GCCOM\_DART: Ensemble Data Assimilation Analysis System for Sub-mesoscale Processes

$: GCCOM\_DART: Ensemble Data Assimilation Analysis System for Sub-mesoscale Processes$
MotivationUCOAM Governing Equations

Data AssimilationGCOM-DART

Ensemble Data Assimilation Analysis System forSub-Mesoscale Processes

GCCOM DART: Sensitivity Analysis

Mariangel Garcia

[email protected]

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

[email protected]

http://www.csrc.sdsu.edu/



Outline

• Motivation

• GCEM Project (Newfeatures)

• Data AssimilationFrameworks

• GCCOM-DARTOSSE

• 3D Perfect ModelExperiment Seamount

• PracticalImplementation




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




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/


http://www.theseusproject.eu/



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

http://dx.doi.org/10.1016/j.mcm.2011.03.023

http://linkinghub.elsevier.com/retrieve/pii/S089571771100183X



sigma Vs Curvilinear




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.


http://sdsu-dspace.calstate.edu/handle/10211.3/120387



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.


http://www.csrc.sdsu.edu/research\_reports/CSRCR2010-02.pdf



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.




MATLAB Visualization Toolbox Upgrade

3D Animation Velocity Speed cross-sections




GCCOM Test Cases

Buoyancy Effect




GCCOM Test Cases

Lock Exchange CUBE Experiment 1km x 1km x 1km




GCCOM Test Cases

Lock Exchange Seamount Experiment 3.5km x 2.5km x 1km




GCCOM Application

River meeting with the ocean




Practical Implementation

Stratification and mixing events associated with nearshore internalbores in southern Monterey Bay




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




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




Data Assimilation Framework




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.




Challenge to be addressed

SOURCE: Hotteit, TAMOS workshop NCAR 2015.




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.




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?




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.


http://books.google.com/books?id=zx\_BakP2I5gC



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.


http://dx.doi.org/http://dx.doi.org/10.1016/j.cageo.2012.03.026

http://www.sciencedirect.com/science/article/pii/S0098300412001215



DART Models Directory Details




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)




Questions to be addressed


• What assimilation algorithms do we use? 4

• What type of observations do we assimilate?






Observation to Assimilate

SOURCE: NOAA (San Francisco Operational System)




Observation to Assimilate

Temperature loggers and ADCP at the MN mooring.




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.


create_obs_sequence

create_fixed_network_seq

perfect_model_obs

filter



Questions to be addressed


• What assimilation algorithms do we use? 4

• What type of observations do we assimilate? 4






Dealing with Ensemble Filters Errors

Source: https://proxy.subversion.ucar.edu/DAReS/DART/releases/Lanai/tutorial/section_09.pdf


https://proxy.subversion.ucar.edu/DAReS/DART/releases/Lanai/tutorial/section_09.pdf



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.




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.




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.




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




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




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





Observation control for the State-Space evolution analysis




Experiment 2: State-Space evolution





Was the Assimilation Effective?• Ensemble Spread

• how many observations are getting rejected by the assimilation

• Rank Histogram

• RMSE





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.





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.




Profile Time Evolution




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

0.01

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0.07

Date Since 2015−01−01(HH:MM)

Fo

reca

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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




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)

Fo

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pre

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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







Time Evolution and Profile Diagnostic




State evolution

Plane X-Z




Ensemble size and Computational Cost

Can we go Operational?CSRC cluster 16-core Xeon nodes each w/ 64GB RAM.




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




Southern Monterey Bay Project

Stratification and mixing events associated with nearshore internalbores in southern Monterey Bay

Temperature loggers and ADCP at the MN mooring.




Thank you!


GCCOM\_DART: Ensemble Data Assimilation Analysis System for Sub-mesoscale Processes

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Transcript of GCCOM\_DART: Ensemble Data Assimilation Analysis System for Sub-mesoscale Processes