Text of Reading Parametrizations and data assimilation Marta JANISKOV ECMWF marta.janiskova@ecmwf.int
Linearized physics for the assimilation of cloud propertiesHow the physics is applied in variational data assimilation system ? Which parametrization schemes are used at ECMWF ? What are the problems to be solved before using physics in data assimilation ? What is an impact of including the physical processes in assimilating model ? related to the physical processes ? Parametrization = description of physical processes in the model. Reading IMPORTANCE OF THE ASSIMILATING MODEL the 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) (4D-Var containing physical parametrizations) (on-off processes, non-linearities) = FINDING A TRADE-OFF BETWEEN: Simplicity and linearity (using simplified linear model is a basis of incremental variational approach) Realism Reading Parametrizations and data assimilation IMPORTANCE OF INCLUDING PHYSICS IN THE ASSIMILATING MODEL using an adiabatic linear model can be critical especially in the tropics, planetary boundary layer, stratosphere missing physical processes in assimilation systems can lead to the so-called spin-up/spin-down problem using the adjoint of various physical processes should provide an initial atmospheric state for NWP models which is: more consistent with physical processes producing better agreement between the model and data inclusion of such processes is a necessary step towards: initialization of prognostic variables related to physical processes the use of new (satellite) observations in data assimilation systems (rain, clouds, soil moisture, …) Parametrizations and data assimilation STANDARD FORMULATION OF 4D-VAR the goal of 4D-Var is to define the atmospheric state x(t0) such that the “distance” between the 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 : xi is the model state at time step ti such as: M is the nonlinear forecast model integrated between t0 and ti H is the observation operator (model space observation space) Parametrizations and data assimilation INCREMENTAL FORMULATION OF 4D-VAR 4D-Var can be then approximated to the first order as minimizing: where is the innovation vector 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 model Gradient of the cost function to be minimized: computed with the non-linear model at high resolution using full physics M computed with the tangent-linear model at low resolution using simplified physics M’ computed with a low resolution adjoint model using simplified physics MT Adjoint operators Tangent-linear operators classical one (TL - Taylor formula, AD - test of adjoint identity) Comparison: computed using the full nonlinear model Reading Reading SIMPLIFICATIONS OF THE LINEARIZED PHYSICS done with the aim to have a physical package for data assimilation: simple – for the linearization of the model equations regular – to avoid strong non-linearities and thresholds effective – to reduce the computational cost for operational applications Reading threshold processes: (some on/off processes: condensation, precipitation formation, …) discontinuities of the derivative of a continuous function strong nonlinearities Reading Without adequate treatment of most serious threshold processes, the TL approximation can turn to be useless. Reading dyNL dx dyTL Reading dx1 dyNL dyTL2 … may just postpone the problem and influence the performance of NL scheme dyTL3 dx2 Reading dyTL2 Reading EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (1) In NWP – a tendency to develop more and more sophisticated physical parametrizations they may contain more discontinuities For the “perturbation” model – more important to describe basic physical tendencies while avoiding the problem of discontinuities Level of simplifications and/or required complexity depends on: which level of improvement is expected (for different variables, vertical and horizontal resolution, …) necessity to remove threshold processes Different ways of simplifications: development of simplified physics from simple parametrizations used in the past selecting only certain important parts of the code to be linearized Reading Regularization of vertical diffusion scheme: perturbation of the exchange coefficients (which are function of the Richardson number Ri) is neglected, K’ = 0 (Mahfouf, 1999) EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (2) reduced perturbation of the exchange coefficients (Janisková et al., 1999): original computation of Ri modified in order to modify/reduce f’(Ri), or reducing a derivative, f’(Ri), by factor 10 in the central part (around the point of singularity ) Ri number Reading selective regularization of the exchange coefficients K based on the linearization error and a criterion for the numerical stability (Laroche et al., 2002) reduction of the time step to 10 seconds to guarantee stable time integrations of the associated TL model (Zhu and Kamachi, 2000) EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (3) Reading SW: 2 spectral intervals LW:neural network+mean Jacob. physical processes are characterized by: threshold processes: (some on/off processes) strong nonlinearities regularizations help to remove the most important threshold processes in physical parametrizations which can effect the range of validity of the tangent linear approximation after solving the threshold problems clear advantage of the diabatic TL evolution of errors compared to the adiabatic evolution TANGENT-LINEAR DIAGNOSTICS Zonal wind increments at model level ~ 1000 hPa [ 24-hour integration] FD TLADIAB TLADIABSVD TLWSPHYS TLADIABSVD – TL model with very simple vertical diffusion (Buizza 1994) TLWSPHYS – TL model with the whole set of simplified physics (Mahfouf 1999) Reading Reading EXP - REF relative improvement Reading adiabsvd || vdif + gwd + radold 10 20 30 40 50 60 80N 60N 40N 20N 0 20S 40S 60S 80S 10 20 30 40 50 60 Reading 80N 60N 40N 20N 0 20S 40S 60S 80S 10 20 30 40 50 60 X X Reading relative improvement relative improvement comparisons of the operational version of 4D-Var against the version without linearized physics included shows: positive impact on analysis and forecast FORECAST VERIFICATION – 500 hPa GEOPOTENTIAL period: 15/11/2000 – 13/12/2000 N.HEM S.HEM in 4D-Var minimization Time evolution of total precipitation in the tropical belt [30S, 30N] averaged over 14 forecasts issued from 4D-Var assimilation IMPACT OF THE LINEARIZED PHYSICS IN 4D-VAR (2) Reading 1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHT OPER (very simple radiation) vs. NEWRAD (new linearized radiation) (27/08/2001 t+24) A1: FC_OPER impact of new linearized radiation 75.4 -30.3 63.8 -23.3 -17.9 -10.0 Reading R = observation and representativeness error covariance matrix H = nonlinear observation operator (model space observation space) (physical parametrization schemes, microwave radiative transfer model, reflectivity model, …) For a given observation yo, 1D-Var searches for the model state x=(T,qv) that minimizes the cost function: Background term Observation term The minimization requires an estimation of the gradient of the cost function: The operator HT can be obtained: explicitly (Jacobian matrix) Schematic description of forward modelling of physical outputs and their corresponding adjoint modelling control variables Parametrizations and data assimilation Precipitation assimilation at ECMWF A bit of history: Work on precipitation assimilation at ECMWF initiated by Mahfouf and Marécal. 1D-Var on TMI and SSM/I rainfall rates (RR) (M&M 2000). Indirect ‘1D-Var + 4D-Var’ assimilation of RR more robust than direct 4D-Var. ‘1D-Var + 4D-Var’ assimilation of RR is able to improve humidity but also the dynamics in the forecasts (M&M 2002). Goal: To assimilate observations related to precipitation and clouds in ECMWF 4D-Var system including parameterizations of atmospheric moist processes. TMI – TRMM Microwave Imager, TRMM – Tropical Rainfall Measuring Mission SSM/I – Special Sensor Microwave/Imager New simplified cloud scheme (Tompkins & Janisková 2004) used in 1D-Var Microwave Radiative Transfer Model (Bauer, Moreau 2002) Assimilation experiments of direct measurements from TRMM and SSM/I (TB or Z) instead of indirect retrievals of rainfall rates, in a ‘1D-Var + 4D-Var’ framework. OPERATIONAL USE: assimilation of precipitation affected microwave radiancess since June 2005 (Bauer et al. 2006) Reading 1D-Var on TBs or reflectivities 1D-Var on TMI or PR rain rates 4D-Var 1D-Var TMI TBs 1D-Var on TMI Rain Rates / Brightness Temperatures Surface rainfall rates (mm h-1) Background 1D-Var on TRMM/ Precipitation Radar data (Benedetti and Lopez, 2003) Tropical Cyclone Zoe (26 December 2002 @1200 UTC) Vertical cross-section of rain rates (top, mm h-1) and reflectivities (bottom, dBZ): observed (left), background (middle), and analysed (right). Black isolines on right panels = 1D-Var specific humidity increments. 2A25 Rain Background Rain 1D+4D-Var assimilation of microwave radiances affected by precipitation (Bauer et al. 2006) rms error differences between RAIN (run with precipitation assimilation) and REF (reference run) geopotential height at 850 hPa (t+24) – mean over 30 days (September 2004) negative values = RAIN improved w.r.t. REF Reading ARM SGP, May 1999 - observations: - surface downward longwave radiation (LWD), - total column water vapour (TCWV) - cloud liquid water path (LWP) Observation operator includes: - shortwave and longwave radiation schemes - diagnostic cloud scheme 1D-Var assimilation of cloud related ARM observations (1) (Janisková et al., 2002) positive values = improvement 1D-Var assimilation of cloud related ARM observations (2) (Benedetti and Janisková, 2004) ARM – Atmospheric Radiation Measurement Cloud reflectivity in dBZ/10 < -20 dBZ AN1= Reflectivity only + Surface LW radiative flux at all levels with respect to radiosoundings % 1D-Var of cloud related ARM observations (3a) (Janisková 2004, Benedetti & Janisková 2004) AN3 = Reflectivity ( W. m^-2) Main objective: to investigate the possibility to assimilate observations affected by cloud and/or precipitation over a certain time window (12 hours), using measurements either with a high temporal resolution (30 min) or that are accumulated or averaged in time 2D-Var framework using ECMWF Single Column Model (SCM, M. Köhler) → much more simple to run and to interpret than 4D-Var So far, test with MW TBs, cloud radar reflectivities, rain-gauge and GPS TCWV data 2D-Var assimilation of ARM observations affected by clouds and precipitation (Lopez et al., 2005) background observations at time ti Hi = “observation operator” (model 2D-Var Reading Parametrizations and data assimilation 2D-Var on 23.8 and 31.4 GHz TBs & mean profiles of cloud radar reflectivities (Lopez et al., 2005) ARM SGP site 4 February 2001 – Assimilation of half-hourly MW TBs over 12 hours is feasible, provided a proper screening is applied ( i.e. |guess – obs| < 3 K ) – Better to assimilate reflectivity profiles averaged over the assimilation window (despite the obvious lost of information) than half-hourly reflectivity profiles due to the sometimes large model-obs departures at such “high” temporal resolution Conclusions: Reading into the assimilating model has been demonstrated. Physical parametrizations become important components in current variational data assimilation systems processes with emphasis on: parametrization of large-scale condensation and clouds (Tompkins and Janisková 2004) Some care must be taken when deriving the linearized parametrization schemes linearity, regularity & efficiency realism This is particularly true for the assimilation of observations related to precipitation, clouds and soil moisture, to which a lot of effort is currently devoted. Reading REFERENCES Bauer, P., Lopez, P., Benedetti, A., Salmond, D. and Moreau, E., 2006: Implementation of 1D+4D-Var assimilation of precipitation affected microwave radiances at ECMWF. Part I: 1D-Va. Quart. J. Roy. Meteor. Soc., accepted. Bauer, P., Lopez, P., Salmond, D., Benedetti, A., Saarinen, S. and Bonazzola, M., 2006: Implementation of 1D+4D-Var assimilation of precipitation affected microwave radiances at ECMWF. Part II: 4D-Var. ECMWF Technical Memorandum 488 Benedetti, A. and Janisková, M., 2004: Advances in cloud assimilation at ECMWF using ARM radar data. Extended abstract for ICCP, Bologna 2004 Errico, R.M., 1997: What is an adjoint model. Bulletin of American Met. Soc., 78, 2577-2591 Fillion, L. and Errico, R., 1997: Variational assimilation of precipitation data using moist convective parametrization schemes: A 1D-Var study. Mon. Wea. Rev., 125, 2917-2942 Fillion, L. and Mahfouf, J.-F., 2000: Coupling of moist-convective and stratiform precipitation processes for variational data assimilation. Mon. Wea. Rev., 128, 109-124 Klinker, E., Rabier, F., Kelly, G. and Mahfouf, J.-F., 2000: The ECMWF operational implementation of four-dimensional variational assimilation. Part III: Experimental results and diagnostics with operational configuration. Quart. J. Roy. Meteor. Soc., 126, 1191-1215 Chevallier, F., Bauer, P., Mahfouf, J.-F. and Morcrette, J.-J., 2002: Variational retrieval of cloud cover and cloud condensate from ATOVS data. Quart. J. Roy. Meteor. Soc., 128, 2511-2526 Chevallier, F., Lopez, P., Tompkins, A.M., Janisková, M. and Moreau, E., 2004: The capability of 4D-Var systems to assimilate cloud_affected satellite infrared radiances. Quart. J. Roy. Meteor. Soc., in press Janisková, M., Thépaut, J.-N. and Geleyn, J.-F., 1999: Simplified and regular physical parametrizations for incremental four-dimensional variational assimilation. Mon. Wea. Rev., 127, 26-45 Janisková, M., Mahfouf, J.-F., Morcrette, J.-J. and Chevallier, F., 2002: Linearized radiation and cloud schemes in the ECMWF model: Development and evaluation. Quart. J. Roy. Meteor. Soc.,128, 1505-1527 Reading Janisková, M., Mahfouf, J.-F. and Morcrette, J.-J., 2002: Preliminary studies on the variational assimilation of cloud-radiation observations. Quart. J. Roy. Meteor. Soc., 128, 2713-2736 Janisková, M., 2004: Impact of EarthCARE products on Numerical Weather Prediction. ESA Contract Report, 59 pp. Laroche, S., Tanguay, M. and Delage, Y., 2002: Linearization of a simplified planetary boundary layer parametrization. Mon. Wea. Rev., 130, 2074-2087 Lopez, P. and Moreau, E., 2005: A convection scheme for data assimilation purposes: Description and initial test. Quart. J. Roy.. Meteor. Soc., 131, 409-436 Lopez., P., Benedetti, A., Bauer, P., Janisková, M. and Köhler, M.., 2005: Experimental 2D-Var assimilation of ARM cloud and precipitation observations. ECMWF Technical Memorandum 456 Mahfouf, J.-F., 1999: Influence of physical processes on the tangent-linear approximation. Tellus, 51A, 147-166 Marécal, V. and Mahfouf, J.-F., 2000: Variational retrieval of temperature and humidity profiles from TRMM precipitation data. Mon. Wea. Rev., 128, 3853-3866 Marécal, V. and Mahfouf, J.-F., 2002: Four-dimensional variational assimilation of total column water vapour in rainy areas. Mon. Wea. Rev., 130, 43-58 Marécal, V. and Mahfouf, J.-F., 2003: Experiments on 4D-Var assimilation of rainfall data using an incremental formulation. Quart. J. Roy. Meteor. Soc., 129, 3137-3160 Moreau, E., Lopez, P., Bauer, P., Tompkins, A.M., Janisková, M. And Chevallier, F., 2004: Rainfall versus microwave brightness temperature assimilation: A comparison of 1D-Var results using TMI and SSM/I observations. Quart. J. Roy. Meteor. Soc., in press. Tompkins, A.M. and Janisková, M. , 2004: A cloud scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc., 130, 2495-2518 Zhu, J. and Kamachi, M., 2000: The role of the time step size in numerical stability of tangent linear models. Mon. Wea. Rev., 128, 1562-1572 -20-15-10-50501002003004005006007008009001000pressure levelsBIAS - Temp-RH for ARM SGPPeriod: 1 - 31 January 2001first-guess departure (o - b)analysis departure (o - a)_1 ( ) ( ) ( ) ( ) ' , 0 J d Ñ x | ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 012345678910111213141516171819202122232425262728293031-40-30-20-1001020304050radiation flux [ W/m2 ]Days since 20010101 00 UTCDifference for LW at TOA: | FG - OBS | - | ANAL - OBS |period: 20010101 - 20010131, site - ARM SGP, observations - TCWV, LWDe)|anal-obs| = 17.994| fg - obs| = 19.015AN_2 ( ) 120°E Wednesday 1 September 2004 00UTC ECMWF Forecast t+24 VT: Thursday 2 September 2004 00UTC 850hPa **geopotential height ECMWF Analysis VT:Thursday 2 September 2004 00UTC 850hPa **geopotential height -1 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.05 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 - RefdBZ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.Days since 20010101 00UTC 984. 977. 962. 939. 905. 861. 807. 745. 676. 603. 528. 454. 383. 316. 256. 201. 154. 113. 80. 55.Pressure (hPa)-12 - -11-11 - -10-10 - -9-9 - -8-8 - -7-7 - -6-6 - -5-5 - -4-4 - -3-3 - -2-2 - -1-1 - 00 - 11 - 22 - 33 - 4 500hPa Z* 2001-08-27 12h fc t+24 A1: fc_oper - anal_oper500hPa Z* 2001-08-27 12h fc t+24 A2: fc_e7gm - anal_oper0.2500hPa Z* 2001-08-27 12h fc t+24 A2 - A14.30.5-5.3500hPa Z* 2001-08-27 12h INIT: anal_e7gm - anal_oper 500hPa Z* 2001-08-27 12h fc t+24 A1: fc_oper - anal_oper500hPa Z* 2001-08-27 12h fc t+24 A2: fc_e7gm - anal_oper0.2500hPa Z* 2001-08-27 12h fc t+24 A2 - A14.30.5-5.3500hPa Z* 2001-08-27 12h INIT: anal_e7gm - anal_oper RefdBZ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.Days since 20010101 00UTC 984. 977. 962. 939. 905. 861. 807. 745. 676. 603. 528. 454. 383. 316. 256. 201. 154. 113. 80. 55.Pressure (hPa)-12 - -11-11 - -10-10 - -9-9 - -8-8 - -7-7 - -6-6 - -5-5 - -4-4 - -3-3 - -2-2 - -1-1 - 00 - 11 - 22 - 33 - 4 RefdBZ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.Days since 20010101 00UTC 984. 977. 962. 939. 905. 861. 807. 745. 676. 603. 528. 454. 383. 316. 256. 201. 154. 113. 80. 55.Pressure (hPa)-12 - -11-11 - -10-10 - -9-9 - -8-8 - -7-7 - -6-6 - -5-5 - -4-4 - -3-3 - -2-2 - -1-1 - 00 - 11 - 22 - 33 - 4 -12-10-8-6-4-202dBZ / 10.01002003004005006007008009001000pressure levelsBIAS - reflectivity for ARM SGPPeriod: 1 - 31 January 2001background departure (o - b)analysis departure (o - a) rmsrms