A Posteriori Diagnostics of the Impact of Observations on the AROME- France Convective-Scale Data-Assimilation System.

Transcription

1 A Posteriori Dignostics of the Impct of Observtions on the AROME- Frnce Convective-Scle Dt-Assimiltion System. Pierre Brousseu, Gérld Desroziers nd Frnçois Bouttier CNRM-GAME, CNRS nd Météo-Frnce, Toulouse, Frnce. AROME-Frnce is n opertionl convective-scle Numericl Wether Prediction system tht uses 3D-Vr Dt Assimiltion (DA) scheme in 3-h continuous ssimiltion cycle in order to determine its initil conditions t the horizontl resolution of the model (2.5 km). In ddition to conventionl nd stellite observtions, regionl high-resolution observtions re ssimilted, such s, screen-level observtions, totl zenith delys from ground bsed GPS sttions nd rdr mesurements (rdil winds nd reflectivities). The impct of the vrious observtion types on AROME-Frnce nlyses is ssessed using n posteriori dignostic, the reduction of the estimtion error vrince. It cn be shown tht, if observtion nd bckground error covrince mtrices re well specified in vritionl DA system, the nlysis error covrince mtrix is given by A = B KHB where B, K nd H respectively stnd for the ssumed bckground error covrince mtrix, the Klmn gin mtrix nd the linerized observtion opertor. The totl vrince reduction provided by the ssimiltion of the observtion r=tr(b)-tr(a) = Tr(KHB) is mesurement of the bility of DA system to pull the nlysis from the bckground with respect to the observtions (Tr stnds for the trce of mtrix). A direct estimte of the vrince reduction Tr(KHB) is not possible in prctice in n opertionl vritionl DA system, since neither B nor K re explicitly known. Then, the vrince reduction which llows one to investigte observtion impct depending on the control vrible field, model levels, dte, nlysis time, nd sptil scles considered, nd the contributions of the different observtion types, re estimted in the AROME-Frnce DA system with rndomiztion method ([1],[2]). The observtions with the lrgest impct in the AROME-Frnce 3D-Vr system re given by ircrft (for temperture nd wind fields) nd rdr (specific humidity nd wind fields) observtions in the middle nd high troposphere, in ccordnce with the verticl distribution of these observtions. Screen-level mesurements (2 m temperture, 2 m reltive humidity nd 10 m wind) re the min contributors t the lowest tmospheric levels. These lrge impct vlues re explined by the number of these observtions ssimilted t ech nlysis time. On riny dy, ircrft, rdr nd screen-level observtions ccount for respectively 22%, 30% nd 18% of the totl ccount of ssimilted observtions. One cn note tht it is possible to evlute the impct of n observtion of given physicl quntity (resp. t given model level) on the nlyzed field of n other physicl quntity (resp. on other levels) through the B mtrix cross- (resp. verticl) correltions. The totl vrince nd the different observtion contributions re lso evluted depending on the sptil scle of the nlyzed fields: most of vrince reduction concerns length scles bove 100 km with mximum round km. Only the rdr mesurements, with n horizontl density of 15 km, contribute to the vrince reduction t scles lower thn 100 km. References [1] Brousseu et l. "A posteriori dignostics of the impct of observtions on the AROME- Frnce convective-scle dt-ssimiltion system." Q. J. Roy. Meteor. Soc., 2013 ccepted. [2] Brousseu et l. "Evlution of dt impct in the mesoscle AROME 3D-Vr system t Météo-Frnce. In Interntionl Symposium On Dt Assimiltion, Offenbch, Germny, October 2012 :

2 Impct on the Use of Different Error Objective Function on the Forecst Sensitivity to Observtion Dignostic Tool Crl Crdinli ECMWF Over the yers, dt ssimiltion nd forecst schemes hve evolved towrds very complicted systems such s the four-dimensionl vritionl ECMWF system. The system hndles lrge vriety of both spce- nd surfce-bsed meteorologicl observtions. It combines the observtions with prior (or short-rnge forecst) informtion of the tmospheric stte nd lso uses comprehensive linerized forecst model to ensure tht the observtions re given dynmiclly nd sttisticlly likely response. Anlysis nd forecst models re therefore blended into single numericl wether prediction system. Efficient monitoring of such complex system, with the order of 10 9 degrees of freedom nd more thn 10 7 observtions is necessity. Recently, djoint method hs been used to evlute the impct of the observtions on the short-rnge forecst nd more generlly, forecst error sensitivity is used s performnce monitor tool. The forecst error reduction due to prticulr mesurement or collectively to specific instrument or dt type is clculted with respect to globl forecst error objective function, typiclly, the energy norm. In this pper the impct on the forecst error reduction from the ssimilted observtions of different error cost function is presented nd discussed.

3 Adjoint Estimtion of the Forecst Impct of Observtion Error Correltions Derived from A Posteriori Covrince Dignosis Dcin N. Descu nd Rolf H. Lnglnd b Portlnd Stte University, Portlnd, Oregon, U.S.A., descu@pdx.edu, b Nvl Reserch Lbortory, Mrine Meteorology Division, Monterey, Cliforni, U.S.A. A posteriori error covrince consistency studies indicte tht both sptil nd interchnnel error correltions re present in the rdinces ssimilted from hyperspectrl sounders [1]. An open reserch question is to ssess whether modeling the observtion error correltions in the dt ssimiltion system (DAS) will entil substntil improvements in the model forecst skill. This tlk presents prcticl pproch to provide guidnce on the forecst impct of n error covrince model prior to its ctul implementtion in the DAS. A synergistic frmework is considered tht combines the computtionl efficiency of the posteriori covrince dignosis estimtes with the comprehensive mount of derivtive informtion extrcted from the djoint- DAS observtion error covrince sensitivity (R-sensitivity). This pproch extends our work [2] to the observtion error correltion structures. An estimte Ř of the observtion error covrince is obtined from the sttisticl nlysis of the observtion residuls [3]; subsequently, the djoint- DAS R-sensitivity evluted in the sttus quo DAS is used to obtin first-order ssessment of the forecst error impct induced by the vrition δr=ř R in the error covrince specifiction. Theoreticl spects re discussed nd proof-of-concept to covrince dignosis nd impct estimtion is provided in idelized experiments with simple Lorenz-40 vrible model. The prcticl pplicbility of the proposed methodology is shown with the djoint versions of the Nvl Reserch Lbortory Atmospheric Vritionl Dt Assimiltion System-Accelerted Representer (NAVDAS-AR) nd the Nvy Opertionl Globl Atmospheric Prediction System (NOGAPS). Estimtes of sptil nd interchnnel error correltions derived from n posteriori dignosis re presented for AIRS nd IASI rdinces; priori first-order estimtes to the forecst error impct re obtined from the djoint-das derivtive informtion. Our preliminry nlysis indictes tht n incresed benefit to the forecsts my be obtined by modeling the error correltions, s compred with covrince tuning procedures tht ignore the correltion structures nd djust only the ssigned observtion error vrince prmeters. References [1] N. Bormnn, A. Collrd, P. Buer, Estimtes of sptil nd interchnnel observtion-error chrcteristics for current sounder rdinces for numericl wether prediction. II: pplictions to AIRS nd IASI dt. Q.J.R. Meteorol. Soc. 136: , April [2] D.N. Descu, R.H. Lnglnd, Error covrince sensitivity nd impct estimtion with djoint 4D-Vr: theoreticl spects nd first pplictions to NAVDAS-AR. Q.J.R. Meteorol. Soc.139: , Jnury [3] G. Desroziers, L. Berre, B. Chpnik, P. Poli, Dignosis of observtion-, bckground- nd nlysis-error sttistics in observtion spce. Q.J.R. Meteorol. Soc. 131: , 2005, doi: /qj

4 Development, Vlidtion, nd Applictions of OSSEs t NASA s Globl Modeling nd Assimiltion Office Ronld M. Errico,b nd Nikki C. Privé,,b GESTAR, Morgn Stte University, U. S.A., ronld.m.errico@ns.gov, b GMAO, NASA, U. S. A. Well-designed OSSEs cn be very informtive since they re not restricted by presently existing observtion types nd the simulted truth is precisely known, both properties being consequence of the simulted context of the experiments. Although most often motivted by the first property, the second cn lso be exploited to better understnd the behvior of dt ssimiltion systems. Essentilly, nlysis nd bckground error cn be explicitly clculted without invoking questionble ssumptions bout their chrcter. Another consequence of this simulted context, however, is tht wht is lerned from the OSSE only pplies to the ssimiltion of rel observtions to the degree tht the OSSE is relistic. Vlidtion of ny OSSE frmework using vriety of metrics is therefore criticl to its useful pplictions. The OSSE frmework recently developed t the GMAO hs been vlidted using severl informtive metrics tht hve not been exmined in previous OSSEs. These include sttistics of innovtions (both vrinces nd correltions), nlysis increments, observtion impcts (estimted using model nd dt ssimiltion djoints), nd forecst errors. It ws reltively esy to mtch innovtion vrinces by dding rndom errors to the observtions, but in order to mtch innovtion correltions nd nlysis increment vrinces, these errors hd to be chnnel or sptilly correlted. For most observtion types, tuning of these errors ws firly esy. After presenting smple of vlidtion results, ppliction of the OSSE to estimte nlysis nd bckground error chrcteristics will be presented. This will include direct clcultion of error vrinces nd sptil correltions, error spectr, nd the percentges tht bckground errors re reduced during the ssimiltion of observtions. A typicl vlue of the ltter for most fields t most loctions is only 10-20%, s cn be expected from theoreticl considertion of the Klmn filter. Error reductions primrily occur t synoptic scles (sphericl hrmonic wve-number n<30). The divergent wind is reltively poorly nlyzed t most verticl levels nd horizontl scles. Horizontl nd verticl scles of bckground error correltions re very different thn wht is estimted using the NMC method; i.e., using sttistics of 48 minus 24-hour forecst errors verifying t the sme time s proxies for bckground error sttistics. The usul dry, forecst skill metrics in the OSSE context re rther insensitive to resonble rnge of observtion error chrcteristics, rendering it difficult to tune the OSSEs relism regrding such metrics. This is prtly due to the influence of model error on forecst error but lso due to the effectiveness of present dt ssimiltion lgorithms t filtering observtion errors. Most pplictions of the GMAO OSSE thus fr hve concerned its id in understnding the behvior of the dt ssimiltion system by vlidting ginst truth itself. Results from some dditionl studies of this kind will be presented s well s plns for the future.

5 Improving Ensemble-bsed Observtion Impct Estimte using Group Filter Technique Nichols A. Gsperoni,b,c nd Xugung Wng,b School of Meteorology, University of Oklhom, Normn, OK 73072, USA b Center for Anlysis nd Prediction of Storms, Normn, OK 73072, USA c ngspero@ou.edu An ensemble-bsed observtion impct estimte [3] is strightforwrd to be pplied for ensemble dt ssimiltion systems. However, due to reltively smll ensemble sizes compred to the lrge number of degrees of freedom in models, it is necessry to pply locliztion techniques to obtin ccurte estimtes. Fixed locliztion techniques do not gurntee ccurte impct estimtes, becuse s forecst time increses the error correltion structures evolve nd move with the flow. For longer led times, we should expect the optiml locliztion function to be shifted downstrem from the observtion nd be spred by vrious model flow dependencies. Klny et l. [3] showed improvements in the ccurcy of the impct estimte by employing timedependent displcement term to Gspri-Cohn locliztion function. The gol of this study is to explore methods to improve the observtion impct estimte by improving the method of locliztion. Our experiments use the LETKF together with two-lyer primitive eqution model nd simulted observtions s in Hollnd nd Wng [2]. We employ Monte Crlo group filter technique developed by Anderson [1] to limit the effects of smpling error. For ech group of ensemble members, regression coefficient, β, is clculted between the nlysis nd forecst of some length. Then regression confidence fctor (RCF) is computed to minimize expected RMS differences between smple β s. An envelope of RCF vlues is then pplied to the observtion impct estimte. Our results hve shown tht the shpe, loction, timedependency nd vrible-dependency of the locliztion function is consistent with underlying dynmicl process of the model. Results of pplying the RCF on observtion impct estimte will be presented in the symposium. References [1] Anderson, J. Exploring the need for locliztion in ensemble dt ssimiltion using hierrchicl ensemble filter. Physic D, vol. 230, pp , June Avilble t: < [2] Hollnd, B. nd Wng, X. Effects of sequentil or simultneous ssimiltion of observtions nd locliztion methods on the performnce of the ensemble Klmn filter. Q.J.R. Meteorol. Soc., vol. 139, no. 672, pp , Apr Avilble t: < [3] Klny, E., Ot, Y., Miyoshi, T., nd Liu, J. A simpler formultion of forecst sensitivity to observtions: ppliction to ensemble Klmn filters. Tellus A, vol. 64, Oct Avilble t: <

6 Scling of GNSS Rdio Occulttion Impct with Observtion Number Using n Ensemble of Dt Assimiltions Florin Hrnisch,b, Sen Hely, Peter Buer nd Stephen English Europen Centre for Medium-Rnge Wether Forecsts, United Kingdom, Sen.Hely@ecmwf.int, b now t: Hns-Ertel-Centre for Wether Reserch, Dt Assimiltion Brnch, LMU München, Germny. Globl Nvigtion Stellite System Rdio Occulttion (GNSS-RO) mesurements re n importnt component of the current Globl Observing System (GOS) used for Numericl Wether Prediction (NWP). Currently, bout 2,000 bending ngle profiles per dy re ssimilted, nd these ccount for round 2 3 % of the totl number of observtions ssimilted t ECMWF. The GNSS-RO mesurements hve sttisticlly significnt positive impct on the nlysis nd forecst ccurcy, prticulrly in res with significnt model bises. There is no indiction of sturtion of forecst impct with the current GNSS-RO observtion numbers, but there is very little guidnce on where this effect might occur. This presenttion will discuss results of study which ims to estimte the optiml number of GNSS-RO mesurements required for NWP. The impct s function of observtion number is nlysed using simulted GNSS-RO observtions. The study is bsed on Ensemble of Dt Assimiltions (EDA) pproch using ten ensemble members. The EDA system provides sttisticl estimte of the nlysis nd short-rnge forecst uncertinty of the NWP system, bsed on the spred of the ensemble members. A set of EDA experiments is performed with different numbers of simulted GNSS-RO profiles, rnging from 2000 to profiles per dy, in ddition to the rel conventionl nd stellite observtions ssimilted opertionlly. The use of the EDA pproch for estimting observtion impct will be discussed. It is shown tht the impct of GNSS-RO profiles per dy in the upper tropospheric nd lower strtospheric tempertures is clerly not sturted, bsed on the behviour of the ensemble spred s function of observtion number.

7 Inclusion of linerized moist physics in NASA's Goddrd Erth Observing System Dt Assimiltion Tools Dniel Holdwy,b, Ronld Errico,c, nd Ronld Gelro Globl Modeling nd Assimiltion Office, NASA Goddrd Spce Flight Center, MD, USA. b Goddrd Erth Sciences Technology nd Reserch, Universities Spce Reserch Assocition, MD, USA. c Goddrd Erth Sciences Technology nd Reserch, Morgn Stte University, MD, USA. Inclusion of moist physics in the linerized version of wether forecst model is beneficil in terms of vritionl dt ssimiltion. Further it improves the cpbility of importnt monitoring nd reserch tools, such s djoint bsed observtion impcts nd sensitivity studies. A linerized version of the Relxed Arkw-Schubert (RAS) convection scheme hs been developed nd tested in NASA's Goddrd Erth Observing System (GEOS) dt ssimiltion tools. A previous study of the nonliner RAS scheme showed it to exhibit resonble degree of linerity nd stbility. This motivtes the development of lineriztion of version of the RAS scheme tht hs only minor modifictions to the lgorithm. Linerized lrge scle condenstion is included through simple scheme tht converts super sturtion into precipittion. The lineriztion of moist physics is vlidted ginst the full nonliner model for 6-hour nd 24-hour intervls, which re relevnt to vritionl dt ssimiltion nd observtion impcts respectively. For smll number of profiles sudden lrge growth in the perturbtion trjectory is encountered. Efficient filtering of these profiles is chieved though the dignosis of steep grdients in reduced version of the opertor of the tngent liner model. With filtering turned on, the inclusion of linerized moist physics increses the correltion between the nonliner perturbtion trjectory nd the liner pproximtion of the perturbtion trjectory. A month long observtion impct experiment is performed nd the effect of including moist physics on the impcts is discussed. Impcts from moist sensitive instruments nd chnnels re incresed. Discussion is presented on the inclusion of moisture in the error metric. The effect of including moist physics is exmined for djoint sensitivity studies. A cse study exmining n intensifying northern hemisphere Atlntic storm over 24-hour period is presented. The results suggest tht in regions of ctive moist physics the mgnitude of the sensitivity with respect to moisture is equivlent to the sensitivity with respect to other model vribles. Results from updting the observtion opertor with the new linerized moist physics re shown.

8 Observtion Impct on Tropicl Cyclone Forecsts: An Adjoint Approch Brett T. Hoover, Chris S. Velden b, nd Rolf H. Lnglnd c Coopertive Institute for Meteorologicl Stellite Studies, University of Wisconsin - Mdison, USA, bthoover@wisc.edu, b Coopertive Institute for Meteorologicl Stellite Studies, University of Wisconsin - Mdison, USA, c Nvl Reserch Lbortory, USA. Using the djoints of the dt ssimiltion system nd NWP forecst model, the impct of individul observtions cn be estimted for some function of the model forecst stte. The Nvy currently uses this technique to ssess the impct of observtions on the 24-hour forecst s mesured by globl energy-bsed error norm [1]. In this study, this system is dopted for monitoring the impct of observtions on the 24-hour tropicl cyclone (TC) forecst for selected cses in the 2012 hurricne seson, by restricting the verifying re over the loction of the TC nd dopting TC intensity response function rther thn n energy-bsed error norm costfunction. An exmintion of observtion impct on TC forecsts indictes tht very smll minority of high-impct observtions within the TC s environment is responsible for the bulk of the impct on TC intensity, following power-lw-like distribution. This is in strk contrst to the observtion impct on the globl error norm, which is contributed to mostly by the integrted impct of mny low-impct observtions, while high-impct observtions contribute little overll. In ddition, the reltive importnce of vrious observing systems to TC intensity cn vry strongly from forecst to forecst, bsed on the context of the TC s environment. For exmple, lnd observtions cn be of reltively low importnce compred to stellite-derived winds while the TC is remote from lnd, but this reltionship cn shift drmticlly s the TC pproches lndfll. References [1] R. H. Lnglnd nd N. L. Bker. Estimtion of observtion impct using the NRL tmospheric vritionl dt ssimiltion djoint system. Tellus, 56A, pp , April (Journl Article)

9 Comprison of Met Office nd ECMWF Bckground Fields with Conventionl Observtions Bruce Ingleby, Lrs Isksen b, nd Mohmed Dhoui b Wether Science, Met Office, UK, bruce.ingleby@metoffice.gov.uk, b Dt Division, ECMWF, UK Met Office nd ECMWF bckground fields (short rnge forecsts) of ner-surfce temperture, humidity nd wind hve been compred with in situ observtions, especilly lnd surfce reports. The 10 meter forecst wind speeds from both centers re slightly stronger thn the reported wind speeds, especilly t night. The night-time bis is known issue in tht forecst models hve too much mixing under stble conditions [1]. In both models the wind speed bises re prticulrly lrge over the Indin sub-continent, this could be due to the roughness lengths used nd/or to observtionl errors. The results for temperture nd humidity show less consistency between the models: overll the Met Office forecsts pper slightly too wet nd the ECMWF forecsts slightly too dry - probbly relted to bises in precipittion [2]. The Met Office forecsts show moist bis in the Northern Hemisphere spring - this moves northwrds s spring progresses nd ppers to be relted to snow-melt being few weeks erly in this model. Temperture bises vry by region nd seson; both models re slightly too wrm over the North Americn Gret Plins (nd to some extent Siberi) in summer. This my be due to the lck of propgtion of convective storms triggered by the Rockies [3], but griculturl irrigtion (not represented in the models) my lso ply prt. The dependence of bises on the proximity of the costline hs lso been exmined, in the Met Office model the trnsition zone for wind seems slightly too wide [4]. Representtion of ner surfce conditions in globl forecst models hs improved in recent yers due to incresed resolution nd improvements to soil, boundry lyer nd cloud prmeteriztion. At the Met Office ssimiltion of most surfce temperture, humidity nd wind observtions hs lso mde some improvements [5]. The remining bises between bckground fields nd observtions often provide vluble insight into model errors, but observtion nd representtivity errors lso hve to be borne in mind. Met Office nlysis increments show humidity bises peking round the top of the boundry lyer [6]. References [1] Sndu, I., A. Beljrs, P. Bechtold, T. Muritsen, nd G. Blsmo, 2013: Why is it so difficult to represent stbly strtified conditions in numericl wether prediction (NWP) models?, J. Adv. Model. Erth Syst., 5, doi: /jme [2] Hiden, T, MJ Rodwell, DS Richrdson, A Okgki, T Robinson, T Hewson, 2012: Intercomprison of Globl Model Precipittion Forecst Skill in 2010/11 Using the SEEPS Score. Mon. We. Rev., 140, doi: [3] Klein, S. A., X. Jing, J. Boyle, S. Mlyshev, nd S. Xie (2006), Dignosis of the summertime wrm nd dry bis over the U.S. Southern Gret Plins in the GFDL climte model using wether forecsting pproch, Geophys. Res. Lett., 33, L18805, doi: /2006gl [4] Ingleby, B., 2010: Fctors Affecting Ship nd Buoy Dt Qulity: A Dt Assimiltion Perspective. J. Atmos. Ocenic Technol., 27, doi: [5] Ingleby, B., 2013: Globl ssimiltion of ir temperture, humidity, wind nd pressure from surfce sttions. (In preprtion) [6] Ingleby, B., A. C. Lorenc, K. Ngn, F. Rwlins nd D. R. Jckson, 2012: Improved vritionl nlyses using nonliner humidity control vrible. Q.J.R. Meteorol. Soc.. doi: /qj.2073

10 Ensemble Forecst Sensitivity to Observtions: Applictions for Proctive Qulity Control Eugeni Klny, Yoichiro Ot b, Disuke Hott c nd Tkems Miyoshi d AOSC, University of Mrylnd, College Prk, MD USA, eklny@tmos.umd.edu, b NCEP, NWS/NOAA, College Prk, MD, USA, nd Jpn Meteorologicl Agency, Tokyo, Jpn, c AMSC, U. of Mrylnd, College Prk, MD, USA, nd Jpn Meteorologicl Agency, Tokyo, Jpn, d University of Mrylnd, College Prk, MD nd RIKEN Advnced Institute for Computtionl Science, Kobe, Jpn A new formultion of the Ensemble Forecst Sensitivity to Observtions (EFSO, Klny et l., Tellus, 2012) is more ccurte nd efficient thn the originl ensemble sensitivity formultion of Liu nd Klny, (2008), nd cn be pplied to the EnSRF used in the NCEP hybrid. Ot et l. (2013, Tellus, under review) pplied EFSO to the GFS coupled with the opertionl EnSRF used t NCEP, nd ssimilted ll the observtions used opertionlly during one month, fter one week of spin-up. In ddition to obtining the verge forecst sensitivity to different observing systems, Ot et l. (2013) developed new pproch to identify regionl "24hr forecst skill dropouts" rther thn the usul 5 dys used t NCEP to define skill dropout. 24hr forecst skill dropouts were identified regionlly when two conditions were stisfied: the 24hr RMS forecst error ws t lest twice s lrge s the verge RMS error for the region, nd the 24hr forecst error ws lrger thn the 36hr error by t lest 20%. Seven cses of 24hr regionl forecst skill dropout were identified during tht month, s well s the observtions tht hd regionl negtive impct, nd denying these observtions reduced the forecst error in every cse identified. The cse with lrgest impct corresponded to problem with MODIS polr winds tht occurred in two contiguous regions. The estimted negtive impct using this method ws shown to be very similr in mplitude nd shpe to the impct obtined with repetition of the experiment without using the MODIS winds. Denying these observtions reduced the regionl forecst error by lmost 40%. We will explore whether this pproch cn be used to provide proctive QC tool nd will present the results t the WMO DA conference. The method will be used to estimte the occurrence of lrge 12hr skill dropouts with the GFS coupled with the LETKF. If successful, this method would hve importnt properties tht cn improve opertionl forecsts: ) The dt ssimiltion in the opertionl system cn be repeted without the identified flwed observtions soon fter rel time; b) The detiled dignostics on the flwed observtions obtined with this method cn help the developers of the instrument lgorithms to identify the origin of the observtionl flws nd correct them. References Klny, E., Y. Ot, T. Miyoshi nd J. Liu, 2012: A simpler formultion of forecst sensitivity to observtions: ppliction to ensemble Klmn filters. Tellus, 64A, 18462, Liu, J. nd Klny, E Estimting observtion impct without djoint model in n ensemble Klmn filter. Qurt. J. Roy. Meteor. Soc., 134, Ot, Y., J. Derber, T. Miyoshi nd E. Klny, 2013: Ensemble-bsed observtion impct estimtes using the NCEP GFS. Tellus, under revision. th

11 Investigtion of Model Covrince with Low-Order Dynmics John M. Lewis, S. Lkshmivrhn b, nd Willim Bourke c Ntionl Severe Storms Lbortory, Normn, OK, 73072, nd Desert Reserch Institute, Reno, NV, 89512, jlewis@dri.edu; b School of Computer Science, University of Oklhom, Normn, OK, 73072; c Middle Prk, Vic 3206, Austrli. Knowledge of dynmicl model s covrince is criticlly importnt element of Byesin dt ssimiltion s prcticed t opertionl wether prediction centers worldwide. This covrince is controlled by uncertinty in initil conditions nd forcing s well s the effect of overll model formultion deficiencies. When these uncertinties re combined with covrince of observtions, the optiml posteriori stte of the system cn be determined. This estimted stte improves the link between existing ensembles of dt ssimiltion nd ssessment of lterntive methods for creting initil conditions [1]. There re three wys to obtin model s covrince: (1) stochstic dynmic prediction (SDP) tht delivers the moments of the probbility density function (pdf), (2) Monte Crlo methods tht generte the covrince through series of forecsts stemming from rndom body of initil sttes nd rndom perturbtions to the prmeteriztion schemes, nd (3) solution to Liouville s eqution tht yields the exct pdf nd therefore the exct covrince through continuity of probbility principle. The determintion of model s covrince is explored through use of Pltzmn s low-order spectrl model of nonliner dvection [2] where uncertinty in initil conditions nd forcing is considered. The consequence of inexct model covrince on optiml sequentil Byesin ssimiltion becomes the focus of the investigtion. For the 2-mode system with uncertinty in initil conditions lone, n nlytic solution to the governing dynmics cn be found nd used to solve Liouville s eqution by the method of chrcteristics. Higher-mode systems re considered for explortion of covrince error due to both initil conditions nd forcing. In the bsence of n nlytic solution for this cse, Liouville s eqution is solved by numericl methods. [1] Europen Centre for Medium Rnge Wether Forecsts (ECMWF), Newsletter No. 134 Winter 2012/13. [2] Pltzmn, G. W., 1964: An exct integrl of complete spectrl equtions for unstedy onedimensionl flow. Tellus, 16,

12 Ensemble-Vritionl Dt Assimiltion Methods Modelling nd Dignosis of Loclized Covrinces Andrew Lorenc, Neill Bowler, Adm Clyton, Dvid Firbirn, Jonthn Flowerdew, nd Stephen Pring. Wether Science, Met Office, UK. Most dt ssimiltion (DA) methods use covrinces to chrcterize the errors they re trying to correct. This enbles them to spred the informtion from scttered observtions to ll the vribles needed to define the nlysis nd strt forecst. In the ensemble Klmn filter (EnKF) the covrinces come from n ensemble of forecsts, giving estimtes which reflect both the meteorologicl sitution, nd the recent observing network. In pplictions like numericl wether prediction (NWP), the ensemble hs to be very smll (O(100)) compred to the degrees of freedom to be nlyzed; the usul compenstion is to loclize the ensemble covrinces. Modern NWP models hve billions of degrees of freedom, so the effectiveness of locliztion t supplying the extr degrees of freedom while retining the rel feture in the ensemble covrince is key to the success of the DA lgorithm. Mny EnKF lgorithms directly loclize the error covrince between the observtion loctions nd model vribles; this constrins the design of locliztion methods. Vritionl (Vr) lgorithms on the other hnd mnipulte model fields, mking vilble opertors for differentition, vrible trnsform, blnce, scle-decomposition nd smoothing. Vr trditionlly uses time-verged climtologicl error covrince estimte, but, using n lph control vrible [6], loclised ensemble covrinces cn lso be used in Ensemble-Vritionl (EnVr) DA. A combintion of the two gives hybrid method. We explore the greter scope for sophisticted locliztion lgorithms within hybrid-envr. As well s the originl horizontl [4] nd verticl, locliztion cn be pplied between vribles, nd in spectrl spce [1]. 4DEnVr methods [5] directly use the 4D covrince from n ensemble of trjectories, so 4D-loclistion is lso pplied. On the other hnd hybrid-4d-vr [2] loclizes the 3D covrince nd gets the time-dimension from its liner nd djoint models. These methods hve ll been implemented s options in the Met Office s VAR system. This pper presents dignostics of the effect of vrious locliztion methods on the implied covrinces used. Trils of some of the DA systems re presented in compnion pper [3]. References [1] M. Buehner. Evlution of Sptil/Spectrl Covrince Locliztion Approch for Atmospheric Dt Assimiltion. Mon. We. Rev., 140, , [2] M. Clyton, A. C. Lorenc nd D. M. Brker 2012 Opertionl implementtion of hybrid ensemble/4d-vr globl dt ssimiltion system t the Met Office. Qurt. J. R. Met. Soc., to pper, 16pp, [3] J. Flowerdew, Stephen Pring, Peter Jermey, Andrew Lorenc, Neill Bowler, nd Eunjoo Lee Initil Trils of 4D-Ensemble-Vr for Dt Assimiltion nd Ensemble Initiliztion. 6 th WMO DA Symposium, submitted, [4] T. M. Hmill, J. S. Whitker nd C. Snyder. Distnce dependent filtering of bckground error covrince estimtes in n ensemble Klmn filter. Mon. We. Rev., 129, , [5] C. Liu, Q. Xio, B. Wng. An Ensemble-Bsed Four-Dimensionl Vritionl Dt Assimiltion Scheme. Prt II: Observing System Simultion Experiments with Advnced Reserch WRF (ARW). Mon. We. Rev., 137, , [6] A. C. Lorenc. The potentil of the Ensemble Klmn filter for NWP - comprison with 4D-Vr. Qurt. J. Roy. Met. Soc., 129, , 2003.

13 A Criticl Comprison of Methods to Assess Observtion Impct in NWP Cristin Lupu nd Anthony P. McNlly Stellite Section, Europen Centre for Medium-Rnge Wether Forecsts (ECMWF), United Kingdom, In numericl wether prediction the vlue of prticulr observing system cn be ssessed both in terms of its impct upon tmospheric nlyses nd forecsts. Understnding this impct llows the dt ssimiltion nd forecst system to be optimised to mke best use of the vilble observtions. The clssicl pproch is to perform Observing System Experiments (OSEs) where prticulr observtion is delibertely withheld (or dded) nd the qulity of the resulting nlyses nd forecsts compred to control system. However these re computtionlly very expensive to perform. Significntly less expensive mesures of impct of ssimilted observtions on nlysis or forecst cn be obtined from evlutions of degrees of freedom for signl (DFS), djoint-bsed methods nd the impct of given observing system upon the nlysis fit to other mesurements. This study tkes criticl look t the extent to which these different mesures of impct cn be considered consistent nd complementry to ech other.

14 Observtion Impct on Forecsts for led-times beyond 24 hours Rhul B. Mhjn b, Ronld Gelro b, nd Ricrdo Todling b Ok Ridge Associted Universities, TN, USA, rhul.mhjn@ns.gov, b Globl Modeling nd Assimiltion Office, NASA Goddrd Spce Flight Center, MD, USA. Observtion impct on forecsts evluted using djoint-bsed techniques (e.g. Lnglnd nd Bker, 2004) re limited by the vlidity of the ssumptions underlying the forecsting model djoint. Most pplictions of this pproch hve been restricted to deriving observtion impcts on 24-hour forecsts to sty well within lineriztion ssumptions. The most widely used mesure of observtion impct relies on the vilbility of the nlysis for verifying the corresponding 24-hour forecsts. As pointed out by Gelro et l. (2007), nd more recently by Todling (2013), this introduces undesirble correltions in the mesure tht re likely to ffect the resulting ssessment of the observing system. Stppers nd Brkmeijer (2012) introduced technique tht, in principle, llows extending the vlidity of tngent liner nd corresponding djoint models to longer ledtimes. The methodology provides the mens to better represent linerized models by mking use of Gussin qudrture reltions to hndle vrious underlying non-liner model trjectories. The formultion is exct for prticulr bi-liner dynmics; it corresponds to n pproximtion for generl-type nonlinerities nd must be tested for lrge tmospheric models. The present work investigtes the pproch of Stppers nd Brkmeijer in the context of NASA s Goddrd Erth Observing System Version 5 (GEOS-5) tmospheric dt ssimiltion system (ADAS). The gol is to clculte observtion impcts in the GEOS-5 ADAS for forecst led-times longer thn 24 hours, both to extend the estimte towrd the medium-rnge nd to reduce the potentil for undesirble correltions tht occur t shorter forecst led times. References [1] Lnglnd, R. H., nd N. L. Bker, 2004: Estimtion of observtion impct using the NRL tmospheric vritionl dt ssimiltion djoint system. Tellus, 56A, [2] Gelro, R., Y. Zhu, nd R. M. Errico, 2007: Exmintion of vrious-order djoint-bsed pproximtions of observtion impct. Meteoroloische Zeitschrift, 16, [3] Stppers, R. J. J., nd J. Brkmeijer, 2012: Optiml lineriztion trjectories for tngent liner models. Q. J. R. Meteorol. Soc., 138, [4] Todling, R. 2013: Compring two pproches for ssessing observtion impct. Mon. We. Rev., 141,

15 A posteriori dignostics in n ensemble of vritionl ssimiltions Y. Michel CNRM-GAME, Météo-Frnce nd CNRS, Toulouse, Frnce. Severl consistency dignostics hve been proposed to evlute vritionl ssimiltion schemes [4]. In prticulr, the vlue of the cost function should be close to its sttisticl expecttion tht is directly relted to the number of observtions in the system. This simple yet powerful dignostic hs been implemented by severl uthors, in prticulr with the purpose of tuning vrinces [1] nd testing hypothesis testing [3]. The im of this work is to extend those results to the covrinces of subprts of the bckground nd observtion cost functions, using stndrd theory of qudrtic forms in rndom vribles [2]. We will first show tht it is possible to derive expressions for the vrinces of subprts of the bckground nd observtion cost functions t the minimum, in the Gussin cse. It is possible to use these expressions for vrince tuning, s illustrted first in simplified vritionl scheme in one-dimensionl context. We then will prove tht bckground nd observtion cost functions t the minimum re sttisticlly wekly but positively correlted. Subprts of observtion cost functions with uncorrelted observtions errors re uncorrelted. This result might serve s bsis for testing for observtion error correltions, recurrent problem for stellite observtions. The expressions for the covrinces of subprts of the cost functions t the minimum involve computing the trce of lrge (nd unvilble) mtrices, which cn be computed using rndomized trce estimte. We will show how to compute them in the ensemble of vritionl ssimiltions with perturbed observtions implemented opertionlly t Météo-Frnce [1]. The Gussin hypothesis will lso be discussed, by pplying univrite normlity tests to n experiment designed with lrger number of ssimiltions. References [1] G. Desroziers, L. Berre, V. Chbot, B. Chpnik: A Posteriori Dignostics in n Ensemble of Perturbed Anlyses. Mon. We. Rev., 137, , 2009 (Journl Article) [2] A.M. Mthi nd S.B. Provost, Qudrtic Forms in Rndom Vribles: Theory nd Applictions, Mrcel Dekker, New York, 1992 (Book) [3] J.C. Muccino, N.F. Hubele, A.F. Bennett: Significnce testing for vritionl ssimiltion. Q.J.R. Meteorol. Soc., 130, , (Journl Article) [4] O. Tlgrnd: Evlution of Assimiltion Algorithms. In Dt Assimiltion: Mking Sense of Observtions, Edts. W. Lhoz, B. Khtttov, R. Menrd, , 2010 (Book)

16 Opertionl Ensemble Klmn Filter Forecsts For Use in Wind Power Forecsting Edwrd Ntenberg, John Zck, nd John Mnobinco MESO Inc., 185 Jordn Rod, Troy, NY 12180, USA Regionl electricl blncing uthorities nd independent wind frm opertors rely on wind power forecsts to estimte the mount of wind energy genertion during the current nd next operting dy. Becuse power genertion is relted to the wind speed cubed, smll chnges in wind speeds cn cuse lrge chnges in power production. Lrge increses or decreses in wind power production, lso known s rmp events, cn impct the blncing of genertion nd demnd, often requiring system opertors to disptch reserve resources. Rmp events cn be triggered by number of meteorologicl phenomenon including cold fronts, low level jets, thunderstorm outflow boundries nd chnges in verticl stbility. Grid nd wind frm opertors require both ccurte short term nd dy-hed forecsts of power production to determine how much wind genertion is vilble to meet current nd forecsted system demnd. In this study, n ensemble forecst system is used to produce wind power forecsts for severl regions in North Americ. Informtion from the ensemble men, spred, nd the member closest to the ensemble men re used generte probbilistic nd deterministic rel-time forecsts. The ensemble, composed of 24 Wether nd Reserch Forecsting members, is run with two nested domins of 51 nd 17 km twice dy for 84 hours. The outer domin extends 12,000 km covering most of North Americ, with the inner domin covering the lower 48 sttes, southern Cnd nd northern Mexico. Perturbed Globl Forecst Systems (GFS) forecsts re used s boundry conditions for ech of the individul ensemble members. Dt ssimiltion is pplied to ech member by using the Dt Assimiltion Reserch Tested (DART) Ensemble Klmn Filter (EnKF) [1] to crete n updted set of initil conditions for ech ensemble member. This configurtion of the EnKF ssimiltes lnd surfce, buoy, ship, stellite winds, rdiosondes, nd profiler observtions. The ensemble ssimiltion performnce cn be exmined by plotting the ensemble spred, nlysis increment, nd covrince infltion. Additionlly, deterministic forecst performnce t ech wind frm loction cn be monitored by compring the ensemble power genertion forecst to the observed power genertion. Probbilistic forecsts will lso be generted using model vribles from the ensemble men or member closest to the men s well s the ensemble spred. The performnce of probbilistic nd deterministic forecsts during severl high impct rmp events will be detiled. Additionlly, the sensitivity of the forecst performnce to regionl profiler observtions will be exmined through the use of n ensemble sensitivity nlysis (ESA) [2]. To vlidte the ESA methodology, profiler observtions in the regions of high forecst sensitivity will be ssimilted nd the improvement in forecst performnce will be clculted. The conference presenttion will highlight the deterministic nd probbilistic forecst results during the rmp events. References [1] Anderson, J. L., "Sptilly nd temporlly vrying dptive covrince infltion for ensemble filters," Tellus, A, 61, pp , [2]Torn, Ryn D., Gregory J. Hkim,. "Ensemble-Bsed Sensitivity Anlysis," Mon. We. Rev., 136, pp , 2008.

17 Investigting Sources of Error in Numericl Wether Forecsting with n Observing System Simultion Experiment Nikki C. Privé,,b nd Ronld M. Errico,b GESTAR, Morgn Stte University, U. S.A., nikki.prive@ns.gov, b GMAO, NASA, U. S. A. It is difficult to evlute the qulity of bckground, nlysis, nd short-rnge forecst errors in numericl wether prediction models due to lck of independent dt for verifiction. A tool tht cn potentilly be used for exmintion of these errors is n Observing System Simultion Experiment (OSSE), where the rel tmosphere is replced by simultion in which the true stte of the entire tmosphere is known. In the OSSE frmework, errors in the dt ssimiltion process nd forecsts cn be explicitly clculted, llowing exmintion of sources of error in sophisticted modeling system. An OSSE frmework hs been developed t the Ntionl Aeronutics nd Spce Administrtion Globl Modeling nd Assimiltion Office (NASA/GMAO). The performnce of the GMAO OSSE hs been extensively vlidted ginst rel observtionl dt to ensure tht the behvior of the OSSE is similr to relity in terms of the sttistics of observtion innovtions, nlysis increments, forecst skill, nd djoint-estimted observtion impcts. In the simulted relity of the OSSE, spects of the dt ssimiltion nd modeling systems tht re hrd to modify in the rel world my be esily ltered in highly controlled or idelized scenrios. A series of experiments is performed in order to exmine the reltive impcts of observtion error, model error, nd initil condition error on the evolution of forecst error nd on the effectiveness of the dt ssimiltion system. The mgnitude of observtion errors is vried from low to high, nd the globl observing network is tested both in stndrd relistic configurtion nd in n idelized globl network of high-qulity sounding observtions. An identicl twin cse employing perfect model scenrio ws lso developed to explore the cse of no model error. Observtion errors re found to hve significnt impct on the vrince of nlysis increments, nd cn contribute to degrdtion of the nlysis qulity in comprison to the bckground stte if there is mismtch between the ctul error vrinces nd those ssumed by the dt ssimiltion system. The smllest nlysis errors re chieved in the cse of the idelized observing network. The cse of the idelized observing network lso fetures the lrgest totl mount of work done by observtions during cycling of the dt ssimiltion system. It is found tht model error is mjor contributor to the evolution of forecst skill. The forecst skill in cses with no model error showed n improvement in skill compred to cses with model error equivlent to decrese in forecst led time of two dys in the extrtropics nd four dys in the tropics. In comprison, when the initil condition error is gretly reduced but with model error included, the forecst error increses rpidly during the first hours of integrtion, nd the improvement in forecst skill is only equivlent to reduction in forecst led time of one dy in the extrtropics nd two dys in the tropics.

18 Sensitivity Experiments with LETKF Dt Assimiltion Scheme Employing the WRF Model Mrcos Sucedo, Jun Ruiz,b, Celeste Sulo,b Centro de Investigciones del Mr y l Atmósfer (CIMA), Universidd de Buenos Aires, Argentin, msucedo@cim.fcen.ub.r, b Deprtmento de Ciencis de l Atmósfer y los Océnos, Universidd de Buenos Aires, Argentin. Abstrct In this work the Locl Ensemble Trnsform Klmn Filter [1] (LETKF) implemented in the Wether Reserch nd Forecsting model (WRF) [2] is used to study the sensitivity of this lgorithm to different error sources. The domin covers South Americ nd its djcent ocens. Our pproch consists in performing different OSSE experiments where the truth is generted using the WRF model, forced with the FNL nlysis. A set of observtions is generted tking rndomly perturbed vlues from this true stte. LETKF nlysis cycle experiments using 40 ensemble members nd dptive covrince infltion [3] were performed using these observtions. The following experiments hve been performed: - Perfect model with perfect boundry conditions - Imperfect model with perfect boundry conditions - Perfect model with imperfect boundry conditions - Imperfect model with imperfect boundry conditions Where Perfect model / Perfect boundry refer to the sme version of WRF nd boundry conditions used to generte the true stte, while imperfect model includes chnges in WRF cumulus nd plnetry boundry lyer prmeteriztions nd imperfect boundry conditions correspond to the utiliztion of the Renlysis I dtset to force the model. Ech of these experiments employs the sme boundry conditions for ll the ensemble members, regrdless whether they re perfect or not. The evolution of the ensemble spred under this constrin is nlyzed. Results show tht the errors in boundry conditions re prticulrly importnt in dt ssimiltion problems with limited re domins. Moreover, they indicte tht there is need to perturb the boundry conditions in order to prevent the ensemble spred from collpsing. Nevertheless, dptive infltion mkes good job in djusting the ensemble spred in ech of the experiments nd helps in mintining the spred under the constrint imposed by the boundry conditions. References [1] B. R. Hunt, E. J. Kostelich, I. Szunyogh: Efficient dt ssimiltion for sptio temporl chos: locl ensemble trnsform Klmn filter. Physic D: Nonliner Phenomen, 77, (2007). [2] T. Miyoshi, M. Kunii: The locl ensemble trnsform Klmn filter with the Wether Reserch nd Forecsting model: Experiments with rel observtions. Pure App. Geoph., DOI /s (2011)

19 [3] T. Miyoshi: The Gussin pproch to dptive covrince infltion nd its implementtion with the locl ensemble trnsform Klmn filter. Mon. We. Rev., 139, (2011)

20 Second nd Third order Adjoint Methods for Sensitivity Anlysis in Pollution Models Innocent Souopgui, Trn Thu H b, M. Yousuff Hussini, nd Frncois-Xvier Le Dimet c Mthemtics Deprtment, Florid Stte University, USA, isouopgui@fsu.edu, b Institut of Mechnics, Hong Quoc Viet nd University, Vietnm, c Lbortoire Jen-Kuntzmnn, Universite de Grenoble, Frnce. Understnding the impct chnges in pollutnt emission from foreign region on trget region of is key fctor for tking pproprite ctions ginst the pollution nd its drwbcks. This cn be crried out by the sensitivity nlysis of response function with respect to the source of pollutnt. The bsic pproch determines the sensitivity by crrying out multiple simultions with vrition of source prmeters. A systemtic pproch uses the first order djoint formultion. Both pproches ssume tht the trnsport velocity nd the initil distribution of the pollutnt re known. However, they re given by the solution of Dt Assimiltion problem whose ingredients include, but re not limited to, the pollutnt source, the mthemticl model nd physicl mesurements. As consequence, the sensitivity nlysis should be crried out on the optimlity system of the Dt Assimiltion problem. It leds to non stndrd problem on second order djoint system whose the solution requires the third order djoint. We present the mthemticl derivtion of the third order djoint method for the sensitivity nlysis, long with some numericl experiments nd comprison with the first order djoint pproch.

21 A Comprison of Impcts of Rdiosonde nd AMSU Rdince Observtions In GSI-bsed Hybrid nd 3DVr Dt Assimiltion Systems for NCEP GFS Govindn Kutty nd Xugung Wng b b School of Meteorology nd Centre for Anlysis nd Prediction of Storms, Normn, OK, USA Corresponding uthor ddress: xugung.wng@ou.edu The impct of observtions cn be dependent on mny fctors in dt ssimiltion (DA) system including dt qulity control, preprocessing, skill of the model nd the DA lgorithm. The present study focuses on exploring the difference of the impcts of observtions ssimilted by two different DA lgorithms. A 3DVr-bsed ensemble-vritionl (3DEnsVr) hybrid dt ssimiltion system ws recently developed bsed on the Gridpoint Sttisticl Interpoltion (GSI) dt ssimiltion system nd ws implemented opertionlly for the GFS. One interesting question is if nd how the impcts of observtions differ when ssimilted by the GSI 3DVr nd 3DEnsVr. Experiments were conducted over 6-week period during Northern Hemisphere winter seson t reduced resolution of T190L64 following the configurtion of [1]. The control runs ssimilted ll opertionl conventionl nd stellite observtions. The impcts of AMSU nd Rdiosonde observtions were studied through dt denil experiments. These pltforms were selected bsed on the significnce shown by these two dt sets in the previous studies. The impcts of AMSU nd Rdiosonde ssimilted by 3DEnsVr were compred with those ssimilted by GSI 3DVr. For both the control nd dt denil experiments, the forecsts produced by the 3DEnsVr re more ccurte thn the GSI3DVr experiments. The AMSU nd Rdiosonde, showed positive impct ssimilted by both DA schemes in generl. In the GSI3DVr, the errors of globl wind nd temperture forecsts were incresed more by denying Rdiosonde thn denying AMSU observtions. In the 3DEnsVr,such impcts of the AMSU nd Rdiosonde re similr. For the humidity forecsts, the AMSU hs lrger impct thn Rdiosonde in both the GSI3DVr nd the 3DEnsVr. For the GSI3DVr, the Rdiosonde nd AMSU observtions show similr impct in both mgnitude nd sptil distribution in the Southern extr-tropics (SH). For the Northern extr-tropics (NH), Rdiosonde shows lrger nd more extensive impct thn AMSU. The lrgest difference of the degrdtion of the forecst between the 3DEnsVr nd GSI3DVr ws seen in the SH when Rdiosonde ws denied, where the forecst ws degrded much less in the 3DEnsVr thn in the GSI3DVr. The percentge degrdtion of the forecst skill fter denying Rdiosonde nd AMSU observtions is less in the 3DEnsVr thn the GSI3DVr. The nomly correltion of forecsts up to 5-dy forecst led time indictes tht the impct of AMSU nd Rdiosonde observtions increses with incresing forecst led time in both DA systems. The AMSU rdince bises estimted by the GSI 3DVr nd the 3DEnsVr show similr vlues. References [1] Wng, X., D. Prrish, D. Kleist nd J. Whitker, 2013: GSI 3DVr-bsed Ensemble- Vritionl Hybrid Dt Assimiltion for NCEP Globl Forecst System: Single Resolution Experiments, Monthly Wether Review, ccepted.