gccom\_dart: ensemble data assimilation analysis system for sub-mesoscale processes
TRANSCRIPT
MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Ensemble Data Assimilation Analysis System forSub-Mesoscale Processes
GCCOM DART: Sensitivity Analysis
Mariangel Garcia
http://www.csrc.sdsu.edu/
Jose Castillo, SDSU-CSERCTim Hoar, NCAR-DAReS
Mary Thomas, Barbara Bailey, SDSU-CSERC
Beijing, ChinaSIAM-ICIAM 2015
Garcia M. PhD Candidate 13th August 2015 SIAM-ICIAM 2015, Beijing, China 1 / 52
MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Outline
• Motivation
• GCEM Project (Newfeatures)
• Data AssimilationFrameworks
• GCCOM-DARTOSSE
• 3D Perfect ModelExperiment Seamount
• PracticalImplementation
Garcia M. PhD Candidate 13th August 2015 SIAM-ICIAM 2015, Beijing, China 2 / 52
MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
The need of high resolution coastal ocean model
To obtain a more realistic representation of the ocean, models will need
to be developed that have higher resolution, improved precision,
simultaneous representation of a number of processes.
photo: Raincoast GeoResearch
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
The need of high resolution coastal ocean model
Relationship between the spatial and temporal scales for differentatmospheric and oceanic processes. The horizontal and vertical scaleranges are 10 to 105 km, and 1 hour to 10,000 years, respectively.
Source: Modified after Dickey (2001). http://www.theseusproject.eu/
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
UCOAM: Unified Curvilinear Ocean Atmosphere Model
1 Primitive 3D Navier-Stokes equationsusing Boussinesq approximation.
2 Nondimensionalization and scaling ofthe NavierStokes equations.
3 Large Eddie Simulation (LES)
4 Fully written in FORTRAN 90.
5 Uses General Curvilinear Coordinates.
6 Using Fully Non-Hydrostatic PressureEquation.
7 Using UNESCO Equation of State fordensity.
11Mohammad Abouali and Jose E. Castillo (2013). “Unified Curvilinear Ocean
Atmosphere Model (UCOAM): A vertical velocity case study”. In: Math. Comput.Model. 57.9-10, pp. 2158–2168. issn: 08957177. doi: 10.1016/j.mcm.2011.03.023.url: http://linkinghub.elsevier.com/retrieve/pii/S089571771100183X.Garcia M. PhD Candidate 13th August 2015 SIAM-ICIAM 2015, Beijing, China 5 / 52
MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
sigma Vs Curvilinear
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
UCOAM Framework
With the goal to be more flexible and easier to use, and offer easyaccess to data analysis and visualization tools.
22Mary P. Thomas (2014). “Parallel Implementation of the Unified Curvilinear
Ocean and Atmospheric (UCOAM) Model and Supporting ComputationalEnvironment”. PhD thesis. San Diego: Claremont Graduate University and SanDiego State University, p. 110. url:http://sdsu-dspace.calstate.edu/handle/10211.3/120387.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
UCOAM Framework
1 General Curvilinear Environmental Model (GCEM)
• General Curvilinear Coastal Ocean Model (GCCOM)• General Curvilinear Atmosphere Model (GCAM)
2 Distributed Coupling Tools (DCT)
3 Computational Environment (CE )
• Cyber-infrastructure Web Application Framework (CyberWeb)
4 Data Assimilation Unit (DAU)
34
3Dany De Cecchis (2012). “Development of a Parallel Coupler Library withMinimal Inter-process Synchronization for Large Scale Computer Simulations”. In:
4M. Abouali and J E Castillo (2010). General Curvilinear Ocean Model (GCOM)Next Generation. Tech. rep. CSRCR2010-02. Computational Sciences ResearchCenter, San Diego State University, pp. 1–6. url:http://www.csrc.sdsu.edu/research\_reports/CSRCR2010-02.pdf.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
GCCOM new features
New features• Netcdf I/O integration
• 19 points Stencil LaplacianCurvilinear Coordinates CSR format
• Two Multigrid libraries implementedto solve non-hydrostatic Pressure
• 50% clock time improvementrespecting GS (SOR)
• Matlab Visualization Tool Upgraded
• Upgrading to 4th order in space
• Test new multigrid libraries
• Building an internal wave idealexperiment
• Coupling GCCOM-ROMS
• 3D Curvilinear mesh generator app.
• Second version of the parallel model.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
MATLAB Visualization Toolbox Upgrade
3D Animation Velocity Speed cross-sections
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
MATLAB Visualization Toolbox Upgrade
3D Animation Velocity Speed cross-sections
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
GCCOM Test Cases
Buoyancy Effect
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Data AssimilationGCOM-DART
GCCOM Test Cases
Lock Exchange CUBE Experiment 1km x 1km x 1km
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
GCCOM Test Cases
Lock Exchange Seamount Experiment 3.5km x 2.5km x 1km
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Data AssimilationGCOM-DART
GCCOM Application
River meeting with the ocean
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Practical Implementation
Stratification and mixing events associated with nearshore internalbores in southern Monterey Bay
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
FACT: Model errors are currently inevitable
Uncertainty quantification (UQ)
UQ is the process by which uncertainty is estimated in a system.
Y − y = e (1)
where e is an unknown error
Uncertainty reduction (UR)
UR which has the purpose of reducing the uncertainty in modelingand simulation. In weather and ocean modeling UR is called
Data Assimilation
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Motivation
Any data assimilation system consists of three components:
1 set of observations
2 a dynamical model
3 data assimilationscheme
The Main goal
Reduce the uncertainty inthe entire system
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Data Assimilation Framework
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Problem Statement
Estimating accurately the state variables in sub-mesoscale processis very difficult, particularly for physical ocean models, which arehighly nonlinear and require a dense spatial discretization in orderto correctly reproduce the dynamics.
1 High computational cost incurred by a high-resolutionnumerical model.
2 The efficiency of Kalman Filter in sub-mesoscale processes isunknown.
3 Sensitivity of the model to perturbation.
4 Resolution and Instrument error can affect the forecast.
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Challenge to be addressed
SOURCE: Hotteit, TAMOS workshop NCAR 2015.
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Data AssimilationGCOM-DART
The Plan
Main Objective
Develop a very highresolution forecast system bycoupling to the GeneralCurvilinear EnvironmentalModel a data assimilationand parametrization schemesbased on ensemble filters.
Design Thinking
1 Work on the development ofGCCOM model.
2 Interfaced with a Data Assimilationframework.
3 Prototype
4 Do Sensitivity Analysis
5 Test and get feedbackRepeat 3-5 as long as need it.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Data Assimilation Scheme
Question to be addressed
• What models do we use? 4
• What assimilation algorithms do we use?
• What type of observations do we assimilate?
• What are the observation errors?
• What are the model and analysis errors?
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
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, SSEnsKF56
5E. Kalnay (2003). Atmospheric Modeling, Data Assimilation, and Predictability.Cambridge University Press. isbn: 9780521791793. url:http://books.google.com/books?id=zx\_BakP2I5gC.
6Geir Evensen (2006). Data Assimilation: The Ensemble Kalman Filter.Secaucus, NJ, USA: Springer-Verlag New York, Inc. isbn: 354038300X.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
DA Frameworks
7897National Center for Atmospheric Research (NCAR). Data Assimilation Research
Testbed - DART. .8Deltares. The OpenDA data-assimilation toolbox.9Lars Nerger and Wolfgang Hiller (2013). “Software for ensemble-based data
assimilation systems—Implementation strategies and scalability”. In: Computers andGeosciences 55.0. Ensemble Kalman filter for data assimilation, pp. 110 –118. issn:0098-3004. doi: http://dx.doi.org/10.1016/j.cageo.2012.03.026. url:http://www.sciencedirect.com/science/article/pii/S0098300412001215.
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Data AssimilationGCOM-DART
DART Models Directory Details
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Data AssimilationGCOM-DART
Assimilation Tools Module
This module provides subroutines that implement the parallelversions of the sequential scalar filter algorithms.
Ensemble Filters
• 1 = EAKF (Ensemble Adjustment Kalman Filter, see Anderson2001)
• 2 = ENKF (Ensemble Kalman Filter)
• 3 = Kernel filter
• 4 = Particle filter
• 5 = Random draw from posterior (talk to Jeff before using)
• 6 = Deterministic draw from posterior with fixed kurtosis (ditto)
• 7 = Boxcar kernel filter
• 8 = Rank histogram filter (see Anderson 2010)
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Questions to be addressed
• What models do we use? 4
• What assimilation algorithms do we use? 4
• What type of observations do we assimilate?
• What are the observation errors?
• What are the model and analysis errors?
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Data AssimilationGCOM-DART
Observation to Assimilate
SOURCE: NOAA (San Francisco Operational System)
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Observation to Assimilate
Temperature loggers and ADCP at the MN mooring.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Observing System Simulation Experiments - OSSEs
The primary strategy is to use (OSSEs) to evaluate the impactof new OR planned observing systems.
1 (create_obs_sequence ) to generate the type of observation(and observation error) desired.
2 (create_fixed_network_seq ) to define the temporaldistribution of the desired observations.
3 perfect_model_obs: to advance the model from a knowninitial condition - and harvest the ’observations’ (with error)from the (known) true state of the model.
4 filter: to assimilate the ’observations’. Since the truemodel state is known, it is possible to evaluate theperformance of the assimilation.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Questions to be addressed
• What models do we use? 4
• What assimilation algorithms do we use? 4
• What type of observations do we assimilate? 4
• What are the observation errors?
• What are the model and analysis errors?
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Dealing with Ensemble Filters Errors
Source: https://proxy.subversion.ucar.edu/DAReS/DART/releases/Lanai/tutorial/section_09.pdf
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Filter Module
most common namelist settings and features built into DART
• Ensemble Size: ensemble sizes between 20 and 100 seem to workbest.
• Localization: To minimizes spurious correlations and reduce thespatial domain of influence of the observations . Also, for largemodels it improves run-time performance because only points withinthe localization radius need to be considered.
• Inflation: The spread of the members in a systematic way to avoidproblems of filter divergence.
• Outlier Rejection: Can be used to avoid bad observations.
• Sampling Error: For small ensemble sizes a table of expectedstatistical error distributions, corrections accounting for these errorsare applied during the assimilation.
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Data AssimilationGCOM-DART
Perfect Model Experiment Seamount
True State
True State of the model for the OSSE Experiment, observationcontrol at grid point (nx,ny,nz)=(64,16,10), the total run is 6hours, data is stored every 10 minutes
• Experiment 1: 1 singleobservation to identifythe best localizationparameter
• Experiment 2: 50observation sea surfaceat 21 random depth.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Initial Ensemble Members
A proper ensemble has sufficient spread to encompass ouruncertainty in our knowledge of the system
• Perturb a single state
• Climatological ensemble
The initial ensemble member for GCCOM
• This techniques assume that the variance of the short-term model forecast can approximate the errordistribution of the model.
• The temporal window used to extract previews model output is typically smaller than the entire system
• Helps to resolves physical processes caused by rapid changes in internal forcing.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Experiment 1: Perfect Model Experiment Sea-mount
Impact of Localization
Innov = PosteriorDiag − PriorDiag
Velocities U− from Innov X-Y (Different localization )
& assim tools nml
• filter kind =11= EAKF, 2= EKF, 3 =Kernel filter, 4 = particlefilter...
• cutoff = 0.000010(radians) about 63.66 meters
• select localization = 1valid values: 1=Gaspari-Cohn;2=Boxcar; 3=Ramped Boxcar
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Experiment 1: Perfect Model Experiment Seamount
How is the output different from the input?
Innov = PosteriorDiag − PriorDiag
Velocities U− from Innov (Plane X−Z. Time Step 1)The vertical layers are tens of meters apart.
& location nml
• horiz dist only = .false.Then full 3D separation
• vert normalization height =6370000.0
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Perfect Model Experiment Seamount
Total of 1000 observation (50 at the top, each one with 21observation in the vertical)
Experiment Set up• 3.5km (lon) x 2.5 km (lat) x 1km (depth) .
• 30 m horizonta.l
• 10 m vertical resolution.
• 10 minutes assimilation window.
• Assimilation variable U component.
• Total Time 6 hours
• 30 Ensemble Members
• Observation variance (0.1 - 1.00)
• Localization =250 m, 500m, 1000 m, 2000m
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Experiment 2: Perfect Model Experiment Seamount
Observation control for the State-Space evolution analysis
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Experiment 2: State-Space evolution
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Experiment 1: Perfect Model Experiment Seamount
Was the Assimilation Effective?• Ensemble Spread
• how many observations are getting rejected by the assimilation
• Rank Histogram
• RMSE
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Experiment 1: Perfect Model Experiment Sea-mount
Ensemble Spread
Number of observations available and the number of observationssuccessfully assimilated.
• U CURRENT COMPONENT spread: DART QC == 7, prior/post 1 1
Any observations with a QC value greater than ’maxgoodQC’ willget plotted on a separate figure color-coded to its QC value, notthe observation value.
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MotivationUCOAM Governing Equations
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Experiment 2: Perfect Model Experiment Sea-mount
Rank Histogram for all time steps• Rank histogram, that the probability that the observation will fall in each bin is equal.
• If this is true, then over a large enough sample, the histogram should be flat or roughly so.
• Then one can conclude that on the average, the ensemble spread correctly represents the uncertainty in theforecast.
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Profile Time Evolution
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RMSE Vs Spread
00:00 00:20 00:40 01:00 01:20 01:40 02:00 02:20 02:40 03:00 03:20 03:40 04:00 04:20 04:40 05:00 05:20 05:400
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Date Since 2015−01−01(HH:MM)
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Depth Average Ensemble Mean RMS Error, GCOM ’u’ Level nz=lev([1:32]), lat(nx=64), lon(ny= 16),
PriorDiag.nc’
Loc 2000m | ObsErrVar 1.0 | Total Error =0.69536
Loc 2000m | ObsErrVar 0.9 | Total Error =0.70941
Loc 2000m | ObsErrVar 0.8 | Total Error =0.77495
Loc 2000m | ObsErrVar 0.5 | Total Error =0.81652
00:00 00:20 00:40 01:00 01:20 01:40 02:00 02:20 02:40 03:00 03:20 03:40 04:00 04:20 04:40 05:00 05:20 05:400
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Depth Average Ensemble Spread, GCOM ’u’ Level nz=lev([1:32]), lat(nx=64), lon(ny= 16),
PriorDiag.nc’
Loc 2000m | ObsErrVar 1.0 | Total Spread =0.56466
Loc 2000m | ObsErrVar 0.9 | Total Spread =0.54438
Loc 2000m | ObsErrVar 0.8 | Total Spread =0.52337
Loc 2000m | ObsErrVar 0.5 | Total Spread =0.42281
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Time Evolution and Profile Diagnostic
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State evolution
Plane X-Z
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Data AssimilationGCOM-DART
Ensemble size and Computational Cost
Can we go Operational?CSRC cluster 16-core Xeon nodes each w/ 64GB RAM.
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MotivationUCOAM Governing Equations
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Conclusion
We demonstrate how data assimilation can be used, with anon-hydrostatic coastal ocean model, to study sub-mesoscaleprocesses and accurately estimate the state variables.
Sensitivity Analysis Summary• The ensemble adjustment Kalman filter (EAKF) has been shown to successfully assimilate very high
resolution data in the DA-GCCOM model.
• Increasing the ensemble size from 30 to 100 was not crucial for the current prediction
• For small domains (kilometers), every observation impacted every state variable. However, the spread ofthe ensembles tended to reduce over time. Adding inflation factor is need it.
• The assimilation system also exhibited some sensitivity to observation error variance, but in general it canhandle large observation error variance from 0.8-1.0
• results suggest that the DA-GCCOM ensemble-based system is able to extract the dynamically importantinformation from the model to provide reliable statistics to map the information from
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Southern Monterey Bay Project
Stratification and mixing events associated with nearshore internalbores in southern Monterey Bay
Temperature loggers and ADCP at the MN mooring.
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MotivationUCOAM Governing Equations
Data AssimilationGCOM-DART
Thank you!
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