# Reading Parametrizations and data assimilation Marta JANISKOV ECMWF marta.janiskova@ecmwf.int

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### 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.
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)
Simplicity and linearity
(using simplified linear model is a basis of incremental variational approach)
Realism
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
Tangent-linear operators
classical one (TL - Taylor formula, AD - test of adjoint identity)
Comparison:
computed using the full nonlinear model
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
threshold processes:
(some on/off processes: condensation, precipitation formation, …)
discontinuities of the derivative of a continuous function
strong nonlinearities
Without adequate treatment of most serious threshold processes, the TL approximation can turn to be useless.
dyNL
dx
dyTL
dx1
dyNL
dyTL2
… may just postpone the problem and influence the performance of NL scheme
dyTL3
dx2
dyTL2
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
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
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)
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
TANGENT-LINEAR DIAGNOSTICS
Zonal wind increments at model level ~ 1000 hPa [ 24-hour integration]
FD
TLWSPHYS
TLADIABSVD – TL model with very simple vertical diffusion (Buizza 1994)
TLWSPHYS – TL model with the whole set of simplified physics (Mahfouf 1999)
EXP - REF
relative improvement
10
20
30
40
50
60
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
X
X
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)
1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHT
A1:
FC_OPER
75.4
-30.3
63.8
-23.3
-17.9
-10.0
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)
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
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)
Cloud reflectivity in dBZ/10
< -20 dBZ
AN1= Reflectivity only
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
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:
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.
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
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
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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
(
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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

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