Data Assimilation Strategies for Operational NWP at Meso-scale and Implication for Nowcasting Thibaut MontmerleCNRM-GAME/GMAPWMO/WWRP Workshop on Use of NWP for NowcastingUCAR, Boulder, CO, USA, 24-26 October, 2011

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IntroductionNon-hydrostatic models (in the 1-3 km horizontal resolution range) allow realistic representation of convection, clouds, precipitation, turbulence, surface interactionsSimulation of a MCS performed with AROMESuch models have specific features that make their operational implementation difficult: They need coupling models to provide LBC and surface conditions They are expensive in computation time Forecasts need to be frequently corrected towards observations to provide the best initial state possible through data assimilation (DA) The presence of many strongly non-linear processes, especially those related to diabatic phenomena, makes the DA task delicate

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Introduction: requirements for NowcastingNowcasting algorithms require the best description of the atmospheric state at a particular time and the best very short term forecast available.

=> To answer to those specifications, operational NWP systems at convective scale have to:

1. provide the best analyses as possible frequentlyThe DA algorithm needs to be fast and efficientA comprehensive set of observation types describing the clear air environment as well as convective systems should be usedThe use of these observations must be as optimal as possible

2. provide physically meaningful forecasts spin-up time must be as short as possiblemaintain a realistic development of the analysed structures

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Outlines1. Introduction 2. Elements of NWP at convective scale- DA algorithms- error covariances- observations and observation operators

3. Example of NWP system at convective scale: AROME

4. Requirements for Nowcasting purposes

5. Conclusions

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DA aims in retrieving the best initial state (or analysis xa) from a previous forecast xb and from various observations yo, the weight of these two entities being given by their respective error covariances B and R.

Elements of NWP at convective scale : DA algorithms B has a key role in DA, by smoothing and spreading the information brought by observations, and by propagating this information to other control variables through balance relationships. Resolving this equation explicitely is infeasible because of the huge dimension of the system in meteorology 2 different approaches can be considered to solve the BLUE: sequential or variationalIf the model trajectory is supposed linear in the vicinity of the background, and if background and observation errors are decorrelated, the analysis is given by the BLUE equation:

Where H is the non-linear observation operator that simulates the observation from the background, and H its linearized version.

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The sequential approaches These methods are based on the Kalman Filter that assimilates observations sequentially.Methods such as the EnKF (Evensen 1994) allow to compute B (or Pf ) in the BLUE by approximating the dispersion of an ensemble of forecast.

Advantages: easy to implement, well suited to parallel computing avoid the computation of the TL/AD version of the modelDrawbacks: severe sampling noise in the raw covariances need to be empirically filtered which brings loss of information sampling errors: the filter can collapse in case of misrepresentation of model error in the filter update very expensive in computation time, especially for CRMs !

Elements of NWP at convective scale : DA algorithms

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Minimization is achieved using the adjoint method based on grad(J(x))

+ All observations within a time window are used to find the new trajectory.+ only one forecast/loop is performedVariational approaches such as 4DVar aim in seeking the minimum of a cost function, which satisfies theoritically the BLUE equation:- B is not flow-dependent but has to be calibrated beforehand - TL/AD version of the model has to be developed to compute grad(J(x))

Elements of NWP at convective scale : DA algorithms

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At convective scale, most of operational NWP centers (MF, UKMO, NCEP) use 3DVar schemes with short assimilation/forecast cycles to limit the gap in time between observations and the forecast to be corrected+ Cheap, fast, no TL/AD of M- no integration in time: only observations valid around the analysis time are considered- as in 4DVar, B is not flow dependent

Elements of NWP at convective scale : DA algorithms

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Elements of NWP at convective scale : DA algorithmsOther possible aproaches:

Hybrid EnVAR: modulation of the static B by filtered covariances computed from an ensemble

3DVarFGAT : allows to compare the observations and the background at the right time (as in 4DVar), but supposes that innovations (obs-guess) are constant in time (as 3DVar: no TL/AD of M)=> Suitable for moving observations, not for static measurements for which the analysis is like a mean of the successive innovations

Nudging Latent Heat Nudging (LHN) allows to retrieve atmospheric profiles consistent with radar derived precipitation rates (oper at UKMO and DWD). RR uses a cloud analysis in order to update cloudy variables that are not considered in the 3DVar. Although retrieved fields are subject to possible inconsistencies with analyzed ones from VAR, nudging is a simple way to take observations of hydrometeors into account.

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Elements of NWP at convective scale : error covariancesRepresentation of the background error covariances matrix B: The true state needed to measure error against is unknown. Differences between forecasts (from different forecast terms or from an ensemble) are generally considered to mimic climatological forecast errors. Because of its size, B can be neither estimated at full rank nor stored explicitly => covariances have to be modelled

B is generally splitted in one balance operator (e.g. geostrophic balance) and one spatial transform, aiming in projecting each parameter onto uncorrelated spatial modes, and then in dividing by the square root of the variance of each mode

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The gap with the geostrophic balance in B increases with precipitation intensities(Carron and Fillon (2010))

Forecast errors of variables linked to clouds and precipitations are inhomogeneous, anisotropic and flow dependent=> Works, mainly based on ensembles, are ongoing in order to add flow dependency to BElements of NWP at convective scale : error covariancesCross covariances between forecast errors of q (y-axis) and divu (x-axis)B OPERMontmerle and Berre (2010) have for instance shown that forecast errors in rain strongly differ from climatological values and reflect diabatic processesMain challenges at convective scale for B: Balance constraints, that were initially developed for DA in global models, are likely to be inadequate, especially in convection

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Elements of NWP at convective scale : error covariancesMuch less attention is given to the representation of the observation error covariances matrix R: diagonal elements (variances) must represent instrumental errors, representativeness and precision errors of H off-diagonal (spatial or inter-channel correlations) are generally neglected. They can however be inferred by a comparison with other observations or with the background (innovations).

IASI inter-channel correlations (Bormann et al, ECMWF, 2011)To ensure the basic hypotheses of the BLUE, a spatial thinning and/or an inflation of variances are applied to prevent possible observation error correlations between adjacent pixels.

It has however been shown that correlated observations are less informative than uncorrelated observations, even if R is well specified

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Elements of NWP at convective scale : observation operatorsTo consider an observation type in DA, the observation operator H and its TL/AD versions have to be developed. Example of the main observation types considered in the operational AROME-France model

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OBS: Z &Wind retrievalBousquet, Montmerle and Tabary 2007AROMELow-level divergenceanalysesWithout VrWith VrElements of NWP at convective scale : observation operatorsExample: radial velocities

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Elements of NWP at convective scale : observation operatorsRadar reflectivities: Very difficult task: weak correlation with hydrometeor contents, strongly nonlinear microphysical processes to be included in H , non-Gaussian error distributions, complex forecast errors. Methods that use precipitation rates: Diabatic DFI and LHN

Other methods allowing to retrieve hydrometeor contents using a nudging approach or directly in 3DVar (Xiao et al (2007)) or in 4DVar (Sun and Crook (1997)) have also been tested on case studies.

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Specific humidity incrementSimulated Z - 3h forecast rangeRadarElements of NWP at convective scale : observation operators6h UTC9h UTCWith ZWithout ZIllustration of the 1D+3DVar assimilation of radar reflectivities(E. Wattrelot)

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Elements of NWP at convective scale : observation operatorsSatellite observations are the main observation type in terms of number and impact in global models IR and MW radiances allow to retrieve q and T profiles with a vertical resolution that depends on the spectral resolution of the instrument Radiances are strongly sensitive to surface conditions and IR measurements are contaminated by clouds other very interesting products such as winds derived from scatterometers or AMV, integrated q from GPSRO, cloud types...

Guidard et al., 2011

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Outlines1. Introduction 2. Elements of NWP at convective scale- DA algorithms- error covariances- observations and observation operators

3. Example of NWP system at convective scale: AROME

4. Requirements for Nowcasting purposes

5. Conclusions

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Example of operational NWP system : AROME-France The non-hydrostatic AROME NWP system became operational at the end of 2008 with a 2.5 km horizontal resolution Lateral boundaries are provided by the global ARPEGE model that has a horizontal resolution around 10 km over France

ARPEGE Global domain AROME France domain

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Example of operational NWP system : AROME-France 3h assimilation/forecast cycles, own surface analysis No temporal dimension in 3DVar: only the closest observations to the assimilation time are considered A temporal gap between forecast and observations from moving platforms is allowed within the +/- 1h30 interval

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Used observations : 24 Doppler radars, growing number of satellite dataTime evolution of monthly values since sept. 2008Efforts are ongoing to assimilate more GPS ZTD data, more channels over land (smaller thinning boxes, better characterization of surface conditions) and to consider cloudy radiances in DA.Example of operational NWP system : AROME-France

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Example of forecast : 6th of October 2011 r12, 12h simulation. Narrow frontal rainband evolving in stratiform precipitationsAROME Z850hPaRadar MosaicExample of operational NWP system : AROME-France

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Example of forecast : 26th of Aug. 2011 r12, 12h simulationComplex LS circulation: Frontal rainband associated with a cyclogenesis over France, stationary convection due to orography in the Rhne basin => Such forecasts clearly demontrates the potential of convective scale NWP for nowcasting applicationsExample of operational NWP system : AROME-France

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Outlines1. Introduction 2. Elements of NWP at convective scale- DA algorithms- error covariances- observations and observation operators

3. Example of NWP system at convective scale: AROME

4. Requirements for Nowcasting purposes

5. Conclusions

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Requierements for Nowcasting purposesCurrent NWP systems at convective scales are not optimal for Nowcasting applications, especially because of too late availability of analyses and forecasts due to : the waiting of LBCs from the coupling model => forecasts from former analysis time must be used the cut-off time => some observations must be sacrified and/or shorter cycle frequencies must be considered the computational time of analysis and forecast => smaller domains or older forecast must be used

A degraded version of AROME has been developed with these specifications (AROME-PI: remember Ludovic Augers talk)

The spin-up of the model=> Initialization procedures and more optimal background error covariances must be applied

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Requierements for Nowcasting purposesSpin-up reduction 1/2Lapse of time necessary for the models equation to be in balance. Can be due to : Inconsistency between LBCs and the models state inside the computational domain=> Can be reduced by considering the analysis as coupling file at t=0 imbalances of analysis increments=> Improvements can be found using ensemble assimilation to compute B=> Flow-dependency of the balance operator should be better represented in BHere OPER uses a climatological B matrix, whereas EXP uses in addition forecast errors representative of precipitations exclusively in rain

(following the heterogeneous B matrix formulation of Montmerle and Berre (2010))OPEREXPNoise = mean absolute sfc pressure tendency (hPa/h)

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Spin-up reduction 2/2 imbalances between analyzed and non-analyzed fields (e.g. dynamics, T and q vs. microphysical or NH variables)=> The resulting numerical waves can be filtered out by digital filters (DFI or incDFI) or by adding fractions of increments within the assimilation window (Incremental Analysis Update, operational at UKMO)Requierements for Nowcasting purposesEfficient methods to reduce spin-up but, for AROME, forecast scores are degraded so far. Small scale analyzed structures (e.g low level convergence) are also considerably smoothed.P. Brousseau

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Requierements for Nowcasting purposes1h-cycle Allows to consider observations with high temporal frequencies while keeping a 3DVar assimilation system possible if spin-up is sufficiently reduced

Operational in RUC/RR. At MF, tests are ongoing using IAU or DFI but so far, scores are degraded compared to 3h-cycle. Possible explanations: cycling of residual numerical waves difficulty to tune values of observation vs. background errorsobs-analysisobs-guess1h cycle3h cycleP. Brousseau

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Outlines1. Introduction 2. Elements of NWP at convective scale- DA algorithms- error covariances- observations and observation operators

3. Example of NWP system at convective scale: AROME

4. Requirements for Nowcasting purposes

5. Conclusions

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Feedback from operational NWP at convective scale: 3DVar used at high frequency is the most frequent choice for DA because of its low computational cost and its (relative) simplicity Adequate balances and flow dependency is needed in B to optimize the use of observations and to reduce spin-up Efforts still are needed to consider observations linked to cloud and precipitations (especially cloudy radiances and radars) in a more optimal way in DAFor the time being, only degraded version of such systems can be used in Nowcasting algorithms, mainly for a question of forecast availability. These versions use shorter cut-off time, shorter cycle frequencies, asynchronous coupling files, and eventually smaller computational domains.In the infra-hour range, spin-up can be problematic and forecasted microphysical quantities should be considered with caution. However, methods to reduce this spin-up exist but often tend to degrade forecast scoresConclusions

Thank you for your attention!

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Brousseau, P.; Berre, L.; Bouttier, F. & Desroziers, G. : 2011. Background-error covariances for a convective-scale data-assimilation system: AROME France 3D-Var. QJRMS., 137, 409-422Berre, L., 2000: Estimation of synoptic and mesoscale forecast error cavariances in a limited area model. MWR. 128, 644667.J.-F Caron and L. Fillion. An examination of background error correlations between mass and rotational wind over precipitation regions. Mon. Wea. Rev., 138 :563578, 2010.O. Caumont, V. Ducrocq, E. Wattrelot, G. Jaubert, and S. Pradier-Vabre. 1d+3dvar assimilation of radar reflectivity data : a proof of concept. Tellus, 62, 2010.V. Guidard, N. Fourri, P. Brousseau, and F. Rabier: 2011. Impact of iasi assimilation at global and convective scales and challenges for the assimilation of cloudy scenes. in press. Quart. J. Roy. Meteor. Soc.Montmerle T, Berre L. 2010. Diagnosis and formulation of heterogeneous background-error covariances at themesoscale. QJRMS, 136, 14081420.Xiao, Q et al, 2007: An Approach of Radar Reflectivity Data Assimilation and Its Assessment with the Inland QPF of Typhoon Rusa (2002) at Landfall. JAMC, 46, 14-22.

References

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3D-FGAT : Draguignan 15/06/2010 Comparaison 3D-Var/3D-FGAT.

Obs : Deux systmes stationnaires conscutifs donnant chacun 200 mm

Simulations : 1er systme ne donne pas plus de 75 mm dans les deux simulations 2ime systme : localisation et intensit meilleure avec FGAT

Lame deau radar De 06 UTC le 15/06 06 UTC le 16/063D-Var3D-FGAT

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ReflectivitiesRadar Arome (guess)Relative humidityPseudo-observation Arome (guess)Elevation 0.44Elements of NWP at convective scale : observation operatorsIllustration of the 1D+3DVar assimilation of radar reflectivities(E. Wattrelot)

*****19/10/11************- We can see on the case of 8 october 2008, that it is possible to dry and desaturate in front of the main squall line. ***19/10/11*******19/10/11******19/10/11*****