Presentation on theme: "Parametrizations and data assimilation"— Presentation transcript:
1Parametrizations and data assimilation Marta JANISKOVÁECMWF
2PARAMETRIZATIONS IN DATA ASSIMILATION Parametrization = description of physical processes in the model.Why is physics needed in data assimilation ?How the physics is applied in variational data assimilation system ?What are the problems to be solved before using physics in dataassimilation ?Which parametrization schemes are used at ECMWF ?What is an impact of including the physical processes inassimilating model ?How the physics is used for assimilation of observationsrelated to the physical processes ?
3POSITION OF THE PROBLEM GOAL OF DATA ASSIMILATIONproduction of an accurate representation of the atmospheric state to initializenumerical weather prediction modelsIMPORTANCE OF THE ASSIMILATING MODELthe better the assimilating model(4D-Var consistently using the information coming from the observations and the model)the better the analysis(and the subsequent forecast)the more sophisticated the model(4D-Var containing physical parametrizations)the more difficult the minimization(on-off processes, non-linearities)DEVELOPMENT OF A PHYSICAL PACKAGE FOR DATA ASSIMILATION= FINDING A TRADE-OFF BETWEEN: Simplicity and linearityRealism
4IMPORTANCE OF INCLUDING PHYSICS IN THE ASSIMILATING MODEL MISSING PHYSICAL PROCESSES:can be critical especially in the tropics, planetary boundary layer, stratospherecan increase the so-called spin-up/spin-down problemINCLUDING PHYSICAL PROCESSES:provides an initial atmospheric state more consistent with physical processescreates a better agreement between the model and dataa necessary step towards:initialization of prognostic variables related to physical processesthe use of new (satellite) observations in data assimilation systems(rain, clouds, soil moisture, …)PARAMETRIZATIONS OF PHYSICAL PROCESSES:constantly being improvedhowever, remain approximate representation of the true atmospheric behaviour
5STANDARD FORMULATION OF 4D-VAR the goal of 4D-Var is to define the atmospheric state x(t0) such that the “distance” betweenthe model trajectory and observations is minimum over a given time period [t0, tn]finding the model state at the initial time t0 which minimizes a cost-function J :H is the observation operator(model space observation space)xi is the model state at time step ti such as:M is the nonlinear forecast model integrated between t0 and ti
6WHY AND WHERE PHYSICAL PARAMETRIZATIONS NEEDED IN DATA ASSIMILATION? In 1D-Var, physical parametrizations can be needed in observationoperator, H (no time evolution involved).Example: to assimilate reflectivity profiles, H must perform the conversion:Model state(T, q, u, v, Ps )Cloud andprecipitationprofilesSimulatedreflectivityprofilemoist physicsreflectivity modelIn 4D-Var, physical parametrizations are involved in the observationoperator, H, but also in the forecast model, M.Physical parametrizations are needed in data assimilation (DA):to link the model state to the observed quantities,to evolve the model state in time during the assimilation(trajectory, tangent-linear (TL) and adjoint (AD) computations in 4D-Var)
7OPERATIONAL 4D-VAR AT ECMWF – INCREMENTAL FORMULATION In incremental 4D-Var, the cost function is minimized in terms of increments:with the model state defined at any time ti as: tangent linear modelTangent-linear operators4D-Var can be then approximated to the first order as minimizing:whereis the innovation vectorGradient of the cost function to be minimized:Adjoint operators computed with the non-linear model at high resolution using full physics M computed with the tangent-linear model at low resolution using simplifiedphysics M’ computed with a low resolution adjoint model using simplified physics MT
8WHY SIMPLIFIED PHYSICS? One of the main assumptions in variational DA is that parametrizations andoperators that describe atmospheric processes should be linear. otherwise, the use of the tangent-linear and adjoint approach is inappropriateand the analysis is suboptimalIn practise, weak nonlinearities can be handled through successive trajectoryupdates (e.g., 3 outer loops in ECMWF 4D-Var)Physical parametrizations used in DA (TL and AD) are usually simplifiedversions of the original parametrizations employed in the forecast models:to avoid nonlinearities (see further),to keep the computational cost reasonable,but they also need to be realistic enough !ECMWF TL and AD models are coded using a manual line-by-line approach.Automatic AD coding softwares exist (but far from perfect and non-optimized).
9finite difference (FD) TL integration LINEARITY ISSUEVariational assimilation is based on the strong assumption that the analysisis performed in quasi-linear framework.However, in the case of physical processes, strong nonlinearities orthresholds can occur in the presence of discontinuous/non-differentiableprocesses(e.g. switches or thresholds in cloud water and precipitation formation, …)finite difference (FD)TL integrationu-wind incrementsfc t+12, ~700 hPax 105Without adequate treatment of most serious threshold processes, the TL approximation can turn to be useless.
10TL increments correspond well to finite differences IMPORTANCE OF THE REGULARIZATION OF TL MODELregularizations help to remove the most important threshold processes in physicalparametrizations which can effect the range of validity of the tangent linear approximationafter solving the threshold problemsTL increments correspond well to finite differencesu-wind incrementsfc t+12, ~700 hPafinite difference (FD)TL integration
11Potential source of problem (example of precipitation formation) dxdyTLdyNL
13… may just postpone the problem and influence the performance of NL scheme dx2dyTL3dyTL2dyNLdx1
14However, the better the model the smaller the increments dyTL1dyTL2dyNLdx
15SIMPLIFCATIONS AND REGULARIZATIONS OF “PERTURBATION” MODEL In NWP – a tendency to develop more and more sophisticated physical parametrizations they may contain more discontinuitiesFor the “perturbation” model – more important to describe basic physical tendencies while avoiding the problem of discontinuitiesLevel of simplifications and/or required complexity depends on:which level of improvement is expected (for different variables, vertical and horizontalresolution, …)which type of observations should be assimilatednecessity to remove threshold processesDifferent ways of simplifications:development of simplified physics from simple parametrizations used in the pastselecting only certain important parts of the code to be linearized
16EXAMPLES OF REGULARIZATIONS (1) Regularization of vertical diffusion scheme:Ri number10.00.0f(Ri)- 10.0- 20.0Function of the Richardson numberExchange coefficients K are function of the Richardson number:reduced perturbation of the exchangecoefficients (Janisková et al., 1999):original computation of Ri modified inorder to modify/reduce f’(Ri), orreducing a derivative, f’(Ri), by factor 10in the central part (around the point ofsingularity )reduction of the time step to 10 seconds to guarantee stable time integrationsof the associated TL model (Zhu and Kamachi, 2000) not possible in operational globalmodels
17EXAMPLES OF REGULARIZATIONS (2) selective regularization of the exchange coefficients K based on the linearizationerror and a criterion for the numerical stability (Laroche et al., 2002)perturbation of the exchange coefficients neglected, K’ = 0 (Mahfouf, 1999) inthe operational ECMWF version used to the middle of 2008New operational ECMWF version:using reduction factor for perturbationof the exchange coefficients
18ECMWF LINEARIZED PHYSICS (as operational in 4D-Var) Currently used schemes in ECMWF operational 4D-Var minimizations – main simplifications with respect to the nonlinear versions are highlighted in red (Janisková and Lopez 2012):No evolution of surface variablesVertical diffusion:– mixing in the surface and planetary boundary layers,– based on K-theory and Blackadar mixing length,– exchange coefficients based on Louis et al. , near surface,– Monin-Obukhov higher up,– mixed layer parameterization and PBL top entrainment recently added,– perturbations of exchange coefficients are smoothed out.Gravity wave drag: [Mahfouf 1999]– subgrid-scale orographic effects [Lott and Miller 1997],– only low-level blocking part is used.Dry processes:Radiation:– TL and AD of longwave and shortwave radiation [Janisková et al. 2002],– shortwave: only 2 spectral intervals (instead of 6 in nonlinear version),– longwave: called every 2 hours only.Non-orographic gravity wave drag:– TL and AD of the non-linear scheme for non-orographic gravity waves [Orr et al. 2010],– suppressing increments for momentum flux for the highest phase speed.
19ECMWF LINEARIZED PHYSICS (as operational in 4D-Var) Large-scale condensation scheme: [Tompkins and Janisková 2004]– based on a uniform PDF to describe subgrid-scale fluctuations of total water,– melting of snow included,– precipitation evaporation included,– reduction of cloud fraction perturbation and in autoconversion of cloudinto rain.Moist processes:Convection scheme: [Lopez and Moreau 2005]– mass-flux approach [Tiedtke 1989],– deep convection (CAPE closure) and shallow convection (q-convergence)– perturbations of all convective quantities included,– coupling with cloud scheme through detrainment of liquid water from updraught,– some perturbations (buoyancy, initial updraught vertical velocity) arereduced.After solving the threshold problemsclear advantage of the diabatic TL evolution of errors compared tothe adiabatic evolution
20VALIDATION OF THE LINEARIZED PARAMETRIZATION SCHEMES Non-linear model:Forecast runs with particular modified/simplified physical parametrization schemesCheck that Jacobians (=sensitivities) with respect to input variables look reasonable(not too noisy in space and time)classical validation: TL - Taylor formula,AD - test of adjoint identityTangent-linear (TL) and adjoint (AD) model:examination of the accuracy of the linearization:comparison between finite differences (FD) and tangent-linear (TL) integrationSingular vectors:Computation of singular vectors to find out whether the new schemes do notproduce spurious unstable modes.
27EXP - REF Temperature Impact of all physical processes (versions before and after July 2009)EXP - REFREF = ADIABEXP = cycle beforeJuly 2009EXP = cycle afterJuly 2009Changes in linearizedradiation schemes
28Impact of all physical processes adiabadiabsvdvdifoper_oldoper_2007EXP - REFZonal windrelative improvement[%]Xconv cyclenewEXP - REF2018Specific humidityXconv cyclenewrelative improvement[%]adiabadiabsvdvdifoper_oldoper_2007
29IMPACT OF THE LINEARIZED PHYSICAL PROCESSES IN 4D-VAR (1) comparisons of the operational version of 4D-Var against the version withoutlinearized physics included shows:positive impact on analysis and forecastreducing precipitation spin-up problemwhen using simplified physics in 4D-Var minimizationN.HEM : 500 hPa geopotentialN.HEM : 700 hPa rel. humidityTropics : 700 hPa rel.humidityAnomaly correlation: grey bars indicate significance at 95% confidence levelJuly – September 2011
30– – A2 – A1 IMPACT OF THE LINEARIZED PHYSICAL PROCESSES IN 4D-VAR (2) 1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHTOPER (very simple radiation) vs. NEWRAD (new linearized radiation) (27/08/ h t+24)75.4-30.363.8-23.3A2:FC_NEWRAD–ANAL_OPERA1:FC_OPER–ANAL_OPER-17.9-10.0A2 – A1impact of new linearized radiation
31Assimilation of rain and cloud related observations at ECMWF Operational:June 2005 – March 2009 – 1D+4D-Var assimilation of SSM/I brightness temperatures (TBs)in regions affected by rain and clouds (Bauer et al a, b)Since March 2009 – active all-sky 4D-Var assimilation of microwave imagers.(Bauer et al. 2010, Geer et al. 2010)Since November direct 4D-Var assimilation of NCEP Stage IV radar and gauge hourlyprecipitation data (Lopez 2011)Experimental:1D-Var assimilation of cloud-related ARM observations (Janisková et al. 2002)surface downward LW radiation, total column water vapour, cloud liquid water pathInvestigation of the capability of 4D-Var systems to assimilate cloud-affected satellite infraredradiances – using cloudy AIRS TBs (Chevallier et al. 2004)1D-Var assimilation of precipitation radar data (Benedetti and Lopez 2003)1D-Var assimilation of cloud radar reflectivity – retrieved from 35 GHz radar at ARM site.(Benedetti and Janisková 2004)2D-Var assimilation of ARM observations affected by clouds & precipitation – using microwaveTBs, cloud radar reflectivity, rain-gauge and GPS TCWV (Lopez et al. 2006)4D-Var assimilation of cloud optical depth from MODIS (Benedetti & Janisková 2007)1D+4D-Var assimilation of NCEP Stage IV hourly precipitation data over USA– combined radar + rain gauge observations (Lopez and Bauer 2007)1D+4D-Var of cloud radar reflectivity from CloudSat (Janisková el al. 2011)AIRS – Advanced Infrared Sounder ARM – Atmospheric Radiation Measurement programmeGPS – Global Positioning System SSM/I – Special Infrared SounderReading, UK
32Relative Humidity Wind Speed -0.1 0.05 0.05 0.1 forecast is better 4D-Var assimilation of SSM/I rainy brightness temperatures (Geer, Bauer et al. 2010)Impact of the direct 4D-Var assimilation of SSM/I all-skies TBs on therelative change in 5-day forecast RMS errors (zonal means).Period: 22 August 2007 – 30 September 2007Relative HumidityWind Speed-0.10.050.050.1forecast is betterforecast is worse
331D-Var assimilation of observations related to the physical processes For a given observation yo, 1D-Var searches for the model state x=(T,qv) that minimizesthe cost function:Background termObservation termB = background error covariance matrixR = observation and representativeness error covariance matrixH = nonlinear observation operator (model space observation space)(physical parametrization schemes, microwave radiative transfer model,reflectivity model, …)The minimization requires an estimation of the gradient of the cost function:The operator HT can be obtained:explicitly (Jacobian matrix)using the adjoint technique
34“1D-Var+4D-Var” assimilation of observations related to precipitation 1D-Var on TBs or reflectivities1D-Var on TMI or PR rain ratesObservations interpolated on model’s T511 Gaussian gridTMI TBsorTRMM-PR reflectivities“Observed” rainfall ratesRetrieval algorithm (2A12,2A25)1D-Varmoist physics+ radiative transferbackground T,qv“TCWVobs”=TCWVbg+∫zqv4D-VarTRMM – Tropical Rainfall Measuring MissionTMI – TRMM Microwave Imager PR – Precipitation Radar
351D-Var on TMI data (Lopez and Moreau, 2003) BackgroundPATER obs1D-Var/RR PATER1D-Var/TBTropical Cyclone Zoe (26 December UTC)1D-Var on TMI Rain Rates / Brightness TemperaturesSurface rainfall rates (mm h-1)
361D-Var assimilation of cloud related observations (1) For a given observation yo, 1D-Var searches for the model state x=(T,qv) that minimizesthe cost function:Background termObservation termH(x): moist physicsor+ radar/lidarradiative model(+ radiation scheme)x_b: BackgroundT,q1D-Var (analyzed T, q)Y: retrieved cloud parameters(level-2 products)backscatter cross-sections,reflectivities (level-1 products)
371D-Var assimilation of CloudSat cloud radar reflectivity (1) (QuARL project) OBS – CloudSat (94 GHz radar)FGAN – 1D-Var of cloud reflectivityCloud reflectivity [dBZ] – 23/01/2007 over PacificQuARL – Quantitative Assessment of Operation.Value of Space-Borne Radar and Lidar Measurements of Cloud and Aerosol Profiles
381D-Var assimilation of CloudSat cloud radar reflectivity (2) (QuARL project) Bias and standard deviation of first-guess FG vs.analysis AN departures for reflectivitySTD.DEV. - reflectivityBIAS - reflectivityFG departureAN-refl departureheight [km]height [km]FG departureAN-refl departureComparison of FG and AN against cloud optical depth (i.e. independent observations)optical depthprofile number
391D+4D-Var assimilation of CloudSat cloud radar reflectivity (Janisková et al. 2011) Impact on the subsequent forecast: Difference of 200-hPa wind rms errors for FC_exp– AN_refT+12T+24RMS:ref 1.304exp 1.259RMS:ref 2.025exp 1.978T+36T+48RMS:ref 2.510exp 2.416RMS:ref 3.438exp 3.361
41Experimental 4D-Var assimilation of cloud optical depth from MODIS (2) Comparison with independent cloud observationsMLS retrievals: Ice Water Content at 215 hPaMLS = MicrowaveLimb SounderIWC [mg/m3]ECMWF model – CNTRL runECMWF model – EXP runCNTRL run – MLS obsEXP run – MLS obsCourtesy of F. Li, Jet Propulsory Laboratory, CA, USA
44Janisková M., 2004: Impact of EarthCARE products on Numerical Weather Prediction. ESA Contract Report, 59 pp.Janisková M., Lopez P. and Bauer P., 2011: Experimental 1D+4D-Var assimilation of CloudSat observations. Q. J. R. Meteorol. Soc., DOI: /qj.988Janisková M. and Lopez P., 2012: Linearized physics for data assimilation at ECMWF. ECMWF Technical Memorandum 666, 26 pp.Laroche S., Tanguay M. and Delage Y., 2002: Linearization of a simplified planetary boundary layer parametrization. Mon. Weather Rev., 130,Lopez P. and Moreau E., 2005: A convection scheme for data assimilation purposes: Description and initial test. Q. J. R. Meteorol. Soc., 131,Lopez. P., Benedetti A., Bauer P., Janisková M. and Köhler M.., 2006: Experimental 2D-Var assimilation of ARM cloud and precipitation observations. Q. J. R. Meteorol. Soc., 132,Lopez P., 2007: Cloud and precipitation parametrizations in modeling and in variational data assimilation. A review. J. Atmos. Sc., 64,Lopez P. and Bauer P., 2007: “1D+4D-Var” assimilation of NCEP Stage IV radar and gauge hourly precipitation data at ECMWF. Mon. Weather Rev., 135,Lopez P., 2011: Direct 4D-Var assimilation of NCEP Stage IV radar and gauge precipitation data at ECMWF. Mon. Weather Rev., 139,Mahfouf J.-F., 1999: Influence of physical processes on the tangent-linear approximation. Tellus, 51A,Marécal V. and Mahfouf J.-F., 2000: Variational retrieval of temperature and humidity profiles from TRMM precipitation data. Mon. Weather Rev., 128,Marécal V. and Mahfouf J.-F., 2002: Four-dimensional variational assimilation of total column water vapour in rainy areas. Mon. Weather Rev., 130, 43-58Marécal V. and Mahfouf J.-F., 2003: Experiments on 4D-Var assimilation of rainfall data using an incremental formulation. Q J. R. Meteorol. Soc., 129,Moreau E., Lopez P., Bauer P., Tompkins A.M., Janisková M. And Chevallier F., 2004: Variational retrieval of temperature and humidity profiles using rain rates versus microwave brightness temperatures. Q. J. R. Meteorol. Soc., 130,Tompkins A.M. and Janisková M. , 2004: A cloud scheme for data assimilation: Description and initial tests. Q. J. R. Meteorol. Soc., 130,Zhu J. and Kamachi M., 2000: The role of the time step size in numerical stability of tangent linear models. Mon. Weather. Rev., 128,