GSI Overview and Recent Application at CWB WanShu

GSI Overview and Recent Application at CWB Wan-Shu Wu NOAA/NWS/NCEP/EMC Acknowledgements: John Derber, Yong Han, Daryl Kleist, Dave Parrish, Manuel Pondeca, Jim Purser, Russ Treadon, Paul van. Delst, 陳雯美 沈彥志 曹伶伶 馮欽賜 11/17/2010 NCU (wu)

Overview • History • Current system • Ongoing / future development • Recent application at CWB 11/17/2010 NCU (wu) 2

History • The GSI system was initially developed as the next generation global analysis system – Wan-Shu Wu, R. James Purser, David Parrish • Three-Dimensional Variational Analysis with spatially Inhomogeneous Covariances. Mon. Wea. Rev. , 130, 2905 -2916. • Originally based on SSI analysis system – Replace spectral definition for background errors with grid point representation • Allows for anisotropic, non-homogenous structures • Allows for situation dependent variation in errors 11/17/2010 NCU (wu) 3

GSI & SSI • Gain: freedom in spatial variation of covariance Price: limited freedom in specifying the shape of the error statistics in wave number space. (The limitation is partially over come by applying multiple recursive filters for structure function) • In extra-tropics 3 D Var in physical space can be as effective as in spectral space. Spatial variation in error stats is beneficial to forecasts in the tropics. • Straightforward to apply to a regional domain. 11/17/2010 NCU (wu) 4

History • After initial global GSI development, EMC management express desire for single global/regional analysis system – Simplify exchange of ideas / developments between global and regional applications • Thus, current GSI is an evolutionary combination of the global SSI analysis system and the regional NMM 3 DVAR – Supports WRF and NCEP infrastructure – transition to ESMF 11/17/2010 NCU (wu) 5

History • Growing number of collaborators / users – NASA: GFSC (GMAO), MSFC – FSL, NESDIS, NCAR – University of Hawaii, Miami, Oklahoma, Utah, Wisconsin • Periodic updates based on submissions from developers – Previous update cycle was bi-monthly – SVN future updates as • System matures • Number of change requests increases 11/17/2010 NCU (wu) 6

Basic Analysis Problem Analysis system produces an analysis through the minimization of an objective function given by J = x. T B-1 x + ( H x – y ) T R-1 ( H x – y ) = Jb + Jo Where x B y R H is a vector of analysis increments, is the background error covariance matrix, is a vector of the observational residuals, y = y obs – H xguess is the observational and representativeness error covariance matrix is the transformation operator from the analysis variable to the form of the observations. Goal: make minimal adjustment of the first guess yet fit the information in the data 11/17/2010 NCU (wu) 7

Analysis (control) vector • xa = stream function, velocity potential, surface pressure, virtual temperature, normalized relative humidity, ozone mixing ratio, and cloud condensate mixing ratio – SSI uses • vorticity & divergence for the wind field • specific humidity for moisture • Ozone and cloud condensate are analyzed univariately • Moisture analysis may be univariate or multivariate 11/17/2010 NCU (wu) 8

Moisture analysis 1) Pseudo-relative humidity (Dee and Da Silva, 2002) • Normalize specific humidity by guess (background) saturation specific humidity q/qs(g) • Univariate moisture analysis 2) Normalized relative humidity (Holm et al. , 2002) • RH / (RHb) = RHb ( P/Pb + q /qb - T / b ) – (RHb) – standard deviation of background error as function of RHb – b = -1 / (RH)/ (T) – multivariate relation between moisture, temperature, and pressure 11/17/2010 NCU (wu) 9

Option 1: univariate • temperature increment forces increment in RH • near zero moisture increment Option 2: multivariate • temperature increment forces increment in q • near zero RH increment 11/17/2010 NCU (wu) 10

Tangent Linear Normal Mode Constraint • J = (x-xb)TB-1(x-xb) + (H(w)-y)T(E+F)-1(H(w)-y) • w = C(x-xb) – analysis state vector after incremental NNMI – C = Correction from Incremental nonlinear normal mode initialization (NNMI) • represents correction to analysis increment that filters out the unwanted “noise” • Based on: – Temperton, C. , 1989: “Implicit Normal Mode Initialization for Spectral Models”, MWR, vol 117, 436 -451. 11/17/2010 NCU (wu) 11

Tangent Linear Normal Mode Constraint • Performs correction to increment to reduce gravity mode tendencies • Applied during minimization to increment, not as postprocessing of analysis fields • Little impact on speed of minimization algorithm • CBCT becomes effective background error covariances for balanced increment – Adds implicit flow dependence • Requires time tendencies of increment – Implemented dry, adiabatic, generalized coordinate tendency model (TL and AD) 11/17/2010 NCU (wu) 12

Surface Pressure Tendency Substantial increase without constraint Zonal-average surface pressure tendency for guess (green), unconstrained GSI analysis (red), and GSI analysis with TLNMC (purple). 11/17/2010 NCU (wu) 13

Fits of Surface Pressure Data in Parallel Tests 11/17/2010 NCU (wu) 14

Implementation of GSI into GDAS • Extensive testing performed – Nearly two years of simulated days – Improvement over SSI based system in retrospective tests • • Hurricane tracks 500 h. Pa AC Scores & RMS Error Tropical Wind RMS Error CONUS Precipitation • Implemented 01 May 2007 – GSI with TLNMC – Data upgrade component (GSI became operational in June 2006 as regional analysis) 11/17/2010 NCU (wu) 15

Impact of TLNMC on 500 h. Pa AC Scores 500 h. Pa Geo. Height AC Scores for period 01 Dec. 2006 to 14 Jan. 2007 11/17/2010 NCU (wu) 16

Short Term Forecast Improvement 11/17/2010 NCU (wu) 17

Background error, B • Multivariate balance relationship with stream function, temperature: velocity potential: surface pressure: Tb = G b = c psb = W where, G = projects increments of stream function at one level to a vertical profile of balanced part of temperature increments. G is latitude dependent. c = coefficient that varies with latitude and height. W = integrates the appropriate contribution of the stream function from each level. 11/17/2010 NCU (wu) 18

Background error estimation • “NMC” method – Use 48 & 24 hour forecasts verifying at same time as a proxy for estimating the background error – Originally developed for SSI because • background error represented in spectral space • not clear at that time (1992) how to derive B-1 from innovation statistics as done with OI – Has worked surprisingly well in SSI • Not clear that NMC method is best approach for estimating parameters in GSI. – For time being use NMC method to estimate statistical balance between , T, , and ps. 11/17/2010 NCU (wu) 19

Background error estimation • For SSI, – complete spectrum of correlation estimated, along with latitude-dependent variances – physical space correlations are isotropic, homogeneous • For GSI, – only correlation length and variance estimated, but both can be functions of position – physical scale correlations may be anisotropic, non -homogeneous 11/17/2010 NCU (wu) 20

Flow Dependent B (variances) • One motivation for GSI was to permit flow dependent variability in background error • Example: take advantage of FGAT (guess at multiple times) to modify variances based on 9 h-3 h differences – Variance increased in regions of rapid change – Variance decreased in “calm” regions – Global mean variance ~ preserved • Discussion: subjective part of background error estimation 11/17/2010 NCU (wu) 21

GSI development: Background errors • Anisotropic, situation dependent background errors – 2 -dvar capability currently exists in GSI • Will be used for regional (US) surface analysis – Extending to full 3 d capability, both globally and regionally 11/17/2010 NCU (wu) 22

Anisotropic vs Isotropic Error Covariances Error Correlations Plotted Over Utah Topography Observation influence extends into mountains indiscriminately 11/17/2010 Observation influence restricted to areas of similar elevation NCU (wu) 23

Assimilated data types – Sondes, ship reports, surface stations, aircraft data, profilers, etc – Cloud drift and water vapor winds – TOVS, AQUA, METOP and GOES sounder brightness temperatures – SBUV ozone profiles and total ozone – SSM/I and Quik. Scat surface winds – SSM/I and TMI rain rates – GPSRO 11/17/2010 NCU (wu) 24

GSI development: Doppler radar data • Code being developed to handle radar radial velocities – data processing, quality control, and superobs issues • Longer term project is to make use of radar reflectivities – Currently working on quality control issues • Bird migration, ground clutter, anomalous propagation, etc 11/17/2010 NCU (wu) 25

Reflectivity QC Before After KFWS 1995 -04 -20. 0453 Z (KFWS = Fort Worth, Texas) 11/17/2010 NCU (wu) 26

GSI development: Analysis variables • SST analysis – Physical retrieval from AVHRR Tb data – Option to add / assimilate in-situ SST data rms Slight, but consistent reduction in rms and bias fits to independent buoy SST data 11/17/2010 bias NCU (wu) 27

GSI development: GPS radio occultation • COSMIC – assimilating local refractivities – tests on local bending angle • QC issues – Tracking errors • Caused by complicated refractivity structure in moist lower troposphere – Super-refraction • Occurs on sharp top of moist PBL 11/17/2010 NCU (wu) 28

GSI development: CRTM development • Proto-type CRTM with modular design – Simplifies user interaction with code – Permits easier evaluation of various algorithms • also include – Algorithms to handle scattering and absorption from clouds for microwave channels • Default climatology in the upper atmosphere – Up to 0. 005 mb, benefit regional system 11/17/2010 NCU (wu) 29

GSI development: Observation errors • Improved specification of observational errors – Plan to examine situation dependent representativeness errors – Will increase granularity in the specification of observation errors • For example, all sonde data has same observation error independent of sonde type. – Could (should) vary error as function of sonde type 11/17/2010 NCU (wu) 30

Adaptive Tuning of Observation errors • Talagrand (1997) on E ( J (Xa) ) • Desroziers & Ivanov (2001) E( Jo )= ½ Tr ( Ip – HK) E( Jb )= ½ Tr (KH) where Ip is identity matrix with order p K is Kalman gain matrix H is linearlized observation forward operator • Chapnik et al. (2004): robust even when B is incorrectly specified 11/17/2010 NCU (wu) 31

GSI development: Additional developments • Improved balance – Add dynamical constraint – Reformulate balance relationship • Advanced data assimilation techniques – 4 DVAR • GMAO is developing tangent linear and adjoint of GSI – Hybrid ensemble • ensemble component added to 3 DVAR 11/17/2010 NCU (wu) 32

全球資料同化/預報系統 first guess observations (data cut=3 hrs) (6 hr-forecast of pre-6 hr post run) Major run observations (data cut=8 hrs) post run analysis system model 8 -day forecast 11/17/2010 model 6 hr-forecast (first guess of next major/post run) NCU (wu) 35

背景場誤差特性 ssi v. s. gsi T_innovaton=1°C at lat=45°, lon=180°, 500 h. Pa SSI T ana increment SSI induced U ana increment 南北垂直剖面 GSI T ana increment 11/17/2010 南北垂直剖面 GSI induced U ana increment NCU (wu) 37

分析參數的調整測試 Temperature analysis increments • 風場與質量場平衡之強約束 動力平衡參數調整： nvmodes_keep=0 nvmodes_keep=4 nvmodes_keep=16 nvmodes_keep=30 動力平衡強約束項TLNMC(Tangent. Linear Normal Mode Constrain)中 調整平衡關係使用的mode個數的參 數: nvmodes_keep 為一經驗值, 與分析的垂直解析度有 關, 必須針對 CWB GFS的垂直解析 度調整 11/17/2010 NCU (wu) 38

對預報的影響- 熱帶地區U-comp rms error 夏季月份 冬季月份 day 5 day 3 11/17/2010 day 3 NCU (wu) 41