Robertson at 13:35, 2 August 2019

2019-08-02T13:35:59Z

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	In the tutorial, you will perform a 4D-Var data assimilation cycle that spans the period 3-6 January, 2004. The 4D-Var control vector ''δ'''''z''' is comprised of increments to the initial conditions, ''δ'''''x'''(''t<sub>0</sub>''), surface forcing, δ'''f'''(''t''), and open boundary conditions, δ'''b'''(''t''). The ''prior'' initial conditions, '''x<sub>b</sub>'''(''t<sub>0</sub>''), are taken from the sequence of 4D-Var experiments described by [[Bibliography#~~MooreAM_2010b~~\|Moore ''et al.'' (~~2010b~~)]] in which data were assimilated every 7 days during the period July 2002- December 2004. The ''prior'' surface forcing, '''f<sub>b</sub>'''(''t''), takes the form of surface wind stress, heat flux, and a freshwater flux computed using the ROMS bulk flux formulation, and using near surface air data from COAMPS ([[Bibliography#DoyleJD_2009\|Doyle ''et al.'', 2009]]). Clamped open boundary conditions are imposed on (''u'',''v'') and tracers, and the ''prior'' boundary conditions, '''b<sub>b</sub>'''(''t''), are taken from the global ECCO product ([[Bibliography#WunschC_2007\|Wunsch and Heimbach, 2007]]). The free-surface height and vertically integrated velocity components are subject to the usual Chapman and Flather radiation conditions at the open boundaries. The ''prior'' surface forcing and open boundary conditions are provided daily and linearly interpolated in time. Similarly, the increments ''δ'''''f'''(''t'') and ''δ'''''b'''(''t'') are also computed daily and linearly interpolated in time.		In the tutorial, you will perform a 4D-Var data assimilation cycle that spans the period 3-6 January, 2004. The 4D-Var control vector ''δ'''''z''' is comprised of increments to the initial conditions, ''δ'''''x'''(''t<sub>0</sub>''), surface forcing, δ'''f'''(''t''), and open boundary conditions, δ'''b'''(''t''). The ''prior'' initial conditions, '''x<sub>b</sub>'''(''t<sub>0</sub>''), are taken from the sequence of 4D-Var experiments described by [[Bibliography#MooreAM_2011b\|Moore ''et al.'' (2011b)]] in which data were assimilated every 7 days during the period July 2002- December 2004. The ''prior'' surface forcing, '''f<sub>b</sub>'''(''t''), takes the form of surface wind stress, heat flux, and a freshwater flux computed using the ROMS bulk flux formulation, and using near surface air data from COAMPS ([[Bibliography#DoyleJD_2009\|Doyle ''et al.'', 2009]]). Clamped open boundary conditions are imposed on (''u'',''v'') and tracers, and the ''prior'' boundary conditions, '''b<sub>b</sub>'''(''t''), are taken from the global ECCO product ([[Bibliography#WunschC_2007\|Wunsch and Heimbach, 2007]]). The free-surface height and vertically integrated velocity components are subject to the usual Chapman and Flather radiation conditions at the open boundaries. The ''prior'' surface forcing and open boundary conditions are provided daily and linearly interpolated in time. Similarly, the increments ''δ'''''f'''(''t'') and ''δ'''''b'''(''t'') are also computed daily and linearly interpolated in time.

	The observations assimilated into the model are satellite SST, satellite SSH in the form of a gridded product from Aviso, and hydrographic observations of temperature and salinity collected from Argo floats and during the GLOBEC/LTOP and CalCOFI cruises off the coast of Oregon and southern California, respectively. The observation locations are illustrated in Fig. 2.		The observations assimilated into the model are satellite SST, satellite SSH in the form of a gridded product from Aviso, and hydrographic observations of temperature and salinity collected from Argo floats and during the GLOBEC/LTOP and CalCOFI cruises off the coast of Oregon and southern California, respectively. The observation locations are illustrated in Fig. 2.
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	==References==		==References==

	The technical description of the algorithms and application used in this tutorial are described in Moore ''et al.'' ([[Bibliography#~~MooreAM_2010a~~\|~~2010a~~]], [[Bibliography#~~MooreAM_2010b~~\|b]], [[Bibliography#~~MooreAM_2010c~~\|c]]).		The technical description of the algorithms and application used in this tutorial are described in Moore ''et al.'' ([[Bibliography#MooreAM_2011a\|2011a]], [[Bibliography#MooreAM_2011b\|b]], [[Bibliography#MooreAM_2011c\|c]]).

Robertson: Created page with "
4-Dimensional Variational (4D-Var) Data Assimilation Tutorial 2010
NOTOC This tutorial shows several examples of ROMS 4D-Var data assimilation al..."

2019-07-18T03:52:23Z

Created page with "<div class="title">4-Dimensional Variational (4D-Var) Data Assimilation Tutorial 2010</div>__NOTOC__ This tutorial shows several examples of ROMS 4D-Var data assimilation al..."

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<div class="title">4-Dimensional Variational (4D-Var) Data Assimilation Tutorial 2010</div>__NOTOC__

This tutorial shows several examples of ROMS 4D-Var data assimilation algorithms in the California Current System (CCS), 1/3 degree resolution ([[WC13]]).


<div style="float: left;margin: 0 20px 0 0;">{{4DVar Tut 2010 TOC}}</div>__TOC__

<div style="clear: both"></div>

<section begin=setup />
==Model Set-up==
The [[WC13]] model domain is shown in Fig. 1 and has open boundaries along the northern, western, and southern edges of the model domain.

[[Image:hraw_coarse_transect.png|500px|thumb|center|<center>'''Fig. 1:''' Model Bathymetry with 37°N Transect</center>]]
<div style="clear: both"></div>

In the tutorial, you will perform a 4D-Var data assimilation cycle that spans the period 3-6 January, 2004. The 4D-Var control vector ''δ'''''z''' is comprised of increments to the initial conditions, ''δ'''''x'''(''t0''), surface forcing, δ'''f'''(''t''), and open boundary conditions, δ'''b'''(''t''). The ''prior'' initial conditions, '''xb'''(''t0''), are taken from the sequence of 4D-Var experiments described by [[Bibliography#MooreAM_2010b|Moore ''et al.'' (2010b)]] in which data were assimilated every 7 days during the period July 2002- December 2004. The ''prior'' surface forcing, '''fb'''(''t''), takes the form of surface wind stress, heat flux, and a freshwater flux computed using the ROMS bulk flux formulation, and using near surface air data from COAMPS ([[Bibliography#DoyleJD_2009|Doyle ''et al.'', 2009]]). Clamped open boundary conditions are imposed on (''u'',''v'') and tracers, and the ''prior'' boundary conditions, '''bb'''(''t''), are taken from the global ECCO product ([[Bibliography#WunschC_2007|Wunsch and Heimbach, 2007]]). The free-surface height and vertically integrated velocity components are subject to the usual Chapman and Flather radiation conditions at the open boundaries. The ''prior'' surface forcing and open boundary conditions are provided daily and linearly interpolated in time. Similarly, the increments ''δ'''''f'''(''t'') and ''δ'''''b'''(''t'') are also computed daily and linearly interpolated in time.

The observations assimilated into the model are satellite SST, satellite SSH in the form of a gridded product from Aviso, and hydrographic observations of temperature and salinity collected from Argo floats and during the GLOBEC/LTOP and CalCOFI cruises off the coast of Oregon and southern California, respectively. The observation locations are illustrated in Fig. 2.

{|align="center"
|-
|[[Image:aviso_ssh.png|thumb|400px|<center>'''c)''' Aviso SSH</center>]]
|[[Image:blended_sst.png|thumb|400px|<center>'''d)''' Blended SST</center>]]
|-
|[[Image:in_situ_T.png|thumb|400px|<center>'''a)''' In Situ Temperature</center>]]
|[[Image:in_situ_S.png|thumb|400px|<center>'''b)''' In Situ Salinity</center>]]
|-
|}<section end=setup />

==Download Lectures and Exercises==

Links to the upcoming [http://www.myroms.org/4DVar_workshop_2010 2010 ROMS 4D-Var workshop] lectures are provided below. We are planning to record the audio for these lectures to combine with the slides for future reference. These lectures are meant to supplement this 4D-Var tutorial.

*'''Lecture 1:'''   [http://www.myroms.org/tutorials/4DVar_1.pdf PDF]   Primal 4D-Var
*'''Lecture 2:'''   [http://www.myroms.org/tutorials/4DVar_2.pdf PDF]   The Mechanics of 4D-Var
*'''Lecture 3:'''   [http://www.myroms.org/tutorials/4DVar_3.pdf PDF]   Dual 4D-Var
*'''Lecture 4:'''   [http://www.myroms.org/tutorials/4DVar_4.pdf PDF]   4D-Var Diagnostics
*'''Lecture 5:'''   [http://www.myroms.org/tutorials/4DVar_5.pdf PDF]   Observation Impact and Observation Sensitivity

Below are some of the tutorials pertinent to the upcoming [http://www.myroms.org/4DVar_workshop_2010 2010 ROMS 4D-Var workshop]:

*'''Tutorial 1:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_1.pdf PDF]   Explanation of CPP Options, roms.in, s4dvar.in (I4D-Var)
*'''Tutorial 2:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_2.pdf PDF]   Multiple Outer Loops
*'''Tutorial 4:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_4.pdf PDF]   Calculation of prior error standard deviations
*'''Tutorial 5:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_5.pdf PDF]   Explanation of CPP Options, roms.in, s4dvar.in (R4D-Var & 4D-PSAS)
*'''Tutorial 6:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_6.pdf PDF]   Semi-variograms
*'''Tutorial 9:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_9.pdf PDF]   Computing normalization coefficients for covariance models
*'''Tutorial 10:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_10.pdf PDF]   Setting up the impact/sensitivity functional, build script, cpp options and s4dvar.in
*'''Tutorial 13:'''   [http://www.myroms.org/tutorials/4DVar_Tutorial_13.pdf PDF]   Building your observation files

Below are the exercises pertinent to the upcoming [http://www.myroms.org/4DVar_workshop_2010 2010 ROMS 4D-Var workshop]:

*'''Exercise 1:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_1.pdf PDF]   Incremental, Strong Constraint 4D-Var
*'''Exercise 2:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_2.pdf PDF]   I4D-Var with Multiple Outer-loops
*'''Exercise 3:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_3.pdf PDF]   Dual Formulation 4D-Var: R4D-Var and 4D-PSAS
*'''Exercise 4:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_4.pdf PDF]   Weak Constraint Dual Formulation 4D-Var
*'''Exercise 5:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_5.pdf PDF]   Array Modes
*'''Exercise 6:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_6.pdf PDF]   Observation Impacts
*'''Exercise 7:'''   [http://www.myroms.org/tutorials/4DVar_EXERCISE_7.pdf PDF]   Observation Sensitivity

==Download Tutorial Files==
All of the data files and scripts necessary to run the 4D-Var tests discussed in this tutorial are available from the ROMS Subversion (SVN) repository. To download execute the following command:

<div class="box"><nowiki>> svn checkout --username joe_roms https://www.myroms.org/svn/src/test my_test</nowiki></div>

==Tutorial Directory Structure==
When the checkout is complete, you will have the following directory structure under your my_test directory.

/WC13 Main California Current System 4D-Var applications
/ARRAY_MODES Stabilized representer matrix array modes and clipping
/Data Input data directory
/Functionals Analytical expression header file
/I4DVAR Primal form of incremental, strong constraint 4D-Var, I4D-Var
/I4DVAR_impact I4D-Var observation impact
/Normalization 4D-Var error covariance normalization coefficients
/plotting 4D-Var plotting scripts (Matlab and ROMS plotting package)
/PSAS Dual form of 4D-Var, Physical-space Statistical Analysis System, 4D-PSAS
/PSAS_impact 4D-PSAS observation impact
/PSAS_sensitivity 4D-PSAS observation sensitivity (adjoint of 4D-PSAS)
/R4DVAR Dual form of 4D-Var, indirect representer method, R4D-Var
/R4DVAR_impact R4D-Var observation impact
/R4DVAR_sensitivity R4D-Var observation sensitivity (adjoint of R4D-Var)

Mostly all the directories have a Readme file with detailed instructions for configuring, compiling, running, and plotting the results.

==References==

The technical description of the algorithms and application used in this tutorial are described in Moore ''et al.'' ([[Bibliography#MooreAM_2010a|2010a]], [[Bibliography#MooreAM_2010b|b]], [[Bibliography#MooreAM_2010c|c]]).

4DVar Tutorial Introduction 2010 - Revision history

Robertson at 13:35, 2 August 2019

Robertson: Created page with "4-Dimensional Variational (4D-Var) Data Assimilation Tutorial 2010__NOTOC__ This tutorial shows several examples of ROMS 4D-Var data assimilation al..."

Robertson: Created page with "
4-Dimensional Variational (4D-Var) Data Assimilation Tutorial 2010
NOTOC This tutorial shows several examples of ROMS 4D-Var data assimilation al..."