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ECMWF, Reading
Physical processes in adjoint models:
potential pitfalls and benefits
Marta JANISKOVÁ ECMWF
Thanks to: P.Lopez, F. Chevallier A. Benedetti, J.-N. Thépaut, M. Leutbecher
ECMWF, Reading
Linearized models in NWP
• different applications:– variational data assimilation incremental 4D-Var at ECMWF
– singular vector computations initial perturbations for EPS
– sensitivity analysis forecast errors
• first applications with adiabatic linearized model
• nowadays, including the physical processes in the linearized model
4D-Var – Four-dimensional Variational Data Assimilation EPS – Ensemble Prediction System
ECMWF, Reading
Linearized model with physical processes
Including physical processes can:
• in variational data assimilation:– reduce spin-up– provide a better agreement between the model and data– produce an initial atmospheric state more consistent with physical processes– allow the use of new (satellite) observations (rain, clouds, soil moisture, …)
• in singular vector computations:– help to represent some atmospheric features
(processes in PBL, tropical instabilities, development of baroclinic instabilities, …)
• in sensitivity analysis:– allow a reduction of forecast error
• adjoint of physical processes can also be used for:– model parameter estimation– sensitivity of the parametrization scheme to input parameters
ECMWF, Reading
Development of a physical package
• for important applications:– incremental 4D-Var (ECMWF, Météo-France),– simplified gradients in 4D-Var (Zupanski 1993),– the initial perturbations computed for EPS (ECMWF),
linearized versions of forecast models are run at lower resolution
the linear model can be “not tangent” to the full model
(different resolution and geometry, different physics)
simplified approaches as a way to include progressively physicalprocesses in TL and AD models
• simplifications done with the aim to have a physical package:– simple – for the linearization of the model equations
– regular – to avoid strong non-linearities and thresholds
– realistic enough– computationally affordable
TL – tangent linear AD – adjoint
ECMWF, Reading
Full nonlinear vs. simplified physical parametrizations
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 horizontalresolution, …)
• which type of observations should be assimilated• necessity to remove threshold processes
Different ways of simplifications:
• development of simplified physics (for instance, gaining from experience with simpler parametrization schemes used in history)
• applying only part of linearization
ECMWF, Reading
Problems with including physics in adjoint models
• Development – requires substantial resources
• Validation – must be very thorough(for non-linear, tangent-linear and adjoint versions)
• Computational cost – may be very high
• Non-linear and threshold nature of physical processes(affecting the range of validity of the tangent-linear approximation)
ECMWF, Reading
Validation of the physical parametrizations
Non-linear model:
• Forecast runs with particular modified/simplified physical parametrization schemes
Comparison:finite differences (FD) ↔ tangent-linear (TL) integration
( ) ( ) ( )( )guess firstfganalysisan
fganfgan MMM
==
−′↔−
,
xxxx
• examination of the accuracy of the linearization
• classical validation (TL - Taylor formula, AD - test of adjoint identity)
Tangent-linear (TL) and adjoint (AD) model:
Singular vectors:
• Computation of singular vectors to find out whether the new schemes do notproduce spurious unstable modes.
ECMWF, Reading
Importance of the regularization of TL model
• 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
ECMWF, Reading
WHY REGULARIZATION IS IMPORTANT
Without any 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]
ECMWF, Reading
SPURIOUS UNSTABLE MODES PRODUCED BY THE LINEARIZED PHYSICS The first singular vectors located around the cyclone (58oE, 18oS) computed
at the resolution T95 (Barkmeijer, 2002)
20OS20
OS
0O 0 O
40 OE
40 OE 60OE
60OE
SL diabatic T95
20OS20
OS
0O 0O
40OE
40OE 60 OE
60 OE
lv19 VO 2001-01-04 12h
all linearized physical parametrization schemes
-0.2 10 - 6
20°S
20°S
0° 0°
40°E
40°E 60°E
60°E
0.1 10-6
20°S
20°S
0° 0°
40°E
40°E 60°E
60°E
0.1 10-6
withoutthe linearized large-scaleprecipitationscheme
ECMWF, Reading
Potential source of problem
dyNL
dx
dyTL
ECMWF, Reading
Possible solution, but …
dx
dy N
L
dy T
L1
dy T
L2
ECMWF, Reading
… may just postpone the problem and influence the performance of NL scheme
dx1
dy N
L
dy T
L2
dy T
L3
dx2
ECMWF, Reading
dx
dy N
L
dy T
L1
dy T
L2
However, the better the model → the smaller the increments
ECMWF, Reading
Examples of regularizations and simplifications (1)
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
ECMWF, Reading
Examples of regularizations and simplifications (2)
• reduction of the time step to 10 seconds to guarantee stable time integrations of the associated TL model (Zhu and Kamachi, 2000)
• selective regularization of the exchange coefficients K based on the linearization
error and a criterion for the numerical stability (Laroche et al., 2002)
ECMWF, Reading
Comparison: FULL TL – K’=0 – reduced K’ – selective K’ (Laroche et al.2002)
RMS linearization errors for the potential temperature perturbations at the 1st level above the surface
∆t = 1800 s
δ = 1 FULL TLM selective K’ reduced K’
K’=0
∆t = 60 sδ = 0.001
∆t = 60 sδ = 1
ECMWF, Reading
Importance of the regularization of TL model
• 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 inphysical 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
ECMWF, Reading
Zonal wind increments at model level ~ 1000 hPa [ 24-hour integration]
TLADIAB
TLWSPHYS
FD
TLADIABSVD
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)
ECMWF, Reading
Simplified physical parametrizations
ECMWF LINEARIZED PHYSICS
vertical diffusion
gravity wave drag
radiation
simplified LW
SW and LW schemes
(cloud accounted)
dry processes
deep convection
large-scale condensation
mass fluxconvection
statisticalcloud scheme
to be
replaced by
to be
replaced by
moist processes
ECMWF, Reading
Tangent-linear diagnostics
Comparison:finite differences (FD) ↔ tangent-linear (TL) integration
( ) ( ) ( )( )guess firstfganalysisan
fganfgan MMM
==
−′↔−
,
xxxx
Diagnostics:
• mean absolute errors:
• relative error
( ) ( )[ ] ( ) fganfgan MMM xxxx −′−−=ε
%100.
REF
REFEXP
ε
εε −
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
10
20
30
40
50
6080N 60N 40N 20N 0 20S 40S 60S 80S
εEXP - εREF
relative improvement
EXP
REF = ADIAB
[%]
pTemperature
adiabsvd
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
EXP
relative improvement
REF = ADIAB
[%]
pTemperature
adiabsvd || vdif
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
EXP
relative improvement
REF = ADIAB
[%]
pTemperature
adiabsvd || vdif + gwd
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
EXP
relative improvement
REF = ADIAB
[%]
pTemperature
adiabsvd || vdif + gwd + radold
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
EXP
relative improvement
REF = ADIAB
[%]
pTemperature
adiabsvd || vdif + gwd + radold + lsp
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
EXP
relative improvement
REF = ADIAB
[%]
pTemperature
adiabsvd || vdif + gwd + radold + lsp + conv
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
EXP
relative improvement
REF = ADIAB
[%]
pTemperature
adiabsvd || vdif + gwd + lsp + conv + radnew
ECMWF, Reading
Impact of physical processes
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-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
80N 60N 40N 20N 0 20S 40S 60S 80S
10
20
30
40
50
60
εEXP - εREF
|FD||FD - TL|
REF = ADIAB
EXP
relative improvement [%]
pTemperature
adiabsvd || vdif + gwd + conv + radnew + cl_new
ECMWF, Reading
Zonal wind
Specific humidityrelative improvement
relative improvement
X
X
|FD||FD - TL|
|FD||FD - TL|
[%]
[%]
X
X
εEXP - εREF
εEXP - εREF
Impact of physical processes
ECMWF, Reading
Temperature: 3.8 %
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-0.2
-0.1
-0.05
-0.025
-0.0125
-0.0050.005
0.0125
0.025
0.05
0.1
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
p
-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
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
50
40
30
20
10
-1.6
-1.2
-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
Zonal wind: 6.1 %
Specifichumidity: 7.7 %
10
20
30
40
50
6080N 60N 40N 20N 0 20S 40S 60S 80S
80N 60N 40N 20N 0 20S 40S 60S 80S 80N 60N 40N 20N 0 20S 40S 60S 80S
εEXP - εREF
REF = ADIAB
p yImpact of moist processes (lsp + conv)
ECMWF, Reading
Physics in 4D-Var
( ) 00 , xx δδ ttM ii'=
• In incremental 4D-Var, the objective function is minimized in terms of increments:
with the model state defined at any time ti as: ( ) bbb00, , xxxxx ttM iiiii =+= δ
← tangent linear model
( ) ( ) ( )iiii
n
iiii HH d)(d)(
21
21 1
00
100 −−+= −
=
− ∑ xRxxBxx TT δδδδδ ''J
( )boiiii Hy x−=d
• 4D-Var can be then approximated to the first order as minimizing:
where is the innovation vector
( ) ( )ii'ii
n
iii Htt d)(,
21 1
000
10
−+=∇ −
=
− ∑ xRHMxB TTx δδδ J
Gradient of the objective function to be minimized:
J0xδ∇
id
ixδ
J0xδ∇
← 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
ECMWF, Reading
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:
– positive impact on analysis and forecast
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
ECMWF, Reading
Impact of the linearized physics in 4D-Var (2)
– reducing spin-up problem when using physical processes
Time evolution of global precipitation in the tropical belt [30S, 30N] averaged over 14 forecasts issued from 4D-Var assimilation
ECMWF, Reading
Impact of the linearized physics in 4D-Var (3) 1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHT
OPER vs. NEWRAD (27/08/2001 t+24)
A1:
FC_OPER –
ANAL_OPER
A2:
FC_NEWRAD –
ANAL_OPER
A2 – A1
75.4
-30.3
63.8
-23.3
0.2
-17.9
-10.0
ECMWF, Reading
1D-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 objective function:
B = 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, …)
)(()((21)()(
21)( 11 oobb yxRyxxxBxxx TT −−+−−= −− )H)HJ
Background term Observation term
• The minimization requires an estimation of the gradient of the objective function:
)(()()( 11 ob yxRHxxBx T −+−=∇ −− )HJ
• The operator HT can be obtained:– explicitly (Jacobian matrix)
– using the adjoint technique
ECMWF, Reading
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 thedynamics in the forecasts (M&M 2002).
More recent developments:• New simplified convection scheme (Lopez 2003)• New simplified cloud scheme (Tompkins & Janisková 2003) 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.
Goal: To assimilate observations related to precipitation and clouds in ECMWF’s 4D-Var system including parameterizations of atmospheric moist processes.
TMI – TRMM Microwave Imager, TRMM – Tropical Rainfall Measuring Mission SSM/I – Special Sensor Microwave/Imager
ECMWF, Reading
“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+mzδqv
ECMWF, Reading
1D-Var on TMI data (Lopez and Moreau, 2003)
Background
PATER obs 1D-Var/RR PATER
1D-Var/TB
Tropical Cyclone Zoe (26 December 2002 @1200 UTC)
1D-Var on TMI Rain Rates / Brightness Temperatures
Surface rainfall rates (mm h-1)
ECMWF, Reading
1D-Var on TRMM/ Precipitation Radar data (Benedetti, 2003)
2A25 Rain Background Rain 1D-Var Analysed Rain
2A25 Reflect. Background Reflect. 1D-Var Analysed Reflect.
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.
ECMWF, Reading
“1D-Var+4D-Var” assimilation of TRMM-PR rain rates/reflectivities:Impact on analysed and forecast TCWV and MSLP (Experiment – Control)
(Tropical Cyclone Zoe, 26-28 December 2002)
Analysis26/12/2002 03UTC
with
PR
rain
rate
s
Forecast26/12/2002 03UTC t+9
Forecast26/12/2002 03UTC t+57
with
PR
refle
ctiv
ities
ECMWF, Reading
1D-Var assimilation of ARM observations (1)
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
positive values = improvement
TCWV LWD
LWP SWD
| FG - OBS | - | ANAL - OBS |
ECMWF, Reading
1D-Var assimilation of ARM observations (2)
Cloud %
| 20. | 21. | 22. | 23. | 24. | 25. | 26. | 960.
880.
800.
720.
640.
560.
480.
Pressu
re (h
Pa)
1 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
Cloud %
| 20. | 21. | 22. | 23. | 24. | 25. | 26. | 960.
880.
800.
720.
640.
560.
480.
Pressu
re (h
Pa)
Cloud %
| 20. | 21. | 22. | 23. | 24. | 25. | 26. |Days since 19990501 00UTC
960.
880.
800.
720.
640.
560.
480.
Pressu
re (h
Pa)
OBS
FG
AN
Sensitivity of LWD to T, q and cloud fraction
ARM – Atmospheric Radiation Measurement
Time series of the cloud fraction (%) for the period 20-26 May 1999.
ECMWF, Reading
Cloudy AIRS Tbs and 4D-Var (Chevallier, 2003)
• 4D-Var assumes that the forward operator is linear in the vicinity of the background
Fairly true for cloudy upper tropospheric channels
6.3 µm4.5 µm14.3 µm
PDF of correlations betweenH.dx and H[x+dx] – H[x]Hemispheric data
• x = T, q profile• H = cloud scheme
+ RTTOVCLD• dx = perturbation
AIRS – Advanced Infrared Sounder
ECMWF, Reading
Cloudy AIRS Tbs and 1D-Var (Chevallier, 2003)
• Linear 1D-Var retrievalsobservations = 35 upper tropospheric AIRS channelsperformed only if clouds are detected in more than 13 channels
Validation:
1D-Var vs European radiosondesNov 2002 and Feb 2003
• If T<243K use Vaisala RS90 only• ~ 250 matches in upper troposphere • ~ 2300 matches in lower troposphere
ECMWF, Reading
20°S
10°S
5
10
20
30
40
50
60
70
80
90
100-48-36-24-12012
243648
7260
8496108120
-48-36-24-1201224
3648
7260
8496108120
10oS
20oS
10oS
20oS
60oE 80oE
Probability that the cyclone KALUNDE will pass within 120 km radius during the next 120 hours
(06/03/2003 12 UTC)
numbers – real position of the cyclone at the certain hour green line – control T255 forecast (unperturbed member of ensemble)
Tropical SV with adiabsvd
Tropical SV with wsphys
Tropical singular vectors (Leutbecher and Van Der Grijn, 2003)
ECMWF, Reading
Sensitivity of the parametrization scheme to input variables
• using the adjoint technique
• adjoint FT of the linear operator F provides the gradient of an objective function Jwith respect to x (input variables) given the gradient of J with respect to y(output variables):
xF
x x ∂∂
=∂∂ JJ T or JJ yxx F ∇=∇ T
xx ∂∂
=∇F
J
∂F / ∂T sensitivity to: temperature ∂F / ∂q spec.humidity ∂F / ∂a cloud cover ∂F / ∂qlw cloud lwc ∂F / ∂qiw cloud iwc
EXAMPLE: sensitivity of radiation scheme - the gradient with respect to y of unity size (i.e., perturbation of some of the radiation fluxes with ± 1 W.m-2)
• experiments done in the global model:– potential for a thorough evaluation of the relative importance of different variables
for parametrization scheme– investigation of spatial and temporal patterns of sensitivity variations
ECMWF, Reading
Sensitivity of the shortwave upward radiation flux at the TOA with respect to specific humidity [W.m-2/g.kg-1] CLEAR SKY
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
55
50
45
40
35
30
25
20
15
10dF/dq_swc 20001215 1200 t+24 Expver h1sc (180.0W-180.0E)
-2.1
-1.8
-1.5
-1.2
-0.9
-0.6
-0.3
-0.1
-0.05
-0.025
-0.0125
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
55
50
45
40
35
30
25
20
15
10dF/dq_swc 20010315 1200 t+24 Expver h2sc (180.0W-180.0E)
-2.1
-1.8
-1.5
-1.2
-0.9
-0.6
-0.3
-0.1
-0.05
-0.025
-0.0125
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
55
50
45
40
35
30
25
20
15
10dF/dq_swc 20010615 1200 t+24 Expver h3sc (180.0W-180.0E)
-2.1
-1.8
-1.5
-1.2
-0.9
-0.6
-0.3
-0.1
-0.05
-0.025
-0.0125
21
12
. 1 . 1
./. 1
−−
−−
→=
=
mWkggdq
kggmWdqdF
winter spring
summer - 0.0125
- 0.025
- 0.05
- 0.1
- 0.3
- 0.6
- 0.9
- 1.2
- 1.5
- 1.8
- 2.1
10
15
20
25
30
35
40
45
50
55
6080N 60N 40N 20N 0 20S 40S 60S 80S
80N 60N 40N 20N 0 20S 40S 60S 80S
10
15
20
25
30
35
40
45
50
55
60
10
15
20
25
30
35
40
45
50
55
60
80N 60N 40N 20N 0 20S 40S 60S 80S
mod
el le
vels
mod
el le
vels
ECMWF, Reading
Level 44 ~ 700 hPa
WINTER
-2.4
-2.4-2.4 -2.4
-2
-2 -2
-1.6 -1.6
-1.6 -1.6
-1.6-1.2 -1.2
-1.2-1.2
-0.8 -0.8
-0.8 -0.8-0.4
-0.4-0.4-0.2 -0.2 -0.2 -0.2-0.1 -0.1
-0.1 -0.1
-0.05
dF/dq_swc 15 December 2000 12UTC ECMWF t+24 Level 44
Sensitivity of the shortwave upward radiation flux at the TOA with respect to specific humidity [W.m-2/g.kg-1] CLEAR SKY
ECMWF, Reading
Sensitivity of the shortwave/longwave upward radiation flux at the TOA with respect to cloud fraction [W.m-2/cloudfr]
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
55
50
45
40
35
30
25
20
15dF/dc_sw 20001215 1200 t+24 Expver h1sw (180.0W-180.0E)
0.25
0.5
1
1.5
2
3
4
5
6
7
8
9
10
2
2
2
.12.0. 5 1
/. 5
−
−
−
→=
→=
=
mWdcmWdc
cloudfrmWdcdF
80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60
55
50
45
40
35
30
25
20
15dF/dc_lw 20001215 1200 t+24 Expver h1lw (180.0W-180.0E)
0.25
0.5
1
2
3
4
5
7.5
10
12.5
15
WINTER
shortwave radiation
longwave radiation
10
15
20
25
30
35
40
45
50
55
60
10
15
20
25
30
35
40
45
50
55
60
80N 60N 40N 20N 0 20S 40S 60S 80S
80N 60N 40N 20N 0 20S 40S 60S 80S
15.0
12.5
10.0
7.5
5.0
4.0
3.0
2.0
1.0
0.5
0.25
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.5
1.0
0.5
0.25
WINTER
mod
el le
vels
mod
el le
vels
ECMWF, Reading
Summary
• Positive impact from including linearized physical parametrization schemes(into the assimilating model, singular vector computations used in EPS)has been demonstrated in experimental and operational runs.
• Adjoint of physical processes can also be used for sensitivity studies and modelparameter estimation.
• Physical parametrizations become important components in recent variationaldata assimilation systems.
• Some care must be taken when deriving the linearized parametrization schemes
(regularizations/simplifications).
• 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.
• One cannot also forget technical difficulties and time-consuming adjointdevelopment → reliable and efficient automatic tool for adjoint coding would be useful.
ECMWF, Reading ZERO BENEFIT
ECMWF, Reading ZERO BENEFIT
ECMWF, Reading ZERO BENEFIT
ECMWF, Reading ZERO BENEFIT
WE AREHERE
ECMWF, Reading ZERO BENEFIT
WE ARE HERE
MAXIMUM POTENTIAL BENEFIT
ECMWF, Reading
FORECAST VERIFICATION – 500 hPa GEOPOTENTIAL period: 11/05/2001 – 26/05/2001
(4D- Var experiments with the new linearized radiation: lin_rad) root mean square error – 16 cases
Northern Hemisphere North America