Deltares. The OpenDA data-assimilation toolbox.
8Lars Nerger and Wolfgang Hiller (2013). “Software for ensemble-based data
assimilation systems—Implementation strategies and scalability”. In: Computers and
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 12 / 43

13. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
OpenDA Scheme
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 13 / 43

14. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Study Region
9,10
9Isabel Ramirez et al. (2012). “The simulation of the circulation of San Quintin
Bay.” In: Joint Numerical Sea Modelling Group. France.
10Jose A. Zertuche-Gonzalez et al. (2014). “Eisenia arborea J.E. Areschoug as
abalone diet on an IMTA farm in Baja California, Mexico”. In: Journal of Applied
Phycology 26.2, pp. 957–960.
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15. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Study Region
5km x 10km Area
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16. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Observations
Station at the Bay Entry
• Temperature Profiles
• Currents from Navy
Secretary of Mexico
• SSH
North Station
• Predicted Tide from Model
MARV0.9 2010 CICESE
MX.
Atmospheric Station
• Air Temperature
• Atmospheric Pressure
• Humidity
• Solar Radiation
• Rain
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17. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Model Set Up
Physical Parametrization
• Assumption of depth
integrated
• Barotropic flow
• Wind forcing
• Time series flow conditions
from TPXO7.2
• Bed Shear Stress: Manning
m−1/3s
• Water density 1024 kg/m3
Grid Domain
• t= 1 min
• x = 32m y = 53m
• Mx × Ny = 131 × 242
• Land elevation 10 m
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 17 / 43

18. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Model Calibrated
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 18 / 43

19. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Data Assimilation Scheme
Questions to be addressed
• What assimilation algorithms do we use?
• What models do we use?
• What type of observations do we assimilate?
• What are the observation errors?
• What are the model and analysis errors?
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 19 / 43

20. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Sensitivity Analysis
A key aspect in the application of data assimilation is the use of known or
assumed uncertainties or errors in both measurements and process model.
Model error
At boundaries (WestWLp
), the noise is added with a random variable γi , i = 1, 2... with mean 0 and a limiting
standard deviation σγ giving by
WestWL
p
i
= WestWLi + γi (1)
where γi is a colored-noise process, AR(1) give by
γi = αγi−1 + µi−1 (2)
the parameter α depends on the noise model time step and a chosen parameter τ is the time correlation scale, in
the following α = exp(− t/τ). µi is a white noise normally distributed with mean 0 and standard deviation
σµ = σγ
√
1 − α2.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 20 / 43

21. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Sensitivity Analysis
The observation noise εi was normally distributed, random white
noise added to each observation location where the analysis step is
performed with a variation of σ
Observation Error
In the Analysis Step, it is essential that observations are treated as
a random variables, so an ensemble of observation can be defined
as
Y
∗(j)
i = yo
i +
(j)
i ,
(j)
i ∼ Po
(0, Ri )j = 1, .., Ns (3)
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 21 / 43

22. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Sensitivity Analysis
Covariance Localization is a process of cutting off longer range
correlations in the error covariances at a specified distance.
Ki = ˆPf
i HT
H ˆPf
i HT
+ Ri
−1
(4)
Localization
To improve the modeling of background-error covariances estimated from the ensemble are subject to modification
by localizationa
. The Kalman Gain in 4 is replaced by a modified gain
K = ρs ◦ ˆP
f
i H
T
H ρs ◦ ˆP
f
i H
T
+ Ri
−1
(5)
where the operation ρs ◦ denotes a Schur product (an element-by-element multiplication) of a correlation matrix
ρs this element is never explicitly formed.
aThomas M. Hamill, Jeffrey S. Whitaker and Chris Snyder (2001).
“Distance-Dependent Filtering of Background Error Covariance Estimates in an
Ensemble Kalman Filter”. In: Monthly Weather Review 129.11, pp. 2776–2790.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 22 / 43

23. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Hamill Localization
11
11Thomas M. Hamill, Jeffrey S. Whitaker and Chris Snyder (2001).
“Distance-Dependent Filtering of Background Error Covariance Estimates in an
Ensemble Kalman Filter”. In: Monthly Weather Review 129.11, pp. 2776–2790.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 23 / 43

24. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
DA SQ Scheme: Experimental Set Up
Table: Parameters Varied in the Assimilation Scheme
Exp Filter
Assimilation
Variables
Assimilation
Observation
Ens Size
1 EnsKF WL Mouth
30 40 60 80
100
2 EnsKF WL
Mouth
North
30 40 60 80
100
Model Noise: τ = 0.93 σ = 0.05
Obs Noise: σµ = 0.03
Hamill Localization: HLoc = 5Km
AssiFr = 30min
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 24 / 43

25. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Ensemble Sizes # 10
10 Water Level Ensembles at ID: Mouth Station
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 25 / 43

26. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Ensemble Sizes # 60
60 Water Level Ensembles at ID: Mouth Station
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27. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Hindcast WL Exp #1 60 Ensemble
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28. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Hindcast WL Exp #1 Model Error Evolution
Model error for different Ensemble Sizes.
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29. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
WL Exp #2 Model Error Evolution
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 29 / 43

30. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
WL Assimilation Improvement and RMSE
%Imp = 1 −
rmseAsimModel
rmseOrigModel
× 100 (6)
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0 30 40 60 80 100
Ensemble Size
rmse
EXP#2 WL MOUTH
EXP#2 WL NORTH
EXP#1 WL MOUTH
EXP#1 WL NORTH
0.000
10.000
20.000
30.000
40.000
50.000
60.000
70.000
80.000
WL Mouth
Exp#1
WLMouth
Exp #2
WL North
(control) Exp #1
WLNorth 2
Exp#2
Percentage Reduction in the Model Error
(Time average WL)
30
60
80
100
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 30 / 43

31. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Hindcast Validation for DAV Control Variable
Table: % Model error improvement for DAV northward direction and
eastward direction, at station ID:Mouth for Exp # 1 and Exp # 2 .
Ensemble Size
30 40 60 80 100
EXP#1 DAV Ux 6.96210 6.4587 6.51223 6.5712 6.71912
EXP#2 DAV Ux 4.8750 4.9318 4.878178 #N/A 4.5824
EXP#1 DAV Uy -1.0217 -1.0381 -0.9880 -1.3391 -0.81894
EXP#2 DAV Uy -3.2377 -3.10718 -2.9282 #N/A -3.3492
-4
-2
0
2
4
6
8
30 40 60 80 100
Ensemble Size
EXP#2 DAV Uy EXP#2 DAV Ux EXP#1 DAV Uy EXP#1 DAV Ux
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32. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
12
12Garcia, Mariangel and Ramirez, Isabel and Verlaan, Martin and Castillo, Jose
(2014). “Application of a three-dimensional hydrodynamic model for San Quintin Bay,
B.C., Mexico. Validation and calibration using OpenDA”. . In: Journal of
Computational and Applied Mathematics 273, pp. 428–437.
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33. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Hydrodynamics in San Quintin Bay
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34. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
During Low Tide
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35. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Hydrodynamics in San Quintin Bay
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36. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
During High Tide
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37. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Numerical Performance of EnsKF
Ens # Ef % Exp #1
Total Wall Clock
(Hours)
Total CPU Time Performance Warnings
0 nan 0.13364 477.58 1.3077E-6 0
30 73.0218 4.1052 17957.49 0.56645 199
40 73.0514 5.41026 23958.82 0.75575 257
60 75.16444 8.14255 35709.75 1.1264 394
100 76.0942 13.3426 60389.67 1.9049 638
The total time consumed for all the experiments is 53 hours for
each experiment around 4 days running simulations to make
decisions on the right ensemble member to use.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 37 / 43

38. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Steady State Kalman Filter
A steady state covariance matrix and a steady state Kalman Gain
matrix are also time invariant as follows13
ˆPf
i → P∞, ˆPa
i → P∞andKi → K∞ (7)
Then the Kalman Gain in equation 4 is reduced to the following
¯Xa
i = ¯Xf
i + K∞
¯Yi − H ¯Xf
i (8)
Once measurements are available, the steady state Kalman Gain
matrix is used to update the system.
13Ghada Y. H. El Serafy and Arthur E. Mynett (2008). “Improving the operational
forecasting system of the stratified flow in Osaka Bay using an ensemble Kalman
filter-based steady state Kalman filter”. In: Water Resources Research 44.6.
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39. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Preliminaries Conclusion
• Optimal ensemble size 40 − 60.
• Increase of ensemble size higher computation effort.
• Provided best predicted water levels for San Quintin Bay.
• WL forecast estimate inside the bay improvement up to 75 % .
• Installing reliable equipment at the bay entry is suggested.
• Assimilating 2 station won t add computational cost to the
system.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 39 / 43

40. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
More to be done
• Look for the spatial correlation and standard deviation
• Run the SSEnsKF
• Compute 7 days forecasta
• Run 3D Thermodynamics and do data assimilation for
temperatureb
• Run the model in parallel
• Make the system operational
aMariangel Garcia et al. (2015). “Data Assimilation for an Operational System in
the Bay of San Quintin”. To be submitted.
bMariangel Garcia and Isabel Ramirez (2015). “The Themodynamics in San
Quintin Bay a 3D simulation”. Under Research.
Garcia M. PhD Candidate 7th June 2015 Gordon-Kenan Research Seminar 40 / 43

41. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
On going project
Data Assimilation Unit for a 3D High Resolution General Curvilinear
Non-hydrostatic Coastal Ocean Model.
Poster 17th, Monday and Tuesday
In collaboration with
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42. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Thank You!
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43. Motivation
Data Assimilation
Hydrodynamics Model
Practical Implementation
On going project
Questions?
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