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**The Operational Data Assimilation System**

Lars Isaksen, Data Assimilation, ECMWF Content of talk 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 ECMWF’s Assimilation System Near future data assimilation implementations

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**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 model’s 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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**The operational configuration at ECMWF**

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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**Observation pre-processing for 0000UTC main cycle**

Extract data for 12h period UTC 70sec (min. 8x1PEs) Pre-process satellite data. Cloud clearing. Scatterometer winds. 340sec (min. 16x1PEs)

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**Analysis: trajectory, minimization and update 4320sec (3072PEs)**

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

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**The ECMWF operational schedule**

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**Operational schedule Early delivery suite introduced June 2004**

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

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**Model/4D-Var dependent QC**

Data extraction 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 Check out duplicate reports Ship tracks check Hydrostatic check Thinning Some data is not used to avoid over-sampling and correlated errors Departures and flags are still calculated for further assessment Model/4D-Var dependent QC First guess based rejections VarQC rejections Used data Increments Analysis

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**Conventional observations used**

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

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**Satellite data sources used in the operational ECMWF analysis**

13 Sounders: NOAA AMSU-A/B, HIRS, AIRS, IASI, MHS 5 imagers: 3xSSM/I, AMSR-E, TMI 3 Scatterometer sea winds: ERS, ASCAT, QuikSCAT Geostationary, 4 IR and 5 winds 4 ozone 2 Polar, winds: MODIS 6 GPS radio occultation

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**Significant increase in number of observations assimilated**

Conventional and satellite data assimilated at ECMWF

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**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 H Model radiance compare Observation Satellite Radiance

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The variational method allows model radiances to be compared directly to observed radiances Enables use of advanced observation operators Model T and q Observation Satellite Radiance H Model Radiance compare

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Jb: 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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**Increments for a single observation of geopotential height at 1000hPa. **

Jb: The Balance Operator ensures the height and wind field balance is retained wind increments at 300hPa wind increments at 150 metre above surf. 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.

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**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 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) The size of the control vector is approx 8M. 09Z Z Z Z Z

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**4D-Var incremental formulation Courtier, Thépaut and Hollingsworth (1994)**

In the incremental formulation the cost function J is expressed in terms of increments x with respect to the background state, x=x-xb, at initial time. and are the TL of and , linearized around The innovations di are calculated using the non-linear operators, Hi and Mi . The i-summation is over N=25 ½-hour long time slots of the hour assimilation period. This ensures the highest possible accuracy for the calculation of the innovations di , which are the primary input to the assimilation!

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**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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**Multi-incremental quadratic 4D-Var at ECMWF**

T1279L91 T159L91 T255L91

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**4D-Var with three outer loop: efficient, accurate and allows non-linearity**

Analysis increments at 900hPa for temperature for each of the three minimizations. Plot shows 2009 setup. From 2010: T95T159 and T799T1279. 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. T95 Add T95 increment to T799 background and re-linearize M, H T159 Add T159 increment and re-linearize M, H T255 Add T255 increment = final T799 analysis

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Physical processes in the ECMWF model An accurate model representation of the atmosphere is an important part of the assimilation system 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.

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**Outer loop model resolution is now T1279L91 Important for accurate comparison against observations**

T799 (25km) 843,490 grid-points per level L91 L60 T1279 (16km) Since January 2010 2,140,704 grid-points per level

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Resolution and QC benefits analysis of extreme events Improved hurricane analyses due to Huber norm and resolution (35r3) Use of improved QC (Huber norm) 961hPa OPS (35r2) 980hPa Hurricane Bill, 20 Aug. 2009 Observed MSL pressure~944hPa (36r1) High-res system T1279+T159/T255/T255 945hPa

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**Scalability of IFS model – T1279 L91**

Can we use our parallel computers efficiently? Scalability of IFS model – T1279 L91 Nodes Cores

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**4D-Var is more difficult to parallelize efficiently**

ideal T1279 model T1279 model T255an T1279obs T159an T1279obs =576 cores =1152 cores =1728 cores =2304 cores

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**Parallel performance is important**

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 512 768 1024 1536

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**Hurricane Lili. Surface scatterometer winds**

Hurricane Lili. Surface scatterometer winds. An example how 4D-Var propagates information vertically First guess MSL pressure Analysis MSL pressure MSL pressure Analysis increments NSCAT analysis No SCAT analysis 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 4DVAR assimilation system’ Mon. Wea. Rev. 131,1,3-26 (2003)**

Hurricane Lili. Surface scatterometer winds. An example how 4D-Var propagates information vertically First guess MSL pressure First guess MSL pressure Analysis MSL pressure MSL pressure Analysis increments NSCAT analysis No SCAT analysis 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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Surface scatterometer wind information is propagated vertically and improve the analysis. Due to flow-dependent structure functions in 4D-Var

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**4D-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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**4D-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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**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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**Improved assimilation of satellite moisture data**

Assimilation of rain-affected microwave 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]

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**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) Old New Changes in cloud cover spin-up. Monthly average zonal mean (Sep 2008) analysis minus a 15h forecast valid at the same time.

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**Improved quality control of observations Huber-norm observation cost function**

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. Gaussian Huber norm (New operational) Gaussian + flat (operational)

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**How to account for model error in 4D-Var**

First step is a weak-constraint 4D-Var that handles biases. Q only applied in stratosphere. Cost function including model error and bias: Model error η Model bias (cycled) ηb

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**Weak-constraint 4D-Var formulation captures part of model error biases in the stratosphere**

AMSU-A first guess departures reduced

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**Enhance diagnostics of the assimilation system**

Forecast Sensitivity to Observations J is a measure of the forecast error (as defined through e.g. dry energy norm) Example: Impact of each observing system in ECMWF’s assimilation system

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**Analysis increments (mm)**

Soil moisture assimilation using Ext. Kalman Filter Will be implemented in June 2010 Analysis increments (mm)

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**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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**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). Analysis Forecast xb+εb Analysis Forecast xb+ηb Background differences

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**Why implementing Ensemble Data Assimilation?**

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

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**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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**Summary of today’s 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 ECMWF’s Assimilation System Near future data assimilation implementations

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