29 June 2011DTC Summer TutorialOverview of GSIJohn C. DerberNOAA/NWS/NCEP/EMC

DTC Summer Tutorial

29 June 2011DTC Summer TutorialHistoryThe Spectral Statistical Interpolation (SSI) analysis system was developed at NCEP in the late 1980s and early 1990s. Main advantages of this system over OI systems were:All observations are used at once (much of the noise generated in OI analyses was generated by data selection)Ability to use forward models to transform from analysis variable to observationsAnalysis variables can be defined to simplify covariance matrix and are not tied to model variables (except need to be able to transform to model variable)The SSI system was the first operationalvariational analysis system system to directly use radiances

DTC Summer Tutorial

29 June 2011DTC Summer TutorialHistoryWhile the SSI system was a great improvement over the prior OI system it still had some basic short-comingsSince background error was defined in spectral space not simple to use for regional systemsDiagonal spectral background error did not allow much spatial variation in the background errorNot particularly well written since developed as a prototype code and then implemented operationally

DTC Summer Tutorial

29 June 2011DTC Summer TutorialHistoryThe Gridpoint Statistical Interpolation (GSI) analysis system was developed as the next generation global/regional analysis systemWan-Shu Wu, R. James Purser, David ParrishThree-Dimensional Variational Analysis with spatially Inhomogeneous Covariances. Mon. Wea. Rev., 130, 2905-2916.Based on SSI analysis systemReplace spectral definition for background errors with grid point version based on recursive filters

DTC Summer Tutorial

29 June 2011DTC Summer TutorialHistoryUsed in NCEP operations forRegionalGlobalHurricaneReal-Time Mesoscale AnalysisFuture Rapid Refresh (ESRL/GSD)GMAO collaborationModification to fit into WRF and NCEP infrastructureEvolution to ESMF

DTC Summer Tutorial

29 June 2011DTC Summer TutorialGeneral CommentsGSI analysis code is an evolving system.Scientific advancessituation dependent background errors -- hybridnew satellite datanew analysis variablesImproved codingBug fixesRemoval of unnecessary computations, arrays, etc.More efficient algorithms (MPI, OpenMP)Bundle structureGeneralizations of code Different compute platformsDifferent analysis variablesDifferent modelsImproved documentationFast evolution creates difficulties for slower evolving research projects

DTC Summer Tutorial

29 June 2011DTC Summer TutorialGeneral CommentsCode is intended to be used OperationallyMust satisfy coding requirementsMust fit into infrastructureMust be kept as simple as possibleExternal usage intended to:Improve external testingReduce transition to operations work/timeReduce duplication of effort

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSimplification to operational 3-D for presentationFor todays introduction, I will be talking about using the GSI for standard operational 3-D var. analysis. Many other options available or under development4d-varhybrid assimilationobservation sensitivityFOTOAdditional observation typesSST retrievalDetailed optionsOptions make code more complex difficult balance between options and simplicity

DTC Summer Tutorial

29 June 2011DTC Summer TutorialBasic analysis problemJ = Jb + Jo + Jc

J = (x-xb)TB-1(x-xb) + (H(x)-y0)T(E+F)-1(H(x)-y0) + JC

J = Fit to background + Fit to observations + constraints

x= Analysisxb= BackgroundB= Background error covarianceH= Forward modely0= ObservationsE+F= R = Instrument error + Representativeness errorJC = Constraint terms

DTC Summer Tutorial

29 June 2011DTC Summer TutorialJc termCurrently Jc term includes 2 termsWeak moisture constraint (q > 0, q < qsat)Can substantially slow convergence if coefficient made too large.Conservation of global dry mass not applicable to regional problem

DTC Summer Tutorial

29 June 2011DTC Summer Tutorial

DTC Summer Tutorial

Data

count177177177177177177

mean985.6609152542985.66947457632.62062564972.6204828249983.040299435983.0489774011

min985.573985.6342.585942.58621982.948983.042

max985.72985.712.66072.65948983.116983.052

max-min0.1470.0760.074760.073270.1680.01

stdev0.02836047670.02158336580.02275395430.02196522610.03297598390.0018120644

mean_psmean_pwmean_pdry

prd10q1mq10mq10pq10mq10pq10mq10pprd10q1p

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200906241298.5650.26272398.30232009062412985.65985.67620090624122.627232.625752009062412983.023983.05200906241298.56760.26257598.305

200906241298.5680.26272998.30532009062412985.68985.67820090624122.627292.627122009062412983.053983.051200906241298.56780.26271298.3051

200906241298.56760.2628298.30482009062412985.676985.67920090624122.62822.627572009062412983.048983.051200906241298.56790.26275798.3051

200906241898.56830.26307298.30522009062418985.683985.68220090624182.630722.631422009062418983.052983.051200906241898.56820.26314298.3051

200906241898.56780.26306998.30482009062418985.678985.68220090624182.630692.631082009062418983.048983.051200906241898.56820.26310898.3051

200906241898.5670.26313598.30392009062418985.67985.68120090624182.631352.63022009062418983.039983.05200906241898.56810.2630298.305

200906250098.56740.26263398.30482009062500985.674985.67820090625002.626332.627292009062500983.048983.051200906250098.56780.26272998.3051

200906250098.56750.26325498.30432009062500985.675985.68220090625002.632542.631672009062500983.043983.05200906250098.56820.26316798.305

200906250098.56710.26332398.30382009062500985.671985.68220090625002.633232.631352009062500983.038983.05200906250098.56820.26313598.305

200906250698.56720.26287498.30432009062506985.672985.67920090625062.628742.628182009062506983.043983.051200906250698.56790.26281898.3051

200906250698.56740.26356798.30382009062506985.674985.68520090625062.635672.635082009062506983.038983.05200906250698.56850.26350898.305

200906250698.56680.26369998.30312009062506985.668985.68620090625062.636992.636172009062506983.031983.05200906250698.56860.26361798.305

200906251298.56740.26364998.30382009062512985.674985.68620090625122.636492.635632009062512983.038983.051200906251298.56860.26356398.3051

200906251298.5690.26423998.30472009062512985.69985.69320090625122.642392.641632009062512983.047983.051200906251298.56930.26416398.3051

200906251298.56760.26430198.30332009062512985.676985.69320090625122.643012.64262009062512983.033983.051200906251298.56930.2642698.3051

200906251898.56920.26444698.30472009062518985.692985.69420090625182.644462.643092009062518983.047983.051200906251898.56940.26430998.3051

200906251898.56790.26503498.30292009062518985.679985.69920090625182.650342.648682009062518983.029983.05200906251898.56990.26486898.305

200906251898.56790.26499398.30292009062518985.679985.69820090625182.649932.648532009062518983.029983.05200906251898.56980.26485398.305

200906260098.56750.26465398.30292009062600985.675985.69420090626002.646532.643722009062600983.029983.05200906260098.56940.26437298.305

200906260098.56720.26506798.30212009062600985.672985.69920090626002.650672.64942009062600983.021983.05200906260098.56990.2649498.305

200906260098.56640.26509898.30132009062600985.664985.69920090626002.650982.649872009062600983.013983.049200906260098.56990.26498798.3049

200906260698.56670.26455798.30212009062606985.667985.69420090626062.645572.64432009062606983.021983.05200906260698.56940.2644398.305

200906260698.56990.26564698.30422009062606985.699985.70520090626062.656462.655392009062606983.042983.05200906260698.57050.26553998.305

200906260698.56950.26575998.30372009062606985.695985.70620090626062.657592.656492009062606983.037983.05200906260698.57060.26564998.305

200906261298.56980.26552598.30432009062612985.698985.70520090626122.655252.65472009062612983.043983.05200906261298.57050.2654798.305

200906261298.57070.26590398.30482009062612985.707985.70920090626122.659032.658642009062612983.048983.05200906261298.57090.26586498.305

200906261298.5710.26588998.30512009062612985.71985.7120090626122.658892.659482009062612983.051983.05200906261298.5710.26594898.305

200906261898.57040.26555798.30482009062618985.704985.70420090626182.655572.654552009062618983.048983.05200906261898.57040.26545598.305

200906261898.56620.26604698.30012009062618985.662985.70720090626182.660462.658112009062618983.001983.049200906261898.57070.26581198.3049

200906261898.56540.2660798.29932009062618985.654985.70520090626182.66072.65762009062618982.993983.048200906261898.57050.2657698.3048

200906270098.56520.26507898.30012009062700985.652985.69620090627002.650782.647992009062700983.001983.049200906270098.56960.26479998.3049

200906270098.57140.26538898.3062009062700985.714985.70220090627002.653882.65342009062700983.06983.049200906270098.57020.2653498.3049

200906270098.57060.26538998.30522009062700985.706985.70420090627002.653892.654232009062700983.052983.049200906270098.57040.26542398.3049

200906270698.57070.26465698.3062009062706985.707985.69620090627062.646562.646372009062706983.06983.049200906270698.56960.26463798.3049

200906270698.56880.26545898.30332009062706985.688985.70320090627062.654582.653842009062706983.033983.049200906270698.57030.26538498.3049

200906270698.56770.26554398.30222009062706985.677985.70420090627062.655432.655232009062706983.022983.048200906270698.57040.26552398.3048

200906271298.56840.26502798.30332009062712985.684985.69920090627122.650272.649872009062712983.033983.049200906271298.56990.26498798.3049

200906271298.57040.26583598.30462009062712985.704985.70820090627122.658352.658222009062712983.046983.049200906271298.57080.26582298.3049

200906271298.56940.26591498.30342009062712985.694985.70820090627122.659142.658692009062712983.034983.049200906271298.57080.26586998.3049

200906271898.56980.26523198.30462009062718985.698985.70120090627182.652312.651512009062718983.046983.05200906271898.57010.26515198.305

200906271898.57010.26587598.30422009062718985.701985.70620090627182.658752.657092009062718983.042983.049200906271898.57060.26570998.3049

200906271898.56940.26585798.30362009062718985.694985.70520090627182.658572.656342009062718983.036983.049200906271898.57050.26563498.3049

200906280098.56880.2646398.30422009062800985.688985.69420090628002.64632.644652009062800983.042983.049200906280098.56940.26446598.3049

200906280098.56940.2649398.30442009062800985.694985.69820090628002.64932.649182009062800983.044983.049200906280098.56980.26491898.3049

200906280098.5680.26506898.30292009062800985.68985.69920090628002.650682.649822009062800983.029983.049200906280098.56990.26498298.3049

200906280698.56840.26396698.30442009062806985.684985.68920090628062.639662.639532009062806983.044983.049200906280698.56890.26395398.3049

200906280698.5640.26502398.2992009062806985.64985.69720090628062.650232.648142009062806982.99983.048200906280698.56970.26481498.3048

200906280698.5630.26516998.29792009062806985.63985.69720090628062.651692.649472009062806982.979983.047200906280698.56970.26494798.3047

200906281298.56350.26454498.2992009062812985.635985.69220090628122.645442.643282009062812982.99983.048200906281298.56920.26432898.3048

200906281298.56420.26514498.2992009062812985.642985.69820090628122.651442.650852009062812982.99983.047200906281298.56980.26508598.3047

200906281298.56360.26525398.29832009062812985.636985.69820090628122.652532.651642009062812982.983983.046200906281298.56980.26516498.3046

200906281898.56370.26459498.29912009062818985.637985.69320090628182.645942.645852009062818982.991983.047200906281898.56930.26458598.3047

200906281898.56390.26478698.29922009062818985.639985.69320090628182.647862.647112009062818982.992983.046200906281898.56930.26471198.3046

200906281898.56320.26476398.29852009062818985.632985.69320090628182.647632.646962009062818982.985983.046200906281898.56930.26469698.3046

200906290098.56290.26373898.29912009062900985.629985.68420090629002.637382.637132009062900982.991983.046200906290098.56840.26371398.3046

200906290098.56570.26462798.30112009062900985.657985.69220090629002.646272.646242009062900983.011983.046200906290098.56920.26462498.3046

200906290098.56440.2647598.29962009062900985.644985.69320090629002.64752.646752009062900982.996983.046200906290098.56930.26467598.3046

200906290698.56490.26378298.30112009062906985.649985.68420090629062.637822.637942009062906983.011983.046200906290698.56840.26379498.3046

200906290698.56190.26495798.2972009062906985.619985.69320090629062.649572.64772009062906982.97983.045200906290698.56930.2647798.3045

200906290698.56120.26510198.29612009062906985.612985.69320090629062.651012.649192009062906982.961983.044200906290698.56930.26491998.3044

200906291298.56150.26445998.2972009062912985.615985.68820090629122.644592.643342009062912982.97983.045200906291298.56880.26433498.3045

200906291298.56590.26511198.30082009062912985.659985.69520090629122.651112.649442009062912983.008983.045200906291298.56950.26494498.3045

200906291298.56560.26530198.30032009062912985.656985.69720090629122.653012.651442009062912983.003983.045200906291298.56970.26514498.3045

200906291898.56540.2646698.30082009062918985.654985.69120090629182.64662.645682009062918983.008983.045200906291898.56910.26456898.3045

200906291898.56210.26525498.29682009062918985.621985.69420090629182.652542.650082009062918982.968983.044200906291898.56940.26500898.3044

200906291898.56120.26531298.29592009062918985.612985.69320090629182.653122.650032009062918982.959983.043200906291898.56930.26500398.3043

200906300098.56090.26408398.29682009063000985.609985.68220090630002.640832.638152009063000982.968983.044200906300098.56820.26381598.3044

200906300098.56060.26460898.2962009063000985.606985.68620090630002.646082.642832009063000982.96983.043200906300098.56860.26428398.3043

200906300098.55950.26468498.29482009063000985.595985.68620090630002.646842.643572009063000982.948983.042200906300098.56860.26435798.3042

Plot_mean_ps

985.641985.641

985.658985.644

985.655985.646

985.654985.64

985.641985.643

985.635985.643

985.633985.636

985.65985.64

985.653985.64

985.644985.634

985.643985.644

985.64985.645

985.641985.642

985.683985.649

985.679985.65

985.679985.646

985.661985.649

985.66985.65

985.653985.642

985.686985.644

985.682985.646

985.681985.639

985.671985.649

985.667985.649

985.669985.646

985.669985.651

985.663985.652

985.667985.65

985.658985.654

985.656985.654

985.653985.648

985.691985.651

985.689985.651

985.686985.647

985.696985.652

985.7985.654

985.693985.649

985.72985.658

985.719985.661

985.716985.654

985.672985.656

985.662985.655

985.665985.649

985.687985.653

985.687985.653

985.682985.647

985.678985.655

985.68985.657

985.672985.651

985.647985.654

985.641985.654

985.644985.651

985.618985.653

985.616985.653

985.609985.644

985.61985.651

985.606985.651

985.603985.643

985.625985.65

985.623985.651

985.621985.646

985.627985.652

985.63985.652

985.623985.649

985.586985.651

985.573985.65

985.579985.644

985.628985.654

985.629985.654

985.625985.651

985.647985.658

985.65985.66

985.647985.657

985.661985.66

985.657985.662

985.66985.66

985.653985.662

985.652985.662

985.646985.655

985.66985.661

985.656985.661

985.655985.655

985.661985.659

985.657985.659

985.658985.655

985.686985.661

985.679985.662

985.685985.66

985.681985.661

985.67985.661

985.674985.654

985.693985.66

985.689985.662

985.687985.655

985.661985.663

985.659985.664

985.658985.661

985.676985.667

985.672985.667

985.675985.666

985.659985.672

985.656985.672

985.653985.667

985.671985.674

985.67985.673

985.669985.671

985.649985.674

985.646985.673

985.65985.676

985.68985.678

985.676985.679

985.683985.682

985.678985.682

985.67985.681

985.674985.678

985.675985.682

985.671985.682

985.672985.679

985.674985.685

985.668985.686

985.674985.686

985.69985.693

985.676985.693

985.692985.694

985.679985.699

985.679985.698

985.675985.694

985.672985.699

985.664985.699

985.667985.694

985.699985.705

985.695985.706

985.698985.705

985.707985.709

985.71985.71

985.704985.704

985.662985.707

985.654985.705

985.652985.696

985.714985.702

985.706985.704

985.707985.696

985.688985.703

985.677985.704

985.684985.699

985.704985.708

985.694985.708

985.698985.701

985.701985.706

985.694985.705

985.688985.694

985.694985.698

985.68985.699

985.684985.689

985.64985.697

985.63985.697

985.635985.692

985.642985.698

985.636985.698

985.637985.693

985.639985.693

985.632985.693

985.629985.684

985.657985.692

985.644985.693

985.649985.684

985.619985.693

985.612985.693

985.615985.688

985.659985.695

985.656985.697

985.654985.691

985.621985.694

985.612985.693

985.609985.682

985.606985.686

985.595985.686

q10m

q10p

date

pressure (hPa)

global mean_ps

Plot_mean_pw

2.593552.59355

2.596122.59655

2.597172.59751

2.592152.59249

2.595842.59577

2.596482.59617

2.587972.58797

2.591782.59202

2.591342.59171

2.585942.58621

2.596082.5962

2.597762.59765

2.594062.59414

2.599572.60048

2.600052.60103

2.596062.59678

2.600292.60058

2.600812.60099

2.592622.59288

2.593582.59491

2.595082.59606

2.588732.58982

2.598082.5991

2.598912.59977

2.59582.5967

2.599932.60134

2.600862.60191

2.598632.59993

2.603342.60448

2.603572.60462

2.597622.59845

2.599482.60142

2.598362.60017

2.595262.5966

2.600342.60192

2.601272.6031

2.596722.598

2.604192.60694

2.606492.60949

2.600332.60268

2.603862.60512

2.602862.60363

2.596562.59746

2.599622.60113

2.599662.60122

2.593792.59493

2.602482.60404

2.603842.60535

2.597412.59914

2.603452.60332

2.603432.60377

2.599612.6

2.603372.60284

2.603872.60387

2.594872.59457

2.601682.60141

2.601962.60198

2.593812.59393

2.600582.60096

2.602062.60222

2.596062.59728

2.601952.60266

2.603482.60348

2.598762.6005

2.603632.60298

2.604022.60309

2.596552.59654

2.605612.60609

2.605852.60635

2.602842.60313

2.60992.60986

2.612172.61142

2.609522.609

2.612062.61174

2.613482.61293

2.611532.61096

2.614572.61399

2.615742.61428

2.607362.60674

2.613032.61291

2.613242.61306

2.607962.60692

2.611292.61092

2.611682.61095

2.608122.60682

2.611142.61146

2.611632.61209

2.61022.6103

2.611222.61134

2.611432.61133

2.604572.60354

2.609622.61009

2.610252.61098

2.603282.60472

2.61212.61283

2.612982.61409

2.609432.61049

2.615672.61627

2.616962.61679

2.613982.61582

2.621322.62207

2.621172.62178

2.615612.6171

2.622612.62356

2.622312.62313

2.619922.6202

2.626152.62402

2.627032.62382

2.627232.62575

2.627292.62712

2.62822.62757

2.630722.63142

2.630692.63108

2.631352.6302

2.626332.62729

2.632542.63167

2.633232.63135

2.628742.62818

2.635672.63508

2.636992.63617

2.636492.63563

2.642392.64163

2.643012.6426

2.644462.64309

2.650342.64868

2.649932.64853

2.646532.64372

2.650672.6494

2.650982.64987

2.645572.6443

2.656462.65539

2.657592.65649

2.655252.6547

2.659032.65864

2.658892.65948

2.655572.65455

2.660462.65811

2.66072.6576

2.650782.64799

2.653882.6534

2.653892.65423

2.646562.64637

2.654582.65384

2.655432.65523

2.650272.64987

2.658352.65822

2.659142.65869

2.652312.65151

2.658752.65709

2.658572.65634

2.64632.64465

2.64932.64918

2.650682.64982

2.639662.63953

2.650232.64814

2.651692.64947

2.645442.64328

2.651442.65085

2.652532.65164

2.645942.64585

2.647862.64711

2.647632.64696

2.637382.63713

2.646272.64624

2.64752.64675

2.637822.63794

2.649572.6477

2.651012.64919

2.644592.64334

2.651112.64944

2.653012.65144

2.64662.64568

2.652542.65008

2.653122.65003

2.640832.63815

2.646082.64283

2.646842.64357

q10m

q10p

date

pressure (hPa)

global mean_pw

Plot_mean_pdry

983.048983.048

983.062983.048

983.058983.048

983.062983.048

983.046983.048

983.039983.047

983.045983.048

983.058983.048

983.061983.048

983.058983.048

983.047983.048

983.042983.047

983.047983.048

983.083983.049

983.079983.049

983.083983.049

983.061983.049

983.059983.049

983.061983.049

983.092983.049

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q10m

q10p

date

pressure (hPa)

global mean_pdry

29 June 2011DTC Summer TutorialSolutionAt minimum, Grad J = 0, Note this is a necessary condition it is sufficient only for a quadratic J

Grad J = 2B-1(x-xb) + HT(E+F)-1(H(x)-y0) + Grad JC

A conjugate gradient minimization algorithm is used to solve for Grad J = 0

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSolution StrategySolve series of simpler problems with some nonlinear components eliminatedOuter iteration, inner iteration structurex = xouter iteration + xinner iteration + xbOuter iterationQCMore complete forward modelInner iterationSeveral different minimization options preconditioned Conjugate GradientEstimate search directionEstimate optimal stepsize in search directionOften simpler forward modelVariational QCSolution used to start next outer iteration

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInner iteration algorithm 1J = xTB-1x + (Hx-o)TO-1(Hx-o) (assume linear)define y = B-1x J = xTy + (Hx-o)TO-1(Hx-o) Grad Jx = B-1x +HTO-1(Hx-o) = y + HTO-1(Hx-o)Grad Jy = x + BHTO-1(Hx-o) = B Grad JxSolve for both x and y using preconditioned conjugate gradient (where the x solution is preconditioned by B and the solution for y is preconditioned by B-1)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInner iteration algorithm 1Specific algorithmx0=y0=0Iterate over nGrad xn = yn-1 + HTO-1(Hxn-1-o) Grad yn = B Grad xnDir xn = Grad yn + Dir xn-1Dir yn = Grad xn + Dir yn-1xn = xn-1 + Dir xn (Update xhatsave (outer iter. x) - as well) yn = yn-1 + Dir yn (Update yhatsave (outer iter. y) - as well)Until max iteration or gradient sufficiently minimized

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInner iteration algorithm 2J = xTB-1x + (Hx-o)TO-1(Hx-o) (assume linear)define y = B-1/2x J = yTy + (HB1/2y-o)TO-1(HB1/2y-o) Grad Jy = y +B1/2HTO-1(HB1/2y-o) Solve for y using preconditioned conjugate gradientFor our definition of the background error matrix, B1/2 is not square and thus y is (3x) larger than x.

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInner iteration algorithm 1intall routine calculate HTO-1(Hx-o) bkerror routines multiplies by B dprod x calculates and magnitude of gradientstpcalc calculates stepsize

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInner iteration algorithm 1 Estimation of (the stepsize)The stepsize is estimated through estimating the ratio of contributions for each term = a bThe as and bs can be estimated exactly for the linear terms.For nonlinear terms, the as and bs are estimated by fitting a quadratic using 3 points around an estimate of the stepsizeThe estimate for the nonlinear terms is re-estimated iteratively using the stepsize for the previous estimate (up to 5 iterations)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialAnalysis variablesBackground errors must be defined in terms of analysis variableStreamfunction ()Unbalanced Velocity Potential (unbalanced)Unbalanced Temperature (Tunbalanced)Unbalanced Surface Pressure (Psunbalanced)Ozone Clouds etc.Satellite bias correction coefficients

DTC Summer Tutorial

29 June 2011DTC Summer TutorialAnalysis variables = unbalanced + A T = Tunbalanced + B Ps = Psunbalanced + C Streamfunction is a key variable defining a large percentage T and Ps (especially away from equator). Contribution to is small except near the surface and tropopause.

DTC Summer Tutorial

29 June 2011DTC Summer TutorialAnalysis variablesA, B and C matrices can involve 2 componentsA pre-specified statistical balance relationship part of the background error statistics fileOptionally a incremental normal model balance Not working well for regional problemSee references for details

DTC Summer Tutorial

29 June 2011DTC Summer TutorialImpact of TLNM constraintZonal-average surface pressure tendency for background (green), unconstrained GSI analysis (red), and GSI analysis with TLNMC (purple).

DTC Summer Tutorial

29 June 2011DTC Summer TutorialFits of Surface Pressure Data in Cycled Experiment with and without TLNM constraint

DTC Summer Tutorial

29 June 2011DTC Summer TutorialAnalysis variablesSize of problem NX x NY x NZ x NVARGlobal = 25.7 million component control vectorRequires multi-tasking to fit on computers

DTC Summer Tutorial

29 June 2011DTC Summer TutorialGrid Sub-domainsThe analysis and background fields are divided across the processors in two different waysSub-Domains an x-y region of the analysis domain with full vertical extent observations defined on sub-domainsHorizontal slabs a single or multiple levels of full x-y fieldsSince the analysis problem is a full 3-D problem we must transform between these decompositions repeatedly

DTC Summer Tutorial

29 June 2011DTC Summer Tutorialu,vAnalysis variables are streamfunction and velocity potentialu,v needed for many routines (int,stp,balmod, etc.) routinesu,v updated along with other variables by calculating derivatives of streamfunction and velocity potential components of search direction x and creating a dir x (u,v)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialBackground fieldsCurrent works for following systemsNCEP GFSNCEP NMM binary and netcdfNCEP RTMANCEP HurricaneGMAO globalARW binary and netcdf (not operationally used yet RR - GSD)FGAT (First Guess at Appropriate Time) enabled up to 100 time levels

DTC Summer Tutorial

29 June 2011DTC Summer TutorialBackground ErrorsThree paths more in talk by D. KleistIsotropic/homogeneousMost common usage. Function of latitude/heightVertical and horizontal scales separableVariances can be location dependentAnisotropic/inhomogeneousFunction of location /stateCan be full 3-D covariancesStill relatively immatureHybrid

DTC Summer Tutorial

29 June 2011DTC Summer TutorialObservationsObservational data is expected to be in BUFR format (this is the international standard)See presentation by Ruifang LiEach observation type (e.g., u,v,radiance from NOAA-15 AMSU-A) is read in on a particular processor or group of processors (parallel read)Data thinning can occur in the reading step.Checks to see if data is in specified data time window and within analysis domain

DTC Summer Tutorial

29 June 2011DTC Summer TutorialData processingData used in GSI controlled 2 waysPresence or lack of input fileControl files input (info files) into analysisAllows data to be monitored rather than usedEach ob type differentSpecify different time windows for each ob typeIntelligent thinning distance specification

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInput data Satellite currently usedRegionalGOES-11 and 12 Sounders Channels 1-15Individual fields of view 4 Detectors treated separatelyOver ocean onlyThinned to 120kmAMSU-ANOAA-15 Channels 1-10, 12-13, 15NOAA-18 Channels 1-8, 10-13, 15METOP Channels1-6, 8-13, 15Thinned to 60kmAMSU-B/MHSNOAA-15 Channels 1-3, 5NOAA-18Channels 1-5METOPChannels 1-5Thinned to 60kmHIRSNOAA-17Channels 2-15METOPChannels 2-15Thinned to 120kmAIRSAQUA148 ChannelsThinned to 120kmGlobalall thinned to 145kmGOES-11 and 12 Sounders Channels 1-15Individual fields of view 4 Detectors treated separatelyOver ocean onlyAMSU-ANOAA-15 Channels 1-10, 12-13, 15NOAA-18 Channels 1-8, 10-13, 15NOAA-19 Channels 1-7, 9-13, 15METOP Channels 1-6, 8-13, 15AQUA Channels 6, 8-13AMSU-B/MHSNOAA-15 Channels 1-3, 5NOAA-18Channels 1-5METOPChannels 1-5HIRSNOAA-17Channels 2-15 NOAA-19 Channels 2-15METOPChannels 2-15AIRS AQUA148 ChannelsIASIMETOP 165 Channels

DTC Summer Tutorial

29 June 2011DTC Summer TutorialInput data Conventional currently usedRadiosondesPibal windsSynthetic tropical cyclone windswind profilersconventional aircraft reportsASDAR aircraft reportsMDCARS aircraft reportsdropsondesMODIS IR and water vapor windsGMS, JMA, METEOSAT and GOES cloud drift IR and visible windsGOES water vapor cloud top winds Surface land observationsSurface ship and buoy observationSSM/I wind speedsQuikScat and ASCATwind speed and directionSSM/I and TRMM TMI precipitation estimatesDoppler radial velocitiesVAD (NEXRAD) windsGPS precipitable water estimatesGPS Radio occultation refractivity and bending angle profilesSBUV ozone profiles and OMI total ozone

DTC Summer Tutorial

29 June 2011DTC Summer TutorialData Sub-domainsObservations are distributed to processors they are used on. Comparison to obs are done on sub-domains.If an observation is on boundary of multiple sub-domains will be put into all relevant sub-domains for communication free adjoint calculations. However, it is necessary to assign the observation only to one sub-domain for the objective function calculationInterpolation of sub-domain boundary observations requires the use of halo rows around each sub-domain

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSimulation of observationsTo use observation, must be able to simulate observationCan be simple interpolation to ob location/timeCan be more complex (e.g., radiative transfer)For radiances we use CRTM Vertical resolution and model top important

DTC Summer Tutorial

Atmospheric analysis problem (Practical)Outer (K) and Inner (L) iteration operators

VariableK operatorL operatorTemperature surface obs. at 2m3-D sigma interpolation adjustment to different orography3-D sigma interpolation Below bottom sigma assumed at bottom sigmaWind surface obs. at 10m over land, 20m over ocean, except scatt.3-D sigma interpolationreduction below bottom level using model factor3-D sigma interpolationreduction below bottom level using model factorOzone used as layersIntegrated layers from forecast modelIntegrated layers from forecast modelSurface pressure2-D interpolation plus orography correction2-D interpolationPrecipitationFull model physicsLinearized model physicsRadiancesFull radiative transferLinearized radiative transfer

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSub-domain 3Sub-domain 1Sub-domain 2ObservationObservation/Sub-domain layout

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSub-domain 3ObservationHalo for Sub-domain 3Sub-domain 3 calculation w/halo

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSub-domain 3ObservationHalo for Sub-domain 3Forward interpolation to ob.

DTC Summer Tutorial

29 June 2011DTC Summer TutorialSub-domain 3ObservationHalo for Sub-domain 3Adjoint of interpolation to grid(values in halo not used)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialQuality controlExternal platform specific QCSome gross checking in PREPBUFR file creationAnalysis QCGross checks specified in input data filesVariational quality control Data usage specification (info files)Outer iteration structure allows data rejected (or downweighted) initially to come back in Ob error can be modified due to external QC marksRadiance QC much more complicated. Tomorrow!

DTC Summer Tutorial

29 June 2011DTC Summer TutorialObservation outputDiagnostic files are produced for each data type for each outer iteration (controllable through namelist)Output from individual processors (sub-domains) and concatenated together outside GSIExternal routines for reading diagnostic files should be supported by DTC

DTC Summer Tutorial

29 June 2011DTC Summer TutorialGSI layout (major routines)(generic names, 3dvar path)gsimain (main code)gsimain_initialize (read in namelists and initialize variablesgsimain_rungsisub deter_subdomain (creates sub-domains)*read_info (reads info files to determine data usage)glbsoiobserver_init (read background field)observer_set (read observations and distribute)prewgt (initializes background error)setuprhsall (calculates outer loop obs. incrementsPcgsoi, sqrtmin or other minimization (solves inner iteration)gsimain_finalize (clean up arrays and finalize mpi)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialGSI layout (major routines)pcgsoi (other minimizations similar)control2state (convert control vector to state vector)intall (compare to observations and adjoint)state2control (convert state vector to control vectorbkerror (multiply by background error)stpcalc (estimate stepsize and update solution)Depreciated: Moved to outer loopupdate_guess (updates outer iteration solution)write_all (write solution)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialUseful ReferencesWan-ShuWu, R. JamesPurser and David F.Parrish, 2002: Three-Dimensional Variational Analysis with Spatially Inhomogeneous Covariances. Monthly Weather Review, Vol. 130, No. 12, pp. 29052916. R. JamesPurser, Wan-ShuWu, David F.Parrish and Nigel M.Roberts, 2003: Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part I: Spatially Homogeneous and Isotropic Gaussian Covariances. Monthly Weather Review, Vol. 131, No. 8, pp. 15241535. R. JamesPurser, Wan-ShuWu, David F.Parrish and Nigel M.Roberts, 2003: Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances. Monthly Weather Review, Vol. 131, No. 8, pp. 15361548.McNally, A.P., J.C. Derber, W.-S. Wu and B.B. Katz, 2000: The use of TOVS level-1B radiances in the NCEP SSI analysis system. Q.J.R.M.S., 126, 689-724. Parrish, D. F. and J. C. Derber, 1992: The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev., 120, 1747 - 1763. Derber, J. C. and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126, 2287 - 2299. Kleist, Daryl T; Parrish, David F; Derber, John C; Treadon, Russ; Wu, Wan-Shu; Lord, Stephen , Introduction of the GSI into the NCEP Global Data Assimilation System, Weather and Forecasting. Vol. 24, no. 6, pp. 1691-1705. Dec 2009 Kleist, Daryl T; Parrish, David F; Derber, John C; Treadon, Russ; Errico, Ronald M; Yang, Runhua, Improving Incremental Balance in the GSI 3DVAR Analysis System, Monthly Weather Review [Mon. Weather Rev.]. Vol. 137, no. 3, pp. 1046-1060. Mar 2009.Kazumori, M; Liu, Q; Treadon, R; Derber, JC, Impact Study of AMSR-E Radiances in the NCEP Global Data Assimilation System Monthly Weather Review,Vol. 136, no. 2, pp. 541-559. Feb 2008.Zhu, Y; Gelaro, R, Observation Sensitivity Calculations Using the Adjoint of the Gridpoint Statistical Interpolation (GSI) Analysis System, Monthly Weather Review. Vol. 136, no. 1, pp. 335-351. Jan 2008. DTC GSI documentation (http://www.dtcenter.org/com-GSI/users/index.php)

DTC Summer Tutorial

29 June 2011DTC Summer TutorialChallengesNegative Moisture and other tracers Diabatic analysisHurricane initializationSituation dependent background errorsUse of satellite radiances in regional modeUse of satellite data over land/ice/snow

DTC Summer Tutorial