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ECMWF DA/SAT Training Course, May The Operational Data Assimilation System Lars Isaksen, Data Assimilation, ECMWF Overview of the operational data assimilation cycle Computational issues Observations used by the ECMWF Assimilation System Multi-incremental 4D-Var Why is 4D-Var performing better than 3D-Var? Recent improvements of ECMWFs Assimilation System Near future data assimilation implementations Content of talk

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ECMWF DA/SAT Training Course, May Data assimilation system The observations are used to correct errors in the short forecast from the previous analysis time. Every 12 hours we assimilate 7 – 9,000,000 observations to correct the 80,000,000 variables that define the models virtual atmosphere. This is done by a careful 4-dimensional interpolation in space and time of the available observations; this operation takes as much computer power as the 10-day forecast.

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ECMWF DA/SAT Training Course, May The operational configuration at ECMWF Configuration: Deterministic model: T1279L91 (~16km) Outer loop of 4D-Var T1279L91 and inner loops T159/T255/T255 (~125km/80km/80km) EPS target resolution T639L62 (to 10 days) and T319L62 thereafter Wave model (25km and 36 directions) Implemented in operations 26 January 2010

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ECMWF DA/SAT Training Course, May Extract data for 12h period UTC 70sec (min. 8x1PEs) Pre-process satellite data. Cloud clearing. Scatterometer winds. 340sec (min. 16x1PEs) Observation pre-processing for 0000UTC main cycle

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ECMWF DA/SAT Training Course, May Analysis and forecast for 0000UTC main cycle BUFR to ODB. 200sec 4x(8-16PEs) Fetch background forecast 275sec 2x(1PE) Analysis: trajectory, minimization and update 4320sec (3072PEs) 10 day forecast t-steps 3070sec (3072PEs) (or 15h fc for cycling: 260sec) Surface analysis. 1010sec 4x(1PEs) 430s 260s 880s 270s 820s 490s 1110s

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ECMWF DA/SAT Training Course, May The ECMWF operational schedule

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ECMWF DA/SAT Training Course, May Operational schedule Early delivery suite introduced June hFC 6h 4D-Var 21-03Z 00 UTC analysis (DA) T day forecast 51*T639/T399 EPS forecasts 03:40 04:00 04:40 06:05 05:00 Disseminate 06:35 Disseminate 02:00 12h 4D-Var, obs 09-21Z 18 UTC analysis 03:30 3hFC 6h 4D-Var 9-15Z 12 UTC analysis (DA) T day forecast 51*T639/T399 EPS forec. 15:40 16:00 16:40 18:05 17:00 Disseminate 14:00 12h 4D-Var, obs 21-09Z 06 UTC analysis 15:30

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ECMWF DA/SAT Training Course, May Data extraction Thinning Some data is not used to avoid over-sampling and correlated errors Departures and flags are still calculated for further assessment Blacklisting Data skipped due to systematic bad performance or due to different considerations (e.g. data being assessed in passive mode) Departures and flags available for further assessment Model/4D-Var dependent QC First guess based rejections VarQC rejections Used data Increments Check out duplicate reports Ship tracks check Hydrostatic check Analysis

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ECMWF DA/SAT Training Course, May Conventional observations used MSL Pressure, 10m-wind, 2m-Rel.Hum. DRIBU: MSL Pressure, Wind-10m Wind, Temperature, Spec. Humidity PILOT/Profilers: Wind Aircraft: Wind, Temperature SYNOP/METAR/SHIP: Radiosonde balloons (TEMP): Note: We only use a limited number of the observed variables; especially over land.

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ECMWF DA/SAT Training Course, May Satellite data sources used in the operational ECMWF analysis Geostationary, 4 IR and 5 winds 5 imagers: 3xSSM/I, AMSR-E, TMI 4 ozone 13 Sounders: NOAA AMSU-A/B, HIRS, AIRS, IASI, MHS 2 Polar, winds: MODIS 3 Scatterometer sea winds: ERS, ASCAT, QuikSCAT 6 GPS radio occultation

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ECMWF DA/SAT Training Course, May Significant increase in number of observations assimilated Conventional and satellite data assimilated at ECMWF

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ECMWF DA/SAT Training Course, May The observation operator Observations are not made at model grid points Satellites often measure radiances, NOT temperature and humidity We calculate a model radiance estimate of the observation to enable comparison. This is done with the observation operator H. H may be a simple interpolation from model grid to observation location H may possibly perform additional complex transformations of model variables to radiance space for satellite data. Model T,u,v,q Observation Satellite Radiance compare H Model radiance

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ECMWF DA/SAT Training Course, May Model Radiance The variational method allows model radiances to be compared directly to observed radiances Enables use of advanced observation operators Model T and q H compare Observation Satellite Radiance

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ECMWF DA/SAT Training Course, May J b : Ensures that the background model fields are adjusted meteorologically consistently in the region close to the observation location Increments due to a single observation of geopotential height at 1000hPa at 60N with value 10m below the background.

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ECMWF DA/SAT Training Course, May J b : The Balance Operator ensures the height and wind field balance is retained Increments for a single observation of geopotential height at 1000hPa. Left panel: wind increment near 300hPa. Right panel: wind increment about 150m above the surface. wind increments at 300hPa wind increments at 150 metre above surf.

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ECMWF DA/SAT Training Course, May Observation minus model differences are computed at the observation time using the full forecast model at T1279 (16km) resolution 4D-Var finds the 12-hour forecast evolution that optimally fits the available observations. A linearized forecast model is used in the minimization process based on the adjoint method It does so by adjusting surface pressure, the upper-air fields of temperature, wind, specific humidity and ozone The analysis vector consists of 80,000,000 elements at T255 resolution (80km) 4D-Var implementation used at ECMWF All observations within a 12-hour period (~9,000,000) are used simultaneously in one global (iterative) estimation problem 09Z 12Z 15Z 18Z 21Z

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ECMWF DA/SAT Training Course, May D-Var incremental formulation Courtier, Thépaut and Hollingsworth (1994) The i-summation is over N=25 ½-hour long time slots of the 12-hour assimilation period. In the incremental formulation the cost function J is expressed in terms of increments x with respect to the background state, x=x-x b, at initial time. and are the TL of and, linearized around The innovations d i are calculated using the non-linear operators, H i and M i. This ensures the highest possible accuracy for the calculation of the innovations d i, which are the primary input to the assimilation!

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ECMWF DA/SAT Training Course, May Revision of operational 4D-Var algorithm Implementation: Inner/outer iteration algorithm Hessian pre-conditioning Conjug. Gradient minimisation Improved TL approximations Multi-incremental T159/T255/T255 These developments facilitate: Use of higher density data Higher resolution inner loop (T255) and outer loop (T1279) Enhanced use of (relatively costly) TL physics Cloud and rain assimilation More work has been done to improve the representation of the smallest scales in the inner loop – i.e. the analysis increments.

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ECMWF DA/SAT Training Course, May Multi-incremental quadratic 4D-Var at ECMWF T1279L91 T159L91 T255L91

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ECMWF DA/SAT Training Course, May D-Var with three outer loop: efficient, accurate and allows non-linearity T95 T159 T255 Analysis increments at 900hPa for temperature for each of the three minimizations. Plot shows 2009 setup. From 2010: T95 T159 and T799 T1279. Decreasing amplitude of increments: T95>T159>T255. Last analysis step adds small corrections where data density is highest. Note model and observation operators are re-linearized twice. Add T95 increment to T799 background and re-linearize M, H Add T159 increment and re-linearize M, H Add T255 increment = final T799 analysis

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ECMWF DA/SAT Training Course, May The atmosphere does not evolve in isolation, interactions between the atmosphere and the underlying land and ocean are also important in determining the weather. Ocean ice processes, ocean surface waves, land surface, soil, hydrological and snow processes are all represented at ECMWF in the most advanced operational Earth-system model available anywhere. These physical processes have smaller scales than the model grid (16 km) and are therefore represented by so-called Parametrization Schemes which represent the effect of the small-scale processes on the large-scale flow. Physical processes in the ECMWF model An accurate model representation of the atmosphere is an important part of the assimilation system

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ECMWF DA/SAT Training Course, May T1279 (16km) Since January ,140,704 grid-points per level Outer loop model resolution is now T1279L91 Important for accurate comparison against observations L60 L91 T799 (25km) ,490 grid-points per level

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ECMWF DA/SAT Training Course, May OPS (35r2) 980hPa (35r3) Use of improved QC (Huber norm) 961hPa (36r1) High-res system T1279+T159/T255/T hPa Hurricane Bill, 20 Aug Observed MSL pressure~944hPa Resolution and QC benefits analysis of extreme events Improved hurricane analyses due to Huber norm and resolution

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ECMWF DA/SAT Training Course, May Can we use our parallel computers efficiently? Scalability of IFS model – T1279 L91 Cores Nodes

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ECMWF DA/SAT Training Course, May D-Var is more difficult to parallelize efficiently T1279 model =2304 cores ideal T1279 model T255an T1279obs T159an =1728 cores=1152 cores=576 cores

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ECMWF DA/SAT Training Course, May Parallel performance is important. Scalability is not perfect for the 4D-Var analysis 4D-Var T799 outer,T95/T255 inner, 91 levels on IBM system

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ECMWF DA/SAT Training Course, May Hurricane Lili. Surface scatterometer winds. An example how 4D-Var propagates information vertically No SCAT analysis NSCAT analysis First guess MSL pressure Analysis MSL pressure MSL pressure Analysis increments S.M. Leidner, L. Isaksen and R.S. Hoffman Impact of NSCAT Winds on Tropical Cyclones in the ECMWF 4DVAR assimilation system Mon. Wea. Rev. 131,1,3-26 (2003)

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ECMWF DA/SAT Training Course, May No SCAT analysis NSCAT analysis First guess MSL pressure S.M. Leidner, L. Isaksen and R.S. Hoffman Impact of NSCAT Winds on Tropical Cyclones in the ECMWF 4DVAR assimilation system Mon. Wea. Rev. 131,1,3-26 (2003) First guess MSL pressure Analysis MSL pressure Analysis increments Hurricane Lili. Surface scatterometer winds. An example how 4D-Var propagates information vertically

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ECMWF DA/SAT Training Course, May Surface scatterometer wind information is propagated vertically and improve the analysis. Due to flow-dependent structure functions in 4D-Var

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ECMWF DA/SAT Training Course, May D-Var is using more a-synoptic data than 3D-Var 4D-Var is using more data from frequently reporting stations. The plots show the use of SYNOP surface pressure observations. Column height gives the number of observations available, while the black part displays those actually used in the assimilation. 4D-Var SYNOP Screening 3D-Var SYNOP Screening 3D-Var is like 4D-Var without the time dimension. The analysis is performed at synoptic times only (0000, 0600, 1200 and 1800 UTC). Mostly only data valid a synoptic time is used.

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ECMWF DA/SAT Training Course, May D-Var versus 3D-Var and Optimum Interpolation 4D-Var is comparing observations with background model fields at the correct time 4D-Var can use observations from frequently reporting stations The dynamics and physics of the forecast model in an integral part of 4D-Var, so observations are used in a meteorologically more consistent way 4D-Var combines observations at different times during the 4D-Var window in a way that reduces analysis error 4D-Var propagates information horizontally and vertically in a meteorologically more consistent way 4D-Var more complex: needs linearized perturbation forecast model and its adjoint to solve the cost function minimization problem efficiently

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ECMWF DA/SAT Training Course, May Recent revisions to the assimilation system Use of many new satellites and new instruments (will be presented by Peter Bauer tomorrow) Variational bias correction of satellite radiances Adaptive bias correction for radiosondes and SYNOP pressure data Increased resolution from T799/ T95/T159/T255 to T1279/ T159/T255/T255 More advanced Tangent Linear physics scheme in 4D-Var Improved handling of supersaturation in the humidity analysis Huber norm Variational Quality Control Weak-constraint 4D-Var accounting for model error Advanced diagnostic tools to understand impact of observations on analysis/forecast: Forecast Sensitivity to Observations

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ECMWF DA/SAT Training Course, May First version (SSM/I radiances) 2005; extended to SSMIS, TMI, AMSR-E in 2007 Direct 4D-Var radiance assimilation from March 2009 Main difficulties: inaccurate moist physics parameterizations (location/intensity), formulation of observation errors, bias correction, linearity. 4D-Var first guess SSM/I Tb 19v-19h [K]SSM/I observational Tb 19v-19h [K] Improved assimilation of satellite moisture data Assimilation of rain-affected microwave

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ECMWF DA/SAT Training Course, May Humidity analysis improvements New humidity background error model: takes into account how humidity errors are affected by temperature errors in cloudy conditions (statistical relationship) extension of the humidity errors to cater for supersaturated conditions (with respect to ice) Changes in cloud cover spin-up. Monthly average zonal mean (Sep 2008) analysis minus a 15h forecast valid at the same time. Old New

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ECMWF DA/SAT Training Course, May Improved quality control of observations Huber-norm observation cost function Gaussian Huber norm (New operational) Gaussian + flat (operational) L1 metric far from centre, L2 metric close to centre. Robust method: a few erroneous observations does not ruin analysis Adds some weight on observations with large departures A set of observations with consistent large departures will influence the analysis Most obs-bg innovations follow Huber-norm distribut.

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ECMWF DA/SAT Training Course, May Q only applied in stratosphere. Cost function including model error and bias: Model error η Model bias (cycled) η b How to account for model error in 4D-Var First step is a weak-constraint 4D-Var that handles biases.

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ECMWF DA/SAT Training Course, May Weak-constraint 4D-Var formulation captures part of model error biases in the stratosphere AMSU-A first guess departures reduced

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ECMWF DA/SAT Training Course, May J is a measure of the forecast error (as defined through e.g. dry energy norm) Example: Impact of each observing system in ECMWFs 2009 assimilation system Enhance diagnostics of the assimilation system Forecast Sensitivity to Observations

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ECMWF DA/SAT Training Course, May Soil moisture assimilation using Ext. Kalman Filter Will be implemented in June 2010 Analysis increments (mm)

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ECMWF DA/SAT Training Course, May Ensembles of data assimilations Is being implemented now, first for EPS later for 4D-Var Run an ensemble of analyses with randomly perturbed observations and SST fields, and form differences between pairs of analyses (and short-range forecast) fields. These differences will have the statistical characteristics of analysis (and short-range forecast) error. To be used in specification of background errors = errors of the day. To indicate where good data should be trusted in the analysis (yellow shading). Also for initialization of the EPS!

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ECMWF DA/SAT Training Course, May Estimating Background Error Statistics from Ensembles of Data Assimilations (EDA) Run an ensemble of analyses with random observation and SST perturbations, plus stochastic model error representation. Form differences between pairs of background fields. These differences will have the statistical characteristics of background error (but twice the variance). AnalysisForecast x b +ε b AnalysisForecast x b +ε b AnalysisForecast x b +ε b AnalysisForecast x b +η b AnalysisForecast x b +η b AnalysisForecast x b +η b Background differences

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ECMWF DA/SAT Training Course, May To estimate analysis uncertainty To improve the initial perturbations in the Ensemble Prediction To calculate static and seasonal background error statistics To estimate flow-dependent background error in 4D-Var - errors-of-the-day To improve QC decisions and improve the use of observations in 4D-Var Why implementing Ensemble Data Assimilation?

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ECMWF DA/SAT Training Course, May Ongoing developments in data assimilation at ECMWF EKF for soil moisture analysis EDA to provide flow-dependent background error information to 4D-Var Vertical resolution increase planned for later in 2010 (~140+ levels TBD) Long window 4D-Var: extend to 24 hour window, improve model error term Improved assimilation of cloud/aerosols/rain observations Flow-dependent data selection Account for observation error correlations Modularisation of the IFS and scalability of the assimilation system

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ECMWF DA/SAT Training Course, May Summary of todays lecture Overview of the operational data assimilation cycle Computational issues Observations used by the ECMWF Assimilation System Multi-incremental 4D-Var Why is 4D-Var performing better than 3D-Var? Recent improvements of ECMWFs Assimilation System Near future data assimilation implementations

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