Forecast rror sensitivity to the analysis预测误差的敏感性分析

1、ecmwftraining course 2010 slide 1towards an adaptive observation network: monitoring the observations impact in ecmwf forecast carla cardinalioffice 1006ecmwftraining course 2010 slide 2roger daleys ideamid-1995, roger daley joined nrl data assimilation when predictability scientists were preparing

2、the fastex targeting campaign. it was clear that while sensitivity gradients products could identify sensitivity regions, they could not provide any guidance on how deployed extra-observations would have improved the forecast.after one of the frequent discussions on the subject, roger left the offic

3、e wondering if there was some way to find the sensitivity of the forecast model with respect to the observations. unable to sleep that night , he instead derived the equations for the sensitivity of the forecast aspect to the observation and the background. aajjxyyxj is a measure of the forecast err

4、or (as defined through e.g dry energy norm)ecmwftraining course 2010 slide 3outlinelforecast sensitivity to observation or observation impact on forecastlequationlfso diagnostic tooltforecast system performance investigation in two different seasonslmonitoring the forecast impactt ecmwf operational

5、configurationlconclusionecmwftraining course 2010 slide 4forecast sensitivity to observation: equationsfrom a roger daley ideaaxyj is a measure of the forecast error (as defined throughe.g dry energy norm)forecast error sensitivity to the analysisrabier f, et al. 1996ajxajxjyecmwftraining course 201

6、0 slide 5sensitivity gradient ajx60s60s30s30s0030n30n60n60n150w150w120w120w90w90w60w60w30w30w0030e30e60e60e90e90e120e120e150e150e-.2e+06-.1e+06-.8e+05-.5e+05-.3e+05-.1e+05-.8e+040.8e+040.1e+050.3e+050.5e+050.8e+050.1e+060.2e+0639jtsummerwinter60s60s30s30s0030n30n60n60n150w150w120w120w90w90w60w60w30w

7、30w0030e30e60e60e90e90e120e120e150e150e-.2e+07-.1e+07-.8e+06-.5e+06-.2e+06-.8e+05-.4e+050.4e+050.8e+050.2e+060.5e+060.8e+060.1e+070.2e+0760s60s30s30s0030n30n60n60n150w150w120w120w90w90w60w60w30w30w0030e30e60e60e90e90e120e120e150e150e-.2e+07-.1e+07-.8e+06-.5e+06-.2e+06-.8e+05-.4e+050.4e+050.8e+050.2e

8、+060.5e+060.8e+060.1e+070.2e+07+-dry energy normecmwftraining course 2010 slide 6forecast sensitivity to observation: equationsfrom a roger daley ideaaxyj is a measure of the forecast error (as defined throughe.g dry energy norm)forecast error sensitivity to the analysisrabier f, et al. 1996ajxtaxky

9、ajxjyecmwftraining course 2010 slide 71111ttk=(b +h r h) h rb(qxq)=var(xb)r(pxp)=var(y)k(qxp) gain matrixh(pxq) jacobian matrix()aqbxkyihk xtaxkyxbyxbyxbyanalysis solution in model spaceanalysis sensitivity to the observationdfs1tah rttahxk hyin observation spaceecmwftraining course 2010 slide 8defi

10、ne forecast sensitivity1111()ttaxkr h bh r hy1111()tajjr h bh r hyx1ajjr hayxjjaaxyyxanalysis sensitivity to the observation (model space)ecmwftraining course 2010 slide 9equationssolution for forecast sensitivity111) 2) ajja zxr hzyaajjxyyxtajjkyx1ajjr hayxkrylov subspace methodecmwftraining course

11、 2010 slide 10forecast sensitivity to observation: equationsfrom a roger daley ideaaxyj is a measure of the forecast error (as defined throughe.g dry energy norm)forecast error sensitivity to the analysisrabier f, et al. 1996ajxtaxkycompute the forecast impact or forecast error variation j,(),(),taa

12、bbbaaaajjjjjxxxk y-hxky-hxyxxxxy()bjjyhxyajxjyecmwftraining course 2010 slide 11monitoring ecmwf system15 june-15 julysummer 20065 january-12 februarywinter 200724h ose fcecycle 31r2t511t95t159l60ecmwftraining course 2010 slide 12fso: pilot and wind profilers fce contribution summer 2006pilotwind pr

13、ofiler nanegative impactpositive impactecmwftraining course 2010 slide 13fso: wind profilers north america summer 2006north america “problem” (od/rd special topic 2005) strong, moist warm flow from the gulf of mexico large and divergent wind increments at 150-250 hpa the conclusion was that “increme

14、nts are not related to bad observations or a poor 4d-var performance”used uamprofiler-uwind areansew= 46/ 29/ -85/-109exp:eusg /dcda 2006061512-2006071512(12) nobsexp 0 0 76239 133552 106233 75634 25025 20050 25426 21718 692 0 0 0 0 000.81.62.43.24std.dev1000 850 700 500 400 300 250 200 150 100 70 5

15、0 30 20 10 5.0pressure (hpa)-1 -0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81bias1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0background departure o-banalysis departure o-aused vamprofiler-vwind areansew= 46/ 29/ -85/-109exp:eusg /dcda 2006061512-2006071512(12) nobsexp 0 0 76239 133552 106233 75

16、634 25025 20050 25426 21718 692 0 0 0 0 000.81.62.43.24std.dev1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0pressure (hpa)-1-0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81bias1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0background departure o-banalysis departure o-aused wind dataampr

17、ofiler-windspeed areansew= 46/ 29/ -85/-109exp:eusg /dcda 2006061512-2006071512(12) nobsexp 0 0 76239 133552 106233 75634 25025 20050 25426 21718 692 0 0 0 0 000.81.62.43.24std.dev1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0pressure (hpa)-1 -0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81bias of

18、speed1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0background departure o-banalysis departure o-aused uamprofiler-uwind areansew= 46/ 29/ -85/-109exp:eusg /dcda 2006061512-2006071512(12) nobsexp 0 0 76239 133552 106233 75634 25025 20050 25426 21718 692 0 0 0 0 000.81.62.43.24std.dev1000

19、 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0pressure (hpa)-1 -0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81bias1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0background departure o-banalysis departure o-aused vamprofiler-vwind areansew= 46/ 29/ -85/-109exp:eusg /dcda 2006061512-20060715

20、12(12) nobsexp 0 0 76239 133552 106233 75634 25025 20050 25426 21718 692 0 0 0 0 000.81.62.43.24std.dev1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0pressure (hpa)-1-0.8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81bias1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0background departure o-

21、banalysis departure o-aused wind dataamprofiler-windspeed areansew= 46/ 29/ -85/-109exp:eusg /dcda 2006061512-2006071512(12) nobsexp 0 0 76239 133552 106233 75634 25025 20050 25426 21718 692 0 0 0 0 000.81.62.43.24std.dev1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0pressure (hpa)-1 -0.

22、8 -0.6 -0.4 -0.200.2 0.4 0.6 0.81bias of speed1000 850 700 500 400 300 250 200 150 100 70 50 30 20 10 5.0background departure o-banalysis departure o-aecmwftraining course 2010 slide 14hhhhhhlllllll1020202020202030303040404040505015n15n20n20n25n25n30n30n35n35n40n40n45n45n50n50n55n55n60n60n65n65n130w

23、130w120w120w110w110w100w100w90w90w80w80w70w70w60w60w50w50wecmwf analysis vt:thursday 15 june 2006 00utc surface: *total column water2.8535101520253035404550556061.37no ref.date types : 95(28) total : 28 plotted at 2007-09-05 17:18hhhhhhhhllllllll20040040015n15n20n20n25n25n30n30n35n35n40n40n45n45n50n

24、50n55n55n60n60n65n65n130w130w120w120w110w110w100w100w90w90w80w80w70w70w60w60w50w50wthursday 15 june 2006 00utc ecmwf forecast t+18 vt: thursday 15 june 2006 18utc surface: *convective available potential energy0100200300400500600700800 899.1hhhhhhhhllllllll20040040015n15n20n20n25n25n30n30n35n35n40n4

25、0n45n45n50n50n55n55n60n60n65n65n130w130w120w120w110w110w100w100w90w90w80w80w70w70w60w60w50w50wthursday 15 june 2006 00utc ecmwf forecast t+18 vt: thursday 15 june 2006 18utc surface: *convective available potential energy0100200300400500600700800 899.1hhhhhhlllllll1020202020202030303040404040505015n

26、15n20n20n25n25n30n30n35n35n40n40n45n45n50n50n55n55n60n60n65n65n130w130w120w120w110w110w100w100w90w90w80w80w70w70w60w60w50w50wecmwf analysis vt:thursday 15 june 2006 00utc surface: *total column water2.8535101520253035404550556061.37mean tcwvmean capehhhhl5.0m/s20n20n30n30n40n40n50n50n60n60n120w120w9

27、0w90wecmwf analysis vt:thursday 15 june 2006 00utc 500hpa *geopotential/850hpa v velocityh5.0m/s20n20n30n30n40n40n50n50n60n60n120w120w90w90wsummer case 2006era40 janhhl5.0m/s20n20n30n30n40n40n50n50n60n60n120w120w90w90wera40 junmean 850-hpa wind & z500 hpa courtesy by fernando pratesecmwftraining

28、 course 2010 slide 15summary fso wind profilerl fso showed a fc error increase due to the american wind profiler observations.l southerly flow across se usa bringing warm and moist air from gulf of mexico produced strong convective instability in the region, a typical situation at this time of the y

29、ear.l following ackley et al report (1998) on wind profiler measurements validity “in strong unstable conditions (turbulence) the measure of the mean horizontal wind is corrupted affecting the measurements”. suggesting that the forecast impact can change with the meteorological situation for the sum

30、mer 2006 case.ecmwftraining course 2010 slide 16fso: atmospheric motion vector fce contribution summer 2006forecast error contribution of the observed wind grouped by satellite types- positive corresponds to an increase of fc errorforecast error contribution of the wind on pressures levels & gro

31、uped by satellite types- largest degradation comes from the lower troposphereecmwftraining course 2010 slide 17fso amv 700-1000 hpa u-wind: summer 2006 60s60s30s30s0030n30n60n60n150w150w120w120w90w90w60w60w30w30w0030e30e60e60e90e90e120e120e150e150elev=850, par=u, fcdate=20060615-20060715 0zdiff in r

32、ms of fc-error: rms(fc_eu3b - an_eu3b) - rms(fc_etxa - an_etxa)-0.1e+01-0.6e+00-0.3e+00-0.1e+00 0.1e+00 0.4e+00 0.9e+00 0.1e+0160s60s30s30s0030n30n60n60n150w150w120w120w90w90w60w60w30w30w0030e30e60e60e90e90e120e120e150e150elev=850, par=u, fcdate=20060615-20060715 0zdiff in rms of fc-error: rms(fc_eu

33、3b - an_eu3b) - rms(fc_etxa - an_etxa)-0.1e+01-0.6e+00-0.3e+00-0.1e+00 0.1e+00 0.4e+00 0.9e+00 0.1e+01rmse amv- baseline850 hpa uecmwftraining course 2010 slide 18fso amv 700-1000 hpa summer 20065555555555555555555555555510101010101010101010101010151515151510.0m/s60s60s30s30s0030n30n60n60n150w150w12

34、0w120w90w90w60w60w30w30w0030e30e60e60e90e90e120e120e150e150e57.51012.51517.52022.5v-compu-compmean 850hpa windatlantic ocean: transition between sub-tropical and extra-tropical from weak to strong zonal flowindian ocean: well established monsoon circulationcourtesy by fernando pratesecmwftraining co

35、urse 2010 slide 19fso atlantic ocean: observation qualitythe strong sinking motion in sh near 30s represents the southern limit of the hadley circulation where the subtropical high cell is located. cloud suppression or low clouds.an mean vertical velocity (*0.01 pa/s)northsouthera40northsouth40on30o

36、n20on10on0o10os20os30os40os1000900800700600500400300200100-4-4-4-41111111111113333333335557average of vert vel 256550615 00 step 0 expver 0011 (35.0w-0.0e)40on30on20on10on0o10os20os30os40os1000900800700600500400300200100-8-6-6-6-6-6-4-4-4-4-4-4-2-2-2-2-2-200000000000000000222222222222222222222244444

37、44446average of vert vel 20060615 00 step 0 expver 0001 (35.0w-0.0e)cross section 35w-0eamv quality: difficult to assign the height of the cloud topcourtesy by fernando pratesecmwftraining course 2010 slide 20fso indian monsoon summer 2006: model biasa too strong low level flow of indian summer mons

38、oon is a well known problem in the model as is indicated by the jja mean analysis incrementsmean an inc 925-hpa jja 2006v-windu-winddiagnostic explorerecmwftraining course 2010 slide 21amv fso 700-1000 hpa: winter 2007v-windu-windlargest negative impact of amvs to fc error can be seen in central/eas

39、tern pacific (absent in summer case).negative impact seen during summer 06 in south atlantic near 30s has disappeared in winter 07in the indian ocean the degradation is mainly due to u-component of the windoverall impact of the observations to fcerrorpositive impactnegative impactecmwftraining cours

40、e 2010 slide 22u-wind180w 150w 135wwinter 2007 central/eastern pacificcross sectionthe largest negative impact of amvs to the fc error is found between 5n - 15n coinciding to a broad downward mean motion of the hadley circulation. large departures were also found below 700hpa in the same region.40on

41、30on20on10on0o10os20os30os40os1000900800700600500400300200100-12-12-12-12-12-4-4-4-4-4-4-4-4-4-4-4-4111111111111111111133333355557average of vert vel 20070106 00 step 0 expver 0001 (150.0w-140.0w)a second cluster of negative impact near 25n/140w is localized on top of a region of weak winds (strong

42、sinking motion/ high pressure system)era40 mean vertical velocity (*0.01 pa/s)40on30on20on10on0o10os20os30os40os1000900800700600500400300200100-12-12-12-12-12-4-4-4-4-4-4-4-4-4-4-4-4-411111111111111133335average of vert vel 20070105 00 step 0 expver 0001 (180.0w-150.0w)northsouth180-150 wecmwftraini

43、ng course 2010 slide 23summary fso amvs l fso showed a fc error increase due to amvsl the location of the largest negative impact of the amvs in atlantic (summer 2006) and in pacific (winter 2007, el nino) is found close to the region of strong sinking mean motion embedded in the hadley circulation

44、t observation quality problem on the height assignment l detrimental effect is also observed in the indian ocean associated with a too strong indian monsoon circulation developed by the modelt model biasecmwftraining course 2010 slide 24gps ro impact on forecast error winter 200748h fce24h fceecmwft

45、raining course 2010 slide 25automatic&manual surface press synop fce conributionwinter case6000synop sfc-press observations shows an overall globally positive impact to the forecast error but not over europe. ecmwftraining course 2010 slide 26automatic surf press synop fce contribution time seri

46、es - winter 2007storm kyrill 18 -20 jan used psynop-ps (pa) areansew= 54/ 47/ 20/ 0ewnz /da 2007010600-2007021212(12) min= -511. max= 459.mean= 12.1 std= 67.8nb= 207629 rms= 68.9background departure o-b min= -422. max= 387.mean= 4.80 std= 54.5nb= 207629 rms= 54.7analysis departure o-a-300-200-100010

47、020030000.100 1050.200 1050.300 1050.400 1050.500 105-300-200-100010020030000.100 1050.200 1050.300 1050.400 1050.500 105used psynop-ps (pa) areansew= 54/ 47/ 20/ 0ewnz /da 2007010600-2007021212(12) min= -375. max= 371.mean= 23.4 std= 68.3nb= 185224 rms= 72.2background departure o-b min= -332. max=

48、249.mean= 11.7 std= 53.0nb= 185224 rms= 54.3analysis departure o-a-300-200-1000100200300080000.160 1050.240 1050.320 1050.400 105-300-200-1000100200300080000.160 1050.240 1050.320 1050.400 105used pmetar-ps (pa) areansew= 54/ 47/ 20/ 0ewnz /da 2007010600-2007021212(12) min= -467. max= 436.mean= -29.

49、5 std= 66.8nb= 126805 rms= 73.0background departure o-b min= -340. max= 343.mean= -34.8 std= 54.2nb= 126805 rms= 64.4analysis departure o-a-300-200-1000100200300060000.120 1050.180 1050.240 1050.300 105-300-200-1000100200300060000.120 1050.180 1050.240 1050.300 105used psynop-ps (pa) areansew= 54/ 4

50、7/ 20/ 0ewnz /da 2007010600-2007021212(12) min= -511. max= 459.mean= 12.1 std= 67.8nb= 207629 rms= 68.9background departure o-b min= -422. max= 387.mean= 4.80 std= 54.5nb= 207629 rms= 54.7analysis departure o-a-300-200-100010020030000.100 1050.200 1050.300 1050.400 1050.500 105-300-200-1000100200300

51、00.100 1050.200 1050.300 1050.400 1050.500 105used psynop-ps (pa) areansew= 54/ 47/ 20/ 0ewnz /da 2007010600-2007021212(12) min= -375. max= 371.mean= 23.4 std= 68.3nb= 185224 rms= 72.2background departure o-b min= -332. max= 249.mean= 11.7 std= 53.0nb= 185224 rms= 54.3analysis departure o-a-300-200-

52、1000100200300080000.160 1050.240 1050.320 1050.400 105-300-200-1000100200300080000.160 1050.240 1050.320 1050.400 105used pmetar-ps (pa) areansew= 54/ 47/ 20/ 0ewnz /da 2007010600-2007021212(12) min= -467. max= 436.mean= -29.5 std= 66.8nb= 126805 rms= 73.0background departure o-b min= -340. max= 343

53、.mean= -34.8 std= 54.2nb= 126805 rms= 64.4analysis departure o-a-300-200-1000100200300060000.120 1050.180 1050.240 1050.300 105-300-200-1000100200300060000.120 1050.180 1050.240 1050.300 105eu areaeu areamanualmetardaily fc error contribution over europeecmwftraining course 2010 slide 27gps ro impac

54、t on forecast error winter 2007hpa1040500the negative impact is more pronounced in the tropics & subtropicsgps ro at 50-hpaoverall impact of the observations to fc errorecmwftraining course 2010 slide 2850 hpa rmse temperature gpsro-control winter 200750-hpa temp rmse differences between gps ro-

55、control oses (24-hrs fc)the degradation (positive values) are found mainly in the tropical belt which is consistent with the geographical distribution obtained from the fso -80-70-70-70-70-70-70-60-60-60-60-60-60-60-50-50-50-50-40-40-4060s60s30s30s0030n30n60n60n120w120w60w60w0060e60e120e120enh=0.03

56、sh= 0.06 trop= 0.13 eur=-0.05 namer= 0 natl= 0.04 npac= 0.1 atrec0lev=50, par=t, fcdate=20070105-20070211 0z, step=24diff in rms of fc-error: rms(fc_eux1 - an_eux1) - rms(fc_euwz - an_euwz)-2.5-2-1.5-1-0.5-0.25-0.10.10.250.511.522.5the ose shows a positive impact for the gps-ro for the 10-days forec

57、ast with the exception of the first 24hrs forecast.012345678910forecast day0.40.60.811.21.41.61.822.2deg date1=20061215/. date2=20061215/.area=tropics time=00 mean over 66 casesroot mean square error forecast100 hpa temperature/dry bulb temperatureforecast verificationbeux1beuwzmagics 6.11 thrud - s

58、ti tue aug 14 12:46:48 2007 verify scocom012345678910forecast day00.10.20.30.40.50.60.70.80.9 date1=20061215/. date2=20061215/.area=tropics time=00 mean over 66 casesmean error forecast100 hpa temperature/dry bulb temperatureforecast verificationbeux1beuwzmagics 6.11 thrud - sti tue aug 14 12:46:48

59、2007 verify scocom * 1 error(s) found *012345678910forecast day0.40.60.811.21.41.61.82 date1=20061215/. date2=20061215/.area=tropics time=00 mean over 66 casesstandard deviation of error forecast100 hpa temperature/dry bulb temperatureforecast verificationbeux1beuwzmagics 6.11 thrud - sti tue aug 14

60、 12:46:48 2007 verify scocom * 1 error(s) found *012345678910forecast day0.40.60.811.21.41.61.822.2deg date1=20061215/. date2=20061215/.area=tropics time=00 mean over 66 casesroot mean square error forecast100 hpa temperature/dry bulb temperatureforecast verificationbeux1beuwzmagics 6.11 thrud - sti tue aug 14 12:46:48 2