JP2.11 APPLICATION OF THE BRATSETH SCHEME FOR HIGH LATITUDE INTERMITTENT DATA ASSIMILATION USING THE PSU/NCAR MM5 MESOSCALE MODEL Xingang Fan * and Jeffrey S. Tilley University f Alaska Fairbanks, Fairbanks, Alaska 1. INTRODUCTION Interest in messcale frecasting in high latitudes has increased. Fr high reslutin messcale frecasting at high latitudes, the cnventinal data that enters an initializing analysis is spatially sparse cmpared t lwer latitudes. Therefre, it is prudent t investigate 4- dimensinal data assimilatin (FDDA) methds, particularly utilizing remtely sensed infrmatin int frecast systems t imprve bth the initializing analyses and the resulting frecasts. The standard PSU/NCAR MM5 mdeling system cntains a Newtnian nudging FDDA methd (NNFM) (Grell et al, 1994). Nudging t bth gridded analyses and/r cnventinal bservatins is eamined in a cmpanin paper (Tilley and Fan 2001). The result shws that NNFM has a psitive simulatin capability. Hwever, since the nudging is dne befre the bservatin time, it is difficult, frm a frecast systems pint f view, t use the nudging cefficients afterwards fr frecasting purpses. Therefre ther FDDA appraches need t be investigated fr such purpses. The s-called intermittent data assimilatin' (IDA) methd is ne such alternate apprach, in which the successive crrectin methd is widely used as an bective analysis technique. Schemes fllwing Cressman (1959), Barnes (1973), Bratseth (1986) and thers are pssible ways f btaining the analyses used in IDA. Amng thse, the Bratseth scheme avids errrs assciated with the fact that in the ther successive crrectin schemes the analysis always cnverges t the data, which shuld nt be the case when errrs eist in bth the bservatins and the backgrund. The slutin f the Bratseth scheme cnverges tward a slutin btained by Optimal Interplatin (OI). This methd alleviates the shrtcmings f the Cressman scheme and f Crrespnding authr address: Xingang Fan, University f Alaska Fairbanks, Gephysical Institute, Fairbanks, AK 99709; Email: fan@taku.iarc.uaf.edu * On leave f absence frm Chinese Academy f Meterlgical Sciences, Beiing, 100081 ther successive crrectin schemes and als requires much less cmputatinal csts than perfrming a full OI prcedure. Sashegyi et al (1993) used the Bratseth scheme fr analysis f Genesis f Atlantic Lws Eperiment (GALE) simulatins with the U.S. Naval Research Labratry (NRL) messcale mdel. The analysis was dne with a multivariate successive crrectin apprach. Ruggier et al (1996) eamined an assimilatin apprach where surface bservatins are used in the NRL mdel while the Sashegyi et al (1993) methd is applied t the upper air analysis. The MM5 mdel has its wn data preparatin prcedures and initializatin prcedures, including Cressman and Multiquadric bective analysis (e.g., Grell et. al 1994). In this study we apply the Bratseth scheme in the bective analysis, and perfrm the analysis in the bth univariate and multivariate cntets. We further utilize the Bratseth scheme in tandem with the IDA methd in MM5 simulatins f the summer Alaskan heavy rain event eamined in the cmpanin paper with the NNFM methd. In an assimilatin cycle, the 6- hur mdel frecast is reanalyzed using the Bratseth scheme by ingesting new bservatins at the frecast time. Then the analysis is initialized fr an MM5 frecast run. Sectin 2 discusses the IDA cycle used in this study with MM5 mdel. Sectin 3 briefly describes the Bratseth bective analysis scheme. Sectin 4 gives a summary f the case we are studying and eperiment design. Sectin 5 gives the results f the eperiments, with discussin and cnclusins in Sectin 6. 2. INTERMITTENT ASSIMILATION CYCLE The IDA eperiments in this study cnsider a 48-hur perid during the event. A cycle begins with a 6 hur MM5 frecast frm the initial time. An analysis frm the 6-hur frecast is cnstructed with the aid f bservatins and used t re-initialize the mdel fr anther 6 hur frecast perid. Figure 1 shws a flwchart f the IDA cycle with the MM5 mdel. The cycle is repeated fr a ttal length f 24 hurs. The mdel is then run cntinuusly fr anther 24 hurs t
the end f the 48-hur perid. This apprach simulates a real time frecast during which bservatins are available nly befre the current time. Obs Figure 1. Illustratin f IDA scheme. 3. OBJECTIVE ANALYSIS SCHEME The Bratseth analysis scheme used in this study is similar t the ne in Sashegyi et al (1993). The sea level pressure and 3-dimensinal temperature, height, relative humidity and winds are analyzed first by univariate analysis. The first guess field is the MM5 frecast which is interplated t pressure levels. Then, fr efficiency f analysis, the bservatins are srted int bins f dimensin 1010 analysis grid pints after being subected t quality cntrl checks by the MM5 preprcessr prgram LITTLE_R. Observatins that are t clse t each ther t be utilized individually are averaged t frm 'superbs'. A univariate analysis is cnducted t crrect the deviatins f analysis frm the first guess. The Bratseth successive crrectin wrks in an iterative fashin updating bth the interplated grid crrectin and bservatin crrectin using the difference between the bserved values and the bservatinal estimates derived frm the analysis. Fr the geptential crrectins, at grid pint, the updated grid crrectin φ is given by: Initial 1st Guess Analysis InterpF MM5 ( k + 1) = φ ( k ) + α φ φ ( k) n = 1 [ ] φ, (1) while the bservatin crrectin is given by: i ( k + 1) = φ ( k) + α φ φ ( k) i Obs +6hr Frecast InterpB Analysis InterpF MM5 n = 1 i [ ] φ, (2) +12hr φ is the value f the bservatin, φ ( k) and ( ) where φ k are the interplated crrectin at grid pint and the estimated bservatin crrectin respectively fr the kth iteratin. n is the ttal number f bservatins that influence a particular grid pint, and α, α i are weighting functins between (1) the grid pint and the bservatin lcatin, and (2) the bservatin lcatins i and, respectively. The weights are defined fllwing Sashegyi et al (1993), and cntain terms t accunt fr bservatinal errr and crrelatins f true values. The crrelatin functins fllw a basic Gaussian frm, thugh a slightly different frm is used fr the wind fields in rder t allw fr different weights fr different wind cmpnents. The length scale used here is 600 km (13.3 grid pints in this study). After 3 t 4 iteratins, the length scale is reduced t 330 km fr ne mre iteratin t speed cnvergence f the scheme. The starting crrectins φ () 1 and φ () 1 in equatins (1) and (2) are zer. After a 'first tier' univariate analysis, the secnd tier enhancement analysis fr geptential height and winds are cnducted fllwing the prcedure f Sashegyi et al (1993). The lateral bundary analysis result is merged with the standard LITTLE_R analysis that is used in the cntrl run. This makes the lateral bundary cnsistent with bth the riginal envirnment btained frm the NCEP analysis and the new Bratseth analysis. 4. EXPERIMENT DESIGN The Alaskan heavy rain event f Aug. 11-13, 2000, described in Tilley and Fan (2001; this vlume), is eamined in this study. The MM5 mdel is cnfigured with tw nested dmains with grid reslutins f 45 and 15 km, respectively. The dimensins f the tw dmains are 10990 and 10688. Bth have 41 sigma levels vertically. The analysis is perfrmed n the carse dmain and then interplated t the fine grid dmain. The cntrl run uses the standard MM5 initializatin prcedure with n FDDA, and is the same as that in Tilley and Fan (2001). The mdel simulatins are run fr 48 hurs. Figure 2a shws the NCEP analysis 24-hur rainfall and Figure 2b the 24-hur accumulated rainfall difference f the cntrl run frm the analysis at 12 UTC Aug. 12, 2000. Fr the IDA eperiments, the mdel is initialized frm 12 UTC Aug. 11. After the initial cnditins
have been btained fr 06 UTC Aug. 12, the mdel is run cntinuusly frm that time t 12 UTC Aug 13. In rder t d a cmparisn study f the methd, assimilatin cycles were dne withut ingesting bservatin data, thereby mitting the analysis step in Figure 1 (Eperiment NObs). The secnd eperiment ingests bservatins but the analysis methd used is the MM5 LITTLE_R preprcessr prgram with the Cressman scheme (Eperiment Inta_R). The third eperiment tests the Bratseth scheme in IDA (Eperiment Inta_B). The simulatin results will be given in the net sectin. 5. RESULTS Thugh we have run the mdel fr 48 hurs, here we nly shw the results f the 24-hur frecasts, fcusing n the impacts f data assimilatin n the precipitatin frecast since quantitative precipitatin frecasts are a serius frecast prblem in Alaska as well as in the cntinental United States. 5.1 Impact f Data Assimilatin Figures 3a and 3b illustrate the results f eperiments NObs and Inta_R, respectively. In (a) (a) (b) (b) Figure 2. (a) The NCEP analysis 24-hur rainfall and (b) the difference f the frecasted 24-hur accumulated rainfall, Cntrl Run-Analysis, at 12 UTC August 12, 2000. Figure 3. Differences in 24-hur accumulated rainfall between: (a) eperiments NObs; (b) eperiment Inta_R, and the NCEP analysis, at 12 UTC August 12, 2000.
the result f NObs (Figure 3a), the rainfall frecast errr is greater than that f the cntrl run (Figure 2b). This is understandable because the bservatin data were used in the bective analysis f the cntrl run. After the bservatin data are ingested in the eperiment Inta_R thrugh the MM5 bective analysis package LITTLE_R, the rainfall frecast errr field is imprved ver that f NObs. The tw relatively large precipitatin differences in Alaska and nrthwest Canada are reduced in magnitude in the Inta_R simulatin. Althugh the main rainfall center in Alaska is still underfrecast cmpared t the bserved rainfall, the rainfall frecast in this assimilatin run is still imprved cmpared t the cntrl run. The tw large psitive errr centers lcated in the nrthern Bering Sea and nrthwest Pacific Ocean in the previus eperiments (cmpare Figures 2 and 3) d nt ccur in eperiment Inta_R. Nevertheless, the imprtant pint is that the IDA/LITTLE_R apprach imprves the rainfall frecast t sme degree. 5.2 Impacts f Bratseth Analysis Scheme Figure 4 illustrates the result f assimilatin eperiment Inta_B in which the Bratseth analysis scheme is used in the assimilatin cycle. cntrl run. In cmparisn with the Inta_R result (Figure 3), Inta_B is characterized by a smaller negative errr area than Inta_R within Alaska, thugh therwise the results are very similar t thse f eperiment Inta_R. This result indicates that the use f Bratseth scheme has a psitive effect n the rainfall frecast fr this case. 6. SUMMARY AND DISCUSSIONS This study fcused n the IDA methd using the MM5 mdel at high latitudes. An efficient bective analysis scheme develped by Bratseth (1986) and applied by Sashegyi et al (1993) and Ruggier et al (1996) was incrprated int the MM5 mdel. Several eperiments have been perfrmed in rder t investigate the effectiveness f bth IDA cnducted with MM5 and the Bratseth bective analysis methd. The results shw that IDA in MM5 shws prmise in ingesting bservatins and imprving frecasts, while at the same time being rather simple and inepensive. The Bratseth analysis scheme btains better results when bth bservatin and mdel frecast fields cntain errrs. Hwever, it is imprtant t nte that neither the cntrl run nr any f the ther prduced sufficient rainfall in cmparisn with the analysis (Figure 2a). One pssible reasn is that the bservatin data is sufficiently sparse in space that there is a limit t the imprvement frm any f these types f methds emplying cnventinal data. Nnetheless, there appears t be sme ptential f btaining benefit frm applicatin f an IDA system in high latitudes. Further wrk investigating ther cases and applying the methd t ther reginal mdels is indicated t see hw rbust this ptential is. Future wrk related t assimilating satellite derived misture variables will als likely bring imprvements t precipitatin frecasts in high latitudes. REFERENCES Figure 4. Difference in 24-hur accumulated rainfall f eperiment Inta_B frm the NCEP analysis at 12 UTC August 12, 2000. Frm Figure 4 it is clear that the IDA eperiment cnducted with the Bratseth scheme als prduced an imprved rainfall frecast ver the Bratseth, A. M., 1986: Statistical interplatin by means f successive crrectins. Tellus, 38A, 439-447. Cressman, G., 1959: An peratinal bective analysis system. Mn. Wea. Rev., 87, 367-374. Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A descriptin f the fifth-generatin Penn State/NCAR messcale mdel (MM5). NCAR Technical Nte, NCAR/TN-398+ST, 117pp.
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