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 vanDelst, 陳雯美 沈彥志 曹伶伶 馮欽賜

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Overview

• History

• Current system

• Ongoing / future development

• Recent application at CWB

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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

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GSI & SSI

• Gain: freedom in spatial variation of covariancePrice: 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 3D 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.

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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 3DVAR– Supports WRF and NCEP infrastructure

– transition to ESMF

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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

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Basic Analysis Problem

Analysis system produces an analysis through the minimization of an objective function given by

J = xT B-1 x + ( H x – y ) T R-1 ( H x – y ) = Jb + Jo

Where

x is a vector of analysis increments,

B is the background error covariance matrix,

y is a vector of the observational residuals, y = y obs – H xguess

R is the observational and representativeness error covariance matrix

H 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

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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

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Moisture analysis1) 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

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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

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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.

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Tangent Linear Normal Mode Constraint

• Performs correction to increment to reduce gravity mode tendencies

• Applied during minimization to increment, not as post-processing 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)

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Surface Pressure Tendency

Zonal-average surface pressure tendency for guess (green), unconstrained GSI analysis (red), and GSI analysis with TLNMC (purple).

Substantial increase without constraint

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Fits of Surface Pressure Data in Parallel Tests

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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 hPa 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)

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Impact of TLNMC on 500 hPa AC Scores

500 hPa Geo. Height AC Scores for period 01 Dec. 2006 to 14 Jan. 2007

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Short Term Forecast Improvement

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Background error, B• Multivariate balance relationship with stream

function, temperature: Tb = Gvelocity potential: b = c surface pressure: 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.

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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.

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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

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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 9h-3h differences

– Variance increased in regions of rapid change

– Variance decreased in “calm” regions

– Global mean variance ~ preserved

• Discussion: subjective part of background error estimation

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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 3d capability, both globally and regionally

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Observation influence extends into mountains

indiscriminately

Anisotropic vs Isotropic Error Covariances

Observation influence restricted to areas of similar elevation

Error Correlations Plotted Over Utah Topography

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Assimilated data types

– Sondes, ship reports, surface stations, aircraft data, profilers, etc

– Cloud drift and water vapor winds

– TOVS, ATOVS, AQUA, METOP and GOES sounder brightness temperatures

– SBUV ozone profiles and total ozone

– SSM/I and QuikScat surface winds

– SSM/I and TMI rain rates

– GPSRO

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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

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Reflectivity QC

Before After

KFWS 1995-04-20.0453Z

(KFWS = Fort Worth, Texas)

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GSI development: Analysis variables

• SST analysis– Physical retrieval from AVHRR Tb data

– Option to add / assimilate in-situ SST data

Slight, but consistent reduction in rms and bias fits to independent buoy SST data

rms

bias

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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

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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 0.005mb, benefit regional system

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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

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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

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GSI development: Additional developments

• Improved balance– Add dynamical constraint– Reformulate balance relationship

• Advanced data assimilation techniques– 4DVAR

• GMAO is developing tangent linear and adjoint of GSI

– Hybrid ensemble• ensemble component added to 3DVAR

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中央氣象局全球資料同化系統之更新評估

陳雯美 1 沈彥志 1 曹伶伶 1 馮欽賜 2 吳婉淑 3

1 中央氣象局氣象科技研究中心2 中央氣象局氣象資訊中心

3 美國國家環境預報中心環境模擬中心

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全球資料同化系統

數值預報模式 中央氣象局作業全球數值預報模式 t240l30

分析系統 SSI(Spectral Statistical Interpolation)系統 – 由 NCEP引進

觀測資料 major run 即時接收處理的 GTS電碼資料 ( 傳統觀測資料 ) 及 CIMSS 的高解析度衛星風資料 post run NCEP ftp site 的 NCEP 作業使用的觀測資料 (6小時左右延遲 )

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model8-day forecast

model 6hr-forecast(first guess of

next major/post run)

全球資料同化 / 預報系統

observations(data cut=3hrs)

Major run

observations(data cut=8hrs)

post run

first guess (6hr-forecast of

pre-6hr post run)

analysis system

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全球資料同化系統的更新

• 引進 NCEP GSI 分析系統更新作業 SSI 分析系統

• GSI(Gridpoint Statistical Interpolation) - 在 SSI 的基礎下發展，均為三維變分分析系統 - 在物理網格上進行分析 - 分析變數不同 - 背景場誤差以 recursive filter 處理，直接在物理網格上定義，可為 非均勻及非均向，較接近真實大氣 - 同化技術的改善，包括觀測資料的使用策略、 QC 、 cost function 最小化、風場與質量場平衡之強約束、同化新觀測類別、 GPSRO

同化 技術、新的衛星資料 forward model 等。 - 適用全球及區域同化系統 - 為 NCEP作業之全球及區域同化系統的分析系統，持續發展中

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背景場誤差特性 ssi v.s. gsiT_innovaton=1°C at lat=45°,lon=180°, 500hPa

SSI T ana increment SSI induced U ana increment

GSI T ana increment GSI induced U ana increment

南北垂直剖面 南北垂直剖面

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分析參數的調整測試• 風場與質量場平衡之強約束

動力平衡參數調整： 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

nvmodes_keep=0 nvmodes_keep=4

nvmodes_keep=16 nvmodes_keep=30

Temperature analysis increments

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對預報的影響 500hPa 高度場一至七天預報距平相關

夏季 冬季北半球 北半球

南半球 南半球

+0.8%

+1.9%

+0.2%

+2.3%

+1.3%

+4.2%

+3.1%

+6.2%

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對預報的影響 溫度場預報 RMS error

夏季 冬季

北半球 北半球

南半球 南半球

day 5

day7

day 5

day7

day 5

day7

day 5

day7

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對預報的影響 - 熱帶地區 U-comp rms error

夏季月份 冬季月份

day 3

day5

day 3

day5

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總結• 單點觀測資料測試顯示 GSI背景場誤差的水平及垂直尺度均較 SSI小，且在目

前的設定下分析增量也較 SSI 小。

• 動力平衡參數測試顯示此參數除了與分析的垂直解析度有關，與觀測資料量及種類均有關係，增加新觀測資料的同化必須考慮其調整。

• GSI 同化系統平行測試結果顯示： - 對分析而言與作業差異不大。 主要的差異分佈在熱帶地區和南半球。 - 對預報而言 , GSI 對熱帶地區預報與作業的表現相當，對南、北半球的預報

能力則均有提昇 , 符合上線作業的標準。 距平相關與溫度的 RMS 均顯示平行測試較作業的預報表現好 , 南半球尤其明顯 北半球五天與七天預報 AC 為持平及約 2%的改善 南半球五天與七天預報 AC 有 1-3%及 4-6%的改善 , 較北半球明顯。 • 新系統已於 2010.7.28 上線作業。

• 未來將以 GSI 新系統為基礎，持續進行 新觀測資料的使用、背景場誤差的更新、分析參數的微調、分析系統的更新等測

試研究，提昇分析的品質，以提高模式的預報成効。