Observability of flow dependent structure functions and their use in data assimilation
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1 Oserviliy of flow dependen srucure funcions nd heir use in d ssimilion Pierre Guhier nd Crisin Lupu Collorion wih Séphne Lroche, Mrk Buehner nd Ahmed Mhidji (Env. Cnd) 3rd meeing of he HORPEX DAOS-WG Monrél (CANADA), July 8-9, 00 Deprmen of Erh nd Amospheric Sciences Universié du Quéec à Monrél Ouline Impc of flow-dependen srucures in d ssimilion nd link wih precursors o dynmic insiliy * Evluion of he oserviliy of srucure funcions (Lupu nd Guhier, 00) Implicions for hyrid 4D-Vr * he erlier eperimens of Fisher nd Andersson wih reduced rnk Klmn filer * he hyrid 4D-Vr/EnKF (Buehner e l., 00) Conclusions Monrél (CANADA).
2 Oservion impc on oservions (Lnglnd nd Bker, 004) Forecs Verifying nlysis Anlysis error (e 4 ) Anlysis X Forecs error (e 30 ) Bckground X 0-h 4-h e e 30 e 4 6/0 UC L J L J 8/0 UC Ky H L J L J 0 Frcion of Oservions h Improve he Forecs GEOS-5 July z (Gelro, 008) AIRS Conrol No AMSU-A AMSU-AA Conrol No AIRS only smll mjoriy of he oservions improve he forecs Monrél (CANADA).
3 Key nlysis errors lgorihm configurion (Lroche e l., 00) Key nlysis error rue Se of he Amosphere Sensiiviy nlysis Iniil nlysis GEM Reference nlysis 0 hr 4 hr Forecs error (e 4 ) A poseriori sensiiviies Key nlysis error GEM 0 ( ngen liner ) 4 Minimizion lgorihm 3 ierions J 0 GEM (Adjoin) J 4 J J=Energy of ( 4 e 4 ) Cse sudy of Jnury 7, 003 Forecs verificion, UC Jnury 8, 003 CMC nlysis Glol-GEM 4hr operionl forecs Se Level Pressure (4 hp) Monrél (CANADA) 3.
4 Cse sudy Glol sensiiviy funcion Iniil emperure correcions for he UC Jnury 7, 003 nlysis s 700hP Correcions responsile for he forecs improvemen of he Cndin Mriimes sysem nd cross secion of iniil emperure correcion mde long he rrow. Modelling ckground-error covrinces using sensiiviies he dped 3D-Vr (Hello nd Bouier, 00) Srucure funcions defined wih respec o poseriori sensiiviies; Flow dependen srucure funcions were inroduced in he 3D-Vr; ~ B ξ ~ I B I ~~ vv Error vrince long v: σ Does flow-dependen ckground error formulion improve he nlysis nd susequen forecs? (Lupu 006) Monrél (CANADA) 4.
5 Impc of he dped 3D-Vr in he nlysis 700hP Difference eween he emperure nlysis incremens for UC Jnury 7, 003 nlysis 3D dped -3D sndrd nd cross secion. Cse sudy Forecs improvemen Energy (ol) of he forecs error verge over Norhern Hemisphere Er-ropics (5N - 90N) Glol-GEM operionl forecs Ene ergy (J/Kg) Glol-GEM dped forecs Glol-GEM sensiiviy forecs Forecs hour Monrél (CANADA) 5.
6 Fi o he oservionl D Do he correcions decrese or increse he deprure eween he nlysis nd he oservions? Δ J o, J o( ) J o( 3DVr J ( ) o 3DVr ) > 0 = increse < 0 = decrese Difference reliv ve en Jo (%) - Sensiiviy nlysis Difference relive e en Jo (%) - Adped 3D-Vr nlysis RAOB AIREP SURFC AOV SAWIND OAL RAOB AIREP SURFC AOV SAWIND OAL Fi o he oservionl D Posiive vlues men h he sensiiviy nlysis is furher wy from he os. hn he iniil nlysis (sme conclusions from ECMWF, Isksen e l., 004); Negive vlues men h he dped 3D-Vr nlysis is closer o he os. (due o he increse ckground-error vrince); Difference reliv ve en Jo (%) - Sensiiviy nlysis Difference relive e en Jo (%) - Adped 3D-Vr nlysis RAOB AIREP SURFC AOV SAWIND OAL RAOB AIREP SURFC AOV SAWIND OAL Monrél (CANADA) 6.
7 Oserviliy of flow-dependen srucures Adped 3D-Vr for which he srucure funcions where defined y normlizing he poseriori sensiiviy funcion Consider he cse where B vv nd he nlysis incremen is hen δ Ky H Kd αv wih ( Hv) R d σ C σ ( Hv) R ( Hv) σ C nd C ( Hv) R d C ( Hv) R ( Hv) Oserviliy of srucure funcion Correlion eween he innovions nd srucure funcion ρ ( Hv ) R d C / / ( Hv) R ( Hv) d R d / (CJ o(0 )) his defines he oserviliy of srucure funcions * Cn he oservions deec given srucure funcion Monrél (CANADA) 7.
8 Monrél (CANADA) 8. Emple from D-Vr eperimens Consider he following siuion v v 0 v o o Hv y y H y d Oservion error ( o ) nd innovion (d) Signl nd noise Hv R Hv R Hv o C C Signl nd noise Oservions re genered from he rue srucure funcion
9 Impc of oservion error y' ( Hv) N os. ρ 0 os os os y' ( Hv) o = ε o 0 os os os. 0.4 y' ( Hv) o =4 ε o 0 os os os Eperimen wih shifed funcion Monrél (CANADA) 9.
10 Preliminry es: does i work? Normlized nlysis incremen of 3D-Vr s srucure funcion * Limiing cse where B = vv * Does he dped 3D-Vr recover he righ mpliude * his priculr choice insures h we hve srucure h cn fi he oservions. Oserviliy for he es cse Os. ype Jnury 7, 003 Correlion coefficien Jnury 06, 003 Ferury 06, 00 Jnury 9, 00 RAOB AIREP AMV SURFC AOVS OAL Monrél (CANADA) 0.
11 Eperimens wih n dped 3D-Vr A poseriori sensiiviies depend on * rge re * Norm used o mesure he forecs error * Iniil norm * Definiion of he ngen-liner nd djoin model Eperimens wih n dped 3D-Vr sed on EC s 3D-Vr ssimilion * Dry energy norm * Four cses documened in Cron e l. (007): Jnury 9, 00, 00UC, Feurry 6, 00, 00UC Jnury 6, 003 UC; Jnury 7, 003 UC * rge re: glol, hemispheric (5-90N) nd locl (re on he Es Cos of Norh Americ) * Imposiion of nonliner lnce consrin (Cron e l., 007) Oserviliy of differen srucure funcions sed on key nlyses Srucure funcions Os. ype Jnury 7, 003, correlion coefficien Jnury 06, 003 Ferury 06, 00 Jnury 9, 00 GLOBAL RAOB AIREP AOVS OAL LOCAL RAOB AIREP AOVS OAL HEMISPHERIC RAOB AIREP AOVS OAL PV-BAL RAOB AIREP AOVS OAL Monrél (CANADA).
12 Oserviliy of pseudo-inverse oined from finie numer of singulr vecors (Mhidji e l., 007) Leding singulr vecors re he srucures h will grow he mos rpidly over finie period of ime * Leding 60 SVs were compued sed on ol dry energy norm led ime of 48-h * he forecs error is projeced ono hose SVs he finl ime which llows o epress he error iniil ime h eplins h forecs error (pseudo-inverse) Eperimens * 8 cses were considered in Decemer 007 * Are hose srucures oservle from ville oservions? * Oserviliy of SV, he leding singulr vecors * Oserviliy of he pseudo-inverse Oserviliy of he leding singulr vecor nd pseudoinverse De Os. ype SV no. Iniil ime Correlion coefficien SV no. Finl ime Pseudo-inverse OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL OAL Monrél (CANADA).
13 Conclusions Oserviliy of srucure funcions hs een defined in oservion spce s correlion eween innovions nd he srucure funcion Such srucures will grow he mos or grow o correc he forecs error given led ime * A poseriori sensiiviies re no well correled wih oservions his hs een esed for differen wys o compue he sensiiviies * Singulr vecors were no found o e oservle eiher Reduced rnk Klmn filers sed on singulr vecors do no seem o e pproprie o represen he ckground error covrinces in n ssimilion sysem Evolved covrinces s esimed wih n Ensemle Klmn filer would e more pproprie for n hyrid 4D-Vr ssimilion (Buehner e l., 00) Monrél (CANADA) 3.
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