Reading
Parametrizations and data assimilation
Parametrizations and data assimilation
Marta JANISKOVÁ ECMWF
Reading
Parametrizations and data assimilation
• Why is physics needed in data assimilation ?
• How 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 ?
• How the physics is used for assimilation of observations related to the physical processes ?
• Parametrization = description of physical processes in the model.
Reading
Parametrizations and data assimilation
POSITION OF THE PROBLEM
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)
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 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, …)
Reading
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 :
1 10 0 0 0 0
0
1 1( ) y ( ) y
2 2
no o
i i i i i i ii
J H H
T T
x x R x x x B x xb b
xi is the model state at time step ti such as:
00, xx ttM ii
M is the nonlinear forecast model integrated between t0 and ti
H is the observation operator
(model space observation space)
Reading
Parametrizations and data assimilationINCREMENTAL FORMULATION OF 4D-VAR
1 10 0 0
0
1 1( ) d ( ) d
2 2
n
i i i i i i ii
H HJ
TTx x B x x R x' '
boiiii Hy xd
• 4D-Var can be then approximated to the first order as minimizing:
where is the innovation vector
00 , xx ttM ii'
• In incremental 4D-Var, the cost function is minimized in terms of increments:
with the model state defined at any time ti as: bbb00, , xxxxx ttM iiiii
tangent linear model
ii'ii
n
iii Htt d)(,
2
1 1
000
1
0
xRHMxB TTx
• Gradient of the cost function to be minimized:
0J x
id
ix
0J x
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
Reading
Parametrizations and data assimilationVALIDATION OF THE LINEARIZED SCHEMES
• classical one (TL - Taylor formula, AD - test of adjoint identity)
Comparison:
finite differences tangent-linear integration
• examination of the accuracy of the linearization - TL integrations propagating in time finite-size analysis increments with the trajectory computed using the full nonlinear model
'
,an analysis fg first guess
x x x xan anfg fgM M M
Reading
Parametrizations and data assimilation
ECMWF LINEARIZED PHYSICS
vertical
diffusion
gravity
wave drag radiation
dry processes
deep
convection
large-scale
condensation
mass fluxconvection
statisticalcloud scheme
to be
replaced by
to be
replaced by
moist processes already used in 1D-Var precipitation assimilation
Reading
Parametrizations and data assimilation
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
Parametrizations and data assimilation
• physical processes are characterized by:
* threshold processes:
• discontinuities of some functions describing the physical processes
(some on/off processes: condensation, precipitation formation, …)
• discontinuities of the derivative of a continuous function
* strong nonlinearities
IMPORTANCE OF THE REGULARIZATION OF TL MODEL
Reading
Parametrizations and data assimilation
WHY REGULARIZATION IS IMPORTANT
Without adequate treatment of most serious threshold processes, the TL approximation can turn to be useless.
89.651
86.428
6.593
3.103
3.0792.761
2.525
2.296
2.240
2.179
2.166
1.998
1.819
1.340
1.238
1.232
1.204
*******
-11.257
-8.562-5.838
-4.039
-3.314
-2.279
-2.163
-2.061
-2.041
-1.891
-1.782
-1.572
-1.318
-0.988
89.651
86.428
6.593
3.103
3.0792.761
2.525
2.296
2.240
2.179
2.166
1.998
1.819
1.340
1.238
1.232
1.204
*******
-11.257
-8.562-5.838
-4.039
-3.314
-2.279
-2.163
-2.061
-2.041
-1.891
-1.782
-1.572
-1.318
-0.988
lv31 T* 1999-03-15 12h fc t+6 - TL with vdif (no regularization applied) [cont.int: 0.5e+07]
Reading
Parametrizations and data assimilation
dyNL
dx
dyTL
Potential source of problem (example of precipitation formation)
Reading
Parametrizations and data assimilation
dx
dy N
L
dy T
L1
dy T
L2
Possible solution, but …
Reading
Parametrizations and data assimilation
dx1
dy N
L
dy T
L2
… may just postpone the problem and influence the performance of NL scheme
dy T
L3
dx2
Reading
Parametrizations and data assimilation
dx
dy N
L
dy T
L1
dy T
L2
However, the better the model the smaller the increments
Reading
Parametrizations and data assimilation
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, …)
• which type of observations should be assimilated
• 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
Parametrizations and data assimilation
Regularization of vertical diffusion scheme:
• perturbation of the exchange coefficients (which are function of the Richardson
number Ri) is neglected, K’ = 0 (Mahfouf, 1999)
• 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 )
-20. -10. 0. 10. 20.
Ri number
0.010
0.000
f(Ri)
-0.010
-0.020
Function of the Richardson number
EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (2)
Reading
Parametrizations and data assimilation
• 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
Parametrizations and data assimilation
operational version of ECMWF
EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (4)
SW: 2 spectral intervalsLW:neural network+mean Jacob.
Reading
Parametrizations and data assimilation
• physical processes are characterized by:
* threshold processes:
• discontinuities of some functions describing the physical processes
(some on/off processes)
• discontinuities of the derivative of a continuous function
* 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
IMPORTANCE OF THE REGULARIZATION OF TL MODEL
Reading
Parametrizations and data assimilation
Comparison:
finite differences (FD) tangent-linear (TL) integration
TANGENT-LINEAR DIAGNOSTICS
'
,an analysis fg first guess
x x x xan anfg fgM M M
Reading
Parametrizations and data assimilation
Zonal wind increments at model level ~ 1000 hPa [ 24-hour integration]
FD TLADIAB
TLADIABSVD TLWSPHYS
TLADIAB – adiabatic TL model
TLADIABSVD – TL model with very simple vertical diffusion (Buizza 1994)
TLWSPHYS – TL model with the whole set of simplified physics (Mahfouf 1999)
Reading
Parametrizations and data assimilation
Diagnostics:
• mean absolute errors:
• relative error
fganfgan MMM xxxx
%100.
REF
REFEXP
TANGENT-LINEAR DIAGNOSTICS
Comparison:
finite differences (FD) tangent-linear (TL) integration
'
,an analysis fg first guess
x x x xan anfg fgM M M
Reading
Parametrizations and data assimilation
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -4.55 %
-0.8
-0.4
-0.2
-0.1
-0.05
-0.025
-0.010.01
0.025
0.05
0.1
0.2
0.4
Temperature
adiabsvd
10
20
30
40
50
60 80N 60N 40N 20N 0 20S 40S 60S 80S
EXP - REF
relative improvement
EXP
REF = ADIAB
[%]
Impact of very simple vertical diffusion scheme
Reading
Parametrizations and data assimilation
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -6.22 %
-0.8
-0.4
-0.2
-0.1
-0.05
-0.025
-0.010.01
0.025
0.05
0.1
0.2
0.4
Temperature Impact of dry physical processes
adiabsvd || vdif + gwd + radold
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
EXP - REF
EXP
relative improvement
REF = ADIAB
[%]
Reading
Parametrizations and data assimilation
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -10.41 %
-0.8
-0.4
-0.2
-0.1
-0.05
-0.025
-0.010.01
0.025
0.05
0.1
0.2
0.4
Temperature
adiabsvd || vdif + gwd + radold + lsp + conv
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
EXP - REF
EXP
relative improvement
REF = ADIAB
[%]
Impact of dry + moist physical processes
Reading
Parametrizations and data assimilation
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -14.38 %
-0.8
-0.4
-0.2
-0.1
-0.05
-0.025
-0.010.01
0.025
0.05
0.1
0.2
0.4
Temperature
adiabsvd || vdif + gwd + conv + radnew + cl_new
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
EXP - REF
|FD|
|FD - TL|
REF = ADIAB
EXP
relative improvement [%]
Impact of physical processes (including improved schemes)
X X
Reading
Parametrizations and data assimilation
Zonal wind
Specific humidity
Impact of all physical processes
relative improvement
relative improvement
|FD|
|FD - TL|
|FD|
|FD - TL|
[%]
[%]
EXP - REF
EXP - REF
X X
X X
Reading
Parametrizations and data assimilation
IMPACT OF THE LINEARIZED PHYSICS IN 4D-VAR (1)
• comparisons of the operational version of 4D-Var against the version without linearized physics included shows:
FORECAST VERIFICATION – 500 hPa GEOPOTENTIAL period: 15/11/2000 – 13/12/2000
root mean square error – 29 cases
N.HEM S.HEM
oper RD
4v no phys
– positive impact on analysis and forecast
Reading
Parametrizations and data assimilation
– reducing precipitation spin-up problem when using simplified physics 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
Parametrizations and data assimilation
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 –
ANAL_OPER
A2:
FC_NEWRAD –
ANAL_OPER
A2 – A1
500hPa Z* 2001-08-27 12h fc t+24 A1: fc_oper - anal_oper 500hPa Z* 2001-08-27 12h fc t+24 A2: fc_e7gm - anal_oper
0.2
500hPa Z* 2001-08-27 12h fc t+24 A2 - A1
4.3
0.5
-5.3
500hPa Z* 2001-08-27 12h INIT: anal_e7gm - anal_oper
75.4
-30.3
63.8
-23.3
500hPa Z* 2001-08-27 12h fc t+24 A1: fc_oper - anal_oper 500hPa Z* 2001-08-27 12h fc t+24 A2: fc_e7gm - anal_oper
0.2
500hPa Z* 2001-08-27 12h fc t+24 A2 - A1
4.3
0.5
-5.3
500hPa Z* 2001-08-27 12h INIT: anal_e7gm - anal_oper
-17.9
-10.0
IMPACT OF THE LINEARIZED PHYSICS IN 4D-VAR (3)
impact of new linearized radiation
Reading
Parametrizations and data assimilation
B = background error covariance matrix
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
1D-Var assimilation of observations related to the physical processes
• The minimization requires an estimation of the gradient of the cost function:1 1( ) ( ) ( ( )H )J Tx B x x H R x yb o
• The operator HT can be obtained:
– explicitly (Jacobian matrix)
– using the adjoint technique
Reading
Parametrizations and data assimilation
Schematic description of forward modelling of physical outputs and their corresponding adjoint modelling
controlvariablesT, q, ps
physicsoutput
departures
physical
parametrization
schemes
physicsoutput
adjoint
of physical
parametrization
schemes
controlvariables
increments
Reading
Parametrizations and data assimilationPrecipitation 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.
More recent developments:
• New simplified convection scheme (Lopez & Moreau 2005) • 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.
TMI – TRMM Microwave Imager, TRMM – Tropical Rainfall Measuring Mission SSM/I – Special Sensor Microwave/Imager
OPERATIONAL USE: assimilation of precipitation affected microwave radiancess since June 2005 (Bauer et al. 2006)
Reading
Parametrizations and data assimilation“1D-Var+4D-Var” assimilation of observations related to precipitation
4D-Var
1D-Varmoist physics
moist physics + radiative transfer
background T,qv
background T,qv
“Observed” rainfall rates
Retrieval algorithm (2A12,2A25)
1D-Var on TBs or reflectivities 1D-Var on TMI or PR rain rates
Observations interpolated on model’s T511 Gaussian grid
TMI TBs or
TRMM-PR reflectivities
“TCWVobs”=TCWVbg+∫zqv
Reading
Parametrizations and data assimilation
Background
PATER obs 1D-Var/RR PATER
1D-Var/TB
1D-Var on TMI data (Lopez and Moreau, 2003)
Tropical Cyclone Zoe (26 December 2002 @1200 UTC)
1D-Var on TMI Rain Rates / Brightness Temperatures
Surface rainfall rates (mm h-1)
Reading
Parametrizations and data assimilation
2A25 Rain Background Rain 1D-Var Analysed Rain
2A25 Reflect. Background Reflect. 1D-Var Analysed Reflect.
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.
Reading
Parametrizations and data assimilation1D+4D-Var assimilation of microwave radiances affected by precipitation (Bauer et al. 2006)
120
120 120 12060°S60°S
30°S 30°S
0°0°
30°N 30°N
60°N60°N
120°W
120°W 60°W
60°W 0°
0° 60°E
60°E 120°E
120°E
Wednesday 1 September 2004 00UTC ECMWF Forecast t+24 VT: Thursday 2 September 2004 00UTC 850hPa **geopotential heightECMWF Analysis VT:Thursday 2 September 2004 00UTC 850hPa **geopotential height
-1-0.7-0.6-0.5-0.4-0.3-0.2-0.1-0.050.050.10.20.30.40.50.60.71
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. REFrms rms REFRAIN
Reading
Parametrizations and data assimilation
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
TCWV LWD
LWP SWD
| FG - OBS | - | ANAL - OBS |
Reading
Parametrizations and data assimilation1D-Var assimilation of cloud related ARM observations (2) (Benedetti and Janisková, 2004)
ARM – Atmospheric Radiation Measurement
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.
Pre
ssu
re (h
Pa)
-12 - -11 -11 - -10 -10 - -9 -9 - -8 -8 - -7 -7 - -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 0 0 - 1 1 - 2 2 - 3 3 - 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.
Pre
ssu
re (h
Pa)
-12 - -11 -11 - -10 -10 - -9 -9 - -8 -8 - -7 -7 - -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 0 0 - 1 1 - 2 2 - 3 3 - 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.
Pre
ssu
re (h
Pa)
-12 - -11 -11 - -10 -10 - -9 -9 - -8 -8 - -7 -7 - -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 0 0 - 1 1 - 2 2 - 3 3 - 4
OBS
FG
AN -12 -10 -8 -6 -4 -2 0 2dBZ / 10.
0
100
200
300
400
500
600
700
800
900
1000
pres
sure
leve
ls
BIAS - reflectivity for ARM SGPPeriod: 1 - 31 January 2001
background departure (o - b)analysis departure (o - a)
period: January 2001 (retrieved from 35 GHz radar) Cloud reflectivity in dBZ/10
> 20 dBZ
0 dBZ<Z< 10 dBZ
-10 dBZ<Z< 0 dBZ
< -20 dBZ
Reading
Parametrizations and data assimilation
-20 -15 -10 -5 0 5
0
100
200
300
400
500
600
700
800
900
1000
pres
sure
leve
lsBIAS - Temp-RH for ARM SGP
Period: 1 - 31 January 2001
first-guess departure (o - b)analysis departure (o - a)_1
-20 -15 -10 -5 0 5
0
100
200
300
400
500
600
700
800
900
1000
pres
sure
leve
lsBIAS - Temp-RH for ARM SGP
Period: 1 - 31 January 2001
analysis departure (o - a)_2
-20 -15 -10 -5 0 5
0
100
200
300
400
500
600
700
800
900
1000
pres
sure
leve
lsBIAS - Temp-RH for ARM SGP
Period: 1 - 31 January 2001
analysis departure (o - a)_3
Synergy of active and passive observations for cloud assimilationAN1= Reflectivity only AN2= Total Column Water Vapor
+ Surface LW radiative flux
RELATIVE HUMIDITY BIAS
The combination of passive and active observations gives the lowest analysis bias at all levels with respect to radiosoundings
%
1D-Var of cloud related ARM observations (3a) (Janisková 2004, Benedetti & Janisková 2004)
AN3 = Reflectivity + Total Column Water Vapor + Surface LW radiative flux
Reading
Parametrizations and data assimilation
• 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)
x0 = profile of temperature and
specific humidity at initial time
B = error covariance matrix for background
Ri = error covariance matrices for observations at time ti Hi = “observation operator” (model
space observation space) = O Mti
1
1
minimize
1( ) ( ) ( )
21
( ( ) ( ( )2
-i i i i i
i
J
H ) H )
T0 0 0 0 0
T0 0
x x x B x x
x y R x y
b b
o o
i
b0ti
OM x
tiy
2D-Var
Reading
Parametrizations and data assimilation2D-Var on 23.8 and 31.4 GHz TBs & mean profiles of cloud radar reflectivities (Lopez et al., 2005)
Mean Reflectivity
23.8 GHz TB
31.4 GHz TB
TCWV
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
Parametrizations and data assimilation
SUMMARY AND PERSPECTIVES
• Positive impact from including linearized physical parametrization schemes
into the assimilating model has been demonstrated.
• Physical parametrizations become important components in current variational
data assimilation systems
• Recently, improvement/development of the schemes for the linearized moist
processes with emphasis on:
– moist convection (Lopez and Moreau 2005)
– 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
Parametrizations and data assimilation
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
Parametrizations and data assimilation
REFERENCES
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