Jacobian mapping between vertical coordinate systems in data assimilation (ITSC-14 RTSP-WG action c)

Transcription

1 Jacoban mappng between vertcal coordnate systems n data assmlaton (ITSC-14 RTSP-WG acton c) Atmospherc Scence and Technology Drectorate Yves J. Rochon, Lous Garand, D.S. Turner, and Saroja Polavarapu wth contrbutons from Jacques Hallé, Shuzhan Ren, Yula Nezln

2 Content Introducton Interpolators Mappng comparsons 1D assmlaton 3D-Var assmlaton Summary and comments 10/27/2006 Page 2

3 Introducton Context: Fast RTMs for assmlaton of radances from nadr sounders often rely on regresson based models evaluated on fxed pressure levels (e.g. RTTOV). Numercal predcton (e.g. NWP) models often use dfferent vertcal levels and a dfferent vertcal coordnate (e.g. η-hybrd). In ths crcumstance, Jacoban mappng from RTM to model coordnate s requred n data assmlaton (DA). 10/27/2006 Page 3

4 Data assmlaton requres explct parng of the vertcal nterpolator and Jacoban mappng. a) profle x' on RTM levels profle x on model levels x '( p = = x = ) x' s ( ) W, j x j or x' = j Wx b) Jacoban mappng: model vertcal coordnate RTM vertcal coordnate f x j x = f x' x' x' x j = f x' x' T W, or h = W h' j The Jacoban mappng matrx s the adjont W T of a lnear forward model vertcal nterpolator matrx W (or TLM of the nterpolator) 10/27/2006 Page 4

5 Introducton Identfcaton of problem: Model levels not partcpatng n forward nterpolaton (blnd levels) lead to mproper Jacoban mappng. Blnd levels can result when the model vert. resoluton s suffcently hgher than the RTM vert. resoluton. Improper mappng heavly masked by vert. correlatons of background covarances. AMSU-A ch. 13 (40) RTTOV Mapped Model: CMAM 10/27/2006 Page 5

6 Introducton Remander of presentaton: Identfy an approprate desgn for the vertcal nterpolator and ts adjont for use wth fast RTMs n data assmlaton when requred (part 2 of ITSC-14 RTSC-WG acton c) Investgate senstvty to choce of nterpolator and representatveness qualty of mapped Jacobans. 10/27/2006 Page 6

7 Interpolators Interpolators for data assmlaton: Nearest neghbour log-lnear nterpolator (operatonally appled at EC for example) Proposed alternatve: pecewse weghted averagng log-lnear nterpolator x ' = + 1 w w x d evaluated usng the trapezodal rule wth weghts w d ln ln p p w w x d d ln ln p p 10/27/2006 Page 7

8 Weghtng functons: Nearest neghbour and pecewse weghted avg. nterpolators potental blnd level RTM levels 10/27/2006 Page 8

9 Mappng comparsons Jacoban mappngs va adjont of: Nearest neghbour nterpolator Proposed nterpolator Compared to Layer Thckness Scalng (LTS) nterpolaton for Jacoban mappng (no forward nterpolator and adjont parng not applcable to DA) RTM calculatons on model levels (D.S. Turner) usng AMSU-A channels up to 14 and GFLBL (D.S. Turner) Jacoban calculatons for AIRS (5) and HIRS (5) channels. N.B.: LTS mappng method was used n Saunders et al. and Garand et al. RTM ntercomparsons. 10/27/2006 Page 9

10 Mappng of AMSU-A Jacobans RTTOV Ch. 13 (40) Nearest neghbour Orgnal Proposed other Proposed & LTS CMAM levels 10/27/2006 Page 10

11 Jacoban mappngs for HIRS channel 12 for varous (M,N) Orgnal from GFLBL Mapped va Proposed LTS Ref.: GFLBL Profle relatve error measure (%) over AIRS and HIRS channels and varous (M,N): 71% wth <5% 90% wth <15% for cases 10/27/2006 Page 11

12 1D assmlaton: Impact of vert. correl. & vert. nterpolators Sample vert. correlaton fns NMC Sample temperature ncrements NMC stats nearest neghbour 6-hr dff. 6-hr dff. 10/27/2006 Page 12

13 3D-Var assmlaton: Dagonal vert. correlaton matrces Average analyss 0.3 profles over 5 days at the equator Nearest neghbour Proposed Temperature (degrees Celcus) 10/27/2006 Page 13

14 3D-Var assmlaton: Impact of vert. correlaton & vert. nterpolators ~0.001 hpa CMAM-DA: vertcal correlaton matrx from an ensemble perturbaton approach (Yula Nezln) 0.1 hpa 10 hpa hpa Surface 10/27/2006 Page 14

15 3D-Var assmlaton: Ensemble perturbaton scheme vert. correlaton matrces analyses forecasts Average profle dfferences over 5 days at the equator 0.3 for both analyses and forecasts Temperature dfferences 10/27/2006 Page 15 Curves show dfferences of temperatures obtaned from usng - nearest neghbour - proposed methods.

16 3D-Var assmlaton: Impact on geopotental heght (GEM model and NMC statstcs: prelmnary results) std. dev. For 6-hours forecasts n the tropcal regon. 0.3 Based on 12 days. Pressure (hpa) bas Nearest neghbour Proposed (Obs Forecast) bas & std. dev. (dm) 10/27/2006 Page 16

17 Summary and comments Proposed vertcal nterpolator satsfes Jacoban mappng requrements. P.S.: The forward vertcal nterpolator and ts adjont can account for surface pressure dependency of model coordnate when requred. Level of beneft depends on vertcal resolutons and wdth of vertcal correlaton functons. Stand-alone code to be made avalable shortly (contact: and ) Manuscrpt to QJRMS condtonally accepted. 10/27/2006 Page 17

18 10/27/2006 Page 18

19 Extras 10/27/2006 Page 19

20 LIST OF AIRS and HIRS CHANNELS FOR WHICH SIMULATIONS WERE PERFORMED. HWHM STANDS FOR THE HALF-WIDTH AT HALF-MAXIMUM OF THE JACOBIAN PROFILE Channel Frequency (cm -1 ) Pressure (hpa) at Related atmospherc varable(s) peak lower HWHM hgher HWHM AIRS temperature AIRS temperature and water vapour AIRS ozone AIRS water vapour AIRS temperature HIRS temperature HIRS temperature HIRS surface temperature and cloud detecton HIRS ozone HIRS water vapour 10/27/2006 Page 20

21 10/27/2006 Page 21 Dstrbuton of goodness of ft measure m for four bounded ranges. % = = = / N N ref y ref y y m cases