Reading, UK Parametrizations and data assimilation
© ECMWF 2012
Marta JANISKOVÁ ECMWF
Parametrizations and data assimilation
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
• 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.
PARAMETRIZATIONS IN DATA ASSIMILATION
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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
Realism
GOAL OF DATA ASSIMILATION
production of an accurate representation of the atmospheric state to initialize numerical weather prediction models
POSITION OF THE PROBLEM
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IMPORTANCE OF INCLUDING PHYSICS IN THE ASSIMILATING MODEL
• can be critical especially in the tropics, planetary boundary layer, stratosphere
• can increase the so-called spin-up/spin-down problem
• provides an initial atmospheric state more consistent with physical processes
• creates a better agreement between the model and data
• 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, …)
MISSING PHYSICAL PROCESSES:
INCLUDING PHYSICAL PROCESSES:
PARAMETRIZATIONS OF PHYSICAL PROCESSES:
• constantly being improved
• however, remain approximate representation of the true atmospheric behaviour
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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)
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• In 1D-Var, physical parametrizations can be needed in observation operator, H (no time evolution involved).
• In 4D-Var, physical parametrizations are involved in the observation operator, 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)
Example: to assimilate reflectivity profiles, H must perform the conversion:
Model state (T, q, u, v, Ps )
Cloud and precipitation
profiles
Simulated reflectivity
profile
moist physics reflectivity model
WHY AND WHERE PHYSICAL PARAMETRIZATIONS NEEDED IN DATA ASSIMILATION?
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OPERATIONAL 4D-VAR AT ECMWF – INCREMENTAL FORMULATION
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
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• One of the main assumptions in variational DA is that parametrizations and
operators that describe atmospheric processes should be linear.
otherwise, the use of the tangent-linear and adjoint approach is inappropriate
and the analysis is suboptimal
• In practise, weak nonlinearities can be handled through successive trajectory
updates (e.g., 3 outer loops in ECMWF 4D-Var)
• Physical parametrizations used in DA (TL and AD) are usually simplified
versions 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).
WHY SIMPLIFIED PHYSICS?
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• Variational assimilation is based on the strong assumption that the analysis is performed in quasi-linear framework.
• However, in the case of physical processes, strong nonlinearities or thresholds can occur in the presence of discontinuous/non-differentiable processes (e.g. switches or thresholds in cloud water and precipitation formation, …)
Without adequate treatment of most serious threshold processes, the TL approximation can turn to be useless.
LINEARITY ISSUE
Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 44 **u-velocity
-12
-8
-4
-2
-1
-0.50.5
1
2
4
8
12Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 45 **u-velocity
-12
-8
-4
-2
-1
-0.50.5
1
2
4
8
12 finite difference (FD) TL integration
u-wind increments fc t+12, ~700 hPax 105
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• 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
TL increments correspond well to finite differences
Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 44 **u-velocity
-12
-8
-4
-2
-1
-0.50.5
1
2
4
8
12Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 44 **u-velocity
-12
-8
-4
-2
-1
-0.50.5
1
2
4
8
12
u-wind increments
fc t+12, ~700 hPaTL integrationfinite difference (FD)
IMPORTANCE OF THE REGULARIZATION OF TL MODEL
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Potential source of problem (example of precipitation formation)
dx
dyNL
dyTL
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© ECMWF 2012 dx
dy N
L
dy T
L1
dy T
L2
Possible solution, but …
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dy N
L
dy T
L2
… may just postpone the problem and influence the performance of NL scheme
dy T
L3
dx2
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dy N
L
dy T
L1
dy T
L2
However, the better the model the smaller the increments
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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
SIMPLIFCATIONS AND REGULARIZATIONS OF “PERTURBATION” MODEL
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Regularization of vertical diffusion scheme:
• 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
10.0
0.0
f(Ri)
- 10.0
- 20.0
Function of the Richardson number
EXAMPLES OF REGULARIZATIONS (1)
• reduction of the time step to 10 seconds to guarantee stable time integrations of the associated TL model (Zhu and Kamachi, 2000) not possible in operational global models
Exchange coefficients K are function of the Richardson number:
2UK l f Ri
z
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• selective regularization of the exchange coefficients K based on the linearization
error and a criterion for the numerical stability (Laroche et al., 2002)
-20 -15 -10 -5 0 5 10 15 20Ri
-10
0
10
20
30
f(|R
i)
f(Ri) - trajectoryf(Ri) - perturbationreduction factor up to 3kmreduction factor above 3km
• New operational ECMWF version:
using reduction factor for perturbation
of the exchange coefficients
• perturbation of the exchange coefficients neglected, K’ = 0 (Mahfouf, 1999) in
the operational ECMWF version used to the middle of 2008
EXAMPLES OF REGULARIZATIONS (2)
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ECMWF 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):
• 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.
• Vertical diffusion: – mixing in the surface and planetary boundary layers,
– based on K-theory and Blackadar mixing length,
– exchange coefficients based on Louis et al. [1982], 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.
• No evolution of surface variables
Dry
p
roce
sses
:
• 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.
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ECMWF LINEARIZED PHYSICS (as operational in 4D-Var)
• 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) are reduced.
• 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 cloud into rain.
After solving the threshold problems
clear advantage of the diabatic TL evolution of errors compared to the adiabatic evolution
Mo
ist
pro
cess
es:
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VALIDATION OF THE LINEARIZED PARAMETRIZATION SCHEMES
Non-linear model:
• Forecast runs with particular modified/simplified physical parametrization schemes
• Check 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 identity
Tangent-linear (TL) and adjoint (AD) model:
• examination of the accuracy of the linearization:
comparison between finite differences (FD) and tangent-linear (TL) integration
Singular vectors:
• Computation of singular vectors to find out whether the new schemes do not
produce spurious unstable modes.
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Comparison:
finite differences (FD) tangent-linear (TL) integration
'
,an analysis fg first guess
x x x xan anfg fgM M M
TANGENT-LINEAR DIAGNOSTICS
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TLADIAB – adiabatic TL model
TLWSPHYS – TL model with the whole set of simplified physics (Mahfouf 1999)
TLWSPHYS TLADIAB
FD
Zonal wind increments at model level ~ 1000 hPa [ 24-hour integration]
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Diagnostics:
• mean absolute errors:
• relative error
fganfgan MMM xxxx
%100.
REF
REFEXP
Comparison:
finite differences (FD) tangent-linear (TL) integration
'
,an analysis fg first guess
x x x xan anfg fgM M M
TANGENT-LINEAR DIAGNOSTICS
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EXP - REF
EXP
relative improvement
REF = ADIAB
[%]
X
80N 60N 40N 20N 0 20S 40S 60S 80S60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: SPHYSvdif - ADIAB: -5.81 %
-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
60 80N 60N 40N 20N 0 20S 40S 60S 80S
Temperature Impact of operational vertical diffusion scheme
© ECMWF 2011
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© ECMWF 2012 adiabsvd || vdif + gwd + radold + lsp + conv
EXP - REF
EXP
relative improvement
REF = ADIAB
[%]
X
80N 60N 40N 20N 0 20S 40S 60S 80S60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSold_oper - ADIAB: -9.72 %
-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
60 80N 60N 40N 20N 0 20S 40S 60S 80S
Temperature Impact of dry + moist physical processes (1st used setup)
© ECMWF 2011
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16
adiabsvd || vdif + gwd + rad + cloud+conv cycle
new new new 2009
EXP - REF
REF = ADIAB
EXP
10
20
30
40
50
60
Temperature Impact of all physical processes (including improved schemes)
80N 60N 40N 20N 0 20S 40S 60S 80S60
50
40
30
20
10
Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSnew_oper - ADIAB: -14.73 %
-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
relative improvement [%]
X X X X
80N 60N 40N 20N 0 20S 40S 60S 80S
|FD|
|FD - TL|
adiab
adiabsvd
vdif
oper_old
oper_2007
© ECMWF 2011
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EXP - REF
REF = ADIAB
EXP = cycle before July 2009
Temperature Impact of all physical processes (versions before and after July 2009)
80N 60N 40N 20N 0 20S 40S 60S 80S
80
60
40
20
Error difference: EXP_35R2 - ADIAB Temperature - 15/03/2007 12 h t+12
-0.8
-0.4
-0.2
-0.1
-0.05
-0.025
-0.01
0.01
0.025
0.05
0.1
0.2
80N 60N 40N 20N 0 20S 40S 60S 80S
80
60
40
20
Error difference: EXP_35R2_TL_rad_mod - ADIAB Temperature - 15/03/2007 12 h t+12
-0.8
-0.4
-0.2
-0.1
-0.05
-0.025
-0.01
0.01
0.025
0.05
0.1
0.2
EXP = cycle after July 2009
Changes in linearized radiation schemes
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Zonal wind
|FD|
|FD - TL|
EXP - REF
|FD|
|FD - TL|
Impact of all physical processes
relative improvement [%]
XXX X
conv cyclenew 2009
adiab
adiabsvd
vdif
oper_old
oper_2007
adiab
adiabsvd
vdif
oper_old
oper_2007
EXP - REF 20
18 Specific humidity
X X Xconv cyclenew 2009
relative improvement [%]
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IMPACT OF THE LINEARIZED PHYSICAL PROCESSES 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
– reducing precipitation spin-up problem when using simplified physics in 4D-Var minimization
-0.04-0.02
00.020.040.060.080.100.12
0 1 2 3 4 5 6 7 8 9 10 11Forecast Day
(a) NHem: 500hPa geopotential - Anomaly correlation
N.HEM : 500 hPa geopotential
-0.02
0
0.02
0.04
0.06
0.08
0.10
0.12
0 1 2 3 4 5 6 7 8 9 10 11Forecast Day
(c) NHem: 700hPa rel.humidity - Anomaly correlation
N.HEM : 700 hPa rel. humidity
-0.020
0.020.040.060.080.100.120.140.16
0 1 2 3 4 5 6 7 8 9 10 11Forecast Day
(n) Tropics:700hPa rel.humidity - Anomaly correlation
Tropics : 700 hPa rel.humidity
Anomaly correlation: grey bars indicate significance at 95% confidence level
July – September 2011
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1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHT
OPER (very simple radiation) vs. NEWRAD (new linearized radiation) (27/08/2001 12h 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 PHYSICAL PROCESSES IN 4D-VAR (2)
impact of new linearized radiation
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• June 2005 – March 2009 – 1D+4D-Var assimilation of SSM/I brightness temperatures (TBs) in regions affected by rain and clouds. (Bauer et al. 2006 a, b)• Since March 2009 – active all-sky 4D-Var assimilation of microwave imagers. (Bauer et al. 2010, Geer et al. 2010)• Since November 2011- direct 4D-Var assimilation of NCEP Stage IV radar and gauge hourly precipitation data (Lopez 2011)
AIRS – Advanced Infrared Sounder ARM – Atmospheric Radiation Measurement programme
GPS – Global Positioning System SSM/I – Special Infrared Sounder
Operational:
Experimental:• 1D-Var assimilation of cloud-related ARM observations. (Janisková et al. 2002)
‒ surface downward LW radiation, total column water vapour, cloud liquid water path
• Investigation of the capability of 4D-Var systems to assimilate cloud-affected satellite infrared radiances – 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 microwave TBs, 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)
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Assimilation of rain and cloud related observations at ECMWF
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Impact of the direct 4D-Var assimilation of SSM/I all-skies TBs on the
relative change in 5-day forecast RMS errors (zonal means).
Period: 22 August 2007 – 30 September 2007
Wind Speed
4D-Var assimilation of SSM/I rainy brightness temperatures (Geer, Bauer et al. 2010)
0.10.0500.05-0.1
forecast is better forecast is worse
Relative Humidity
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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
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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
“1D-Var+4D-Var” assimilation of observations related to precipitation
TRMM – Tropical Rainfall Measuring Mission TMI – TRMM Microwave Imager PR – Precipitation Radar
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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)
1D-Var on TMI data (Lopez and Moreau, 2003)
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Background term Observation term
• For a given observation yo, 1D-Var searches for the model state x=(T,qv) that minimizes
the cost function:
1D-Var assimilation of cloud related observations (1)
H(x): moist physics or
+ radar/lidar radiative model
(+ radiation scheme)x_b:
Background
T,q
1D-Var (analyzed T, q)
Y: retrieved cloud parameters
(level-2 products)or
backscatter cross-sections,
reflectivities (level-1 products)
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REF_AT AN - refl
c)
60 N 50 N 40 N 30 N 20 N 10 N 0 10 S 20 S 30 S 40 S 50 S 60SLat
175W 170W 165W 160W 155W 150W 145W 140WLon
1.1
1.9
3.1
4.5
6.1
7.9
9.6
11.2
12.9
14.5
Heig
ht (km
)
-24 - -21 -21 - -18 -18 - -15 -15 - -12 -12 - -9 -9 - -6 -6 - -3 -3 - 0 0 - 3 3 - 6 6 - 9 9 - 12 12 - 15 15 - 19
REF_AT FG
c)
60 N 50 N 40 N 30 N 20 N 10 N 0 10 S 20 S 30 S 40 S 50 S 60SLat
175W 170W 165W 160W 155W 150W 145W 140WLon
1.1
1.9
3.1
4.5
6.1
7.9
9.6
11.2
12.9
14.5
Heig
ht (km
)
-24 - -21 -21 - -18 -18 - -15 -15 - -12 -12 - -9 -9 - -6 -6 - -3 -3 - 0 0 - 3 3 - 6 6 - 9 9 - 12 12 - 15 15 - 19
REF_AT OBS averaged
b)
60 N 50 N 40 N 30 N 20 N 10 N 0 10 S 20 S 30 S 40 S 50 S 60SLat
175W 170W 165W 160W 155W 150W 145W 140WLon
1.1
1.9
3.1
4.5
6.1
7.9
9.6
11.2
12.9
14.5
Heig
ht (km
)
-24 - -21 -21 - -18 -18 - -15 -15 - -12 -12 - -9 -9 - -6 -6 - -3 -3 - 0 0 - 3 3 - 6 6 - 9 9 - 12 12 - 15 15 - 19
1D-Var assimilation of CloudSat cloud radar reflectivity (1) (QuARL project)
OBS – CloudSat (94 GHz radar)
FG
AN – 1D-Var of cloud reflectivity
Cloud reflectivity [dBZ] – 23/01/2007 over PacificQuARL – Quantitative Assessment of Operation.Value of Space-Borne Radar and Lidar Measurements of Cloud and Aerosol Profiles
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© ECMWF 2012
Comparison of FG and AN against cloud optical depth (i.e. independent observations)
Bias and standard deviation of first-guess FG vs.analysis AN departures for reflectivity
profile number0 50 100 150 200 250 300 350 400 450 500 550 600 650 700
0
20
40
60
80
100
clo
ud o
ptical depth
opt_MODISopt_AN_reflopt_FG
BIAS - reflectivity
op
tica
l d
epth
0 4 8 12 161
3
5
7
9
11
13
15
17
heig
ht [k
m]
STDV.DEV. - reflectivity
FG departure (o-b)AN departure (o-a) - AN-refl
STD.DEV. - reflectivity
he
igh
t [k
m]
FG departure AN-refl departure
-16 -12 -8 -4 0 41
3
5
7
9
11
13
15
17
heig
ht [k
m]
BIAS - reflectivity
FG departure (o-b) AN departure (o-a) - AN-refl
he
igh
t [k
m]
FG departure AN-refl departure
1D-Var assimilation of CloudSat cloud radar reflectivity (2) (QuARL project)
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
30°N30°N
40°N 40°N
50°N50°N
60°N 60°N
70°N70°N
100°W
100°W 90°W
90°W 80°W
80°W 70°W
70°W 60°W
60°W 50°W
50°W 40°W
40°W
a) Difference of rms errors for wind at 200 hPa - 20080424 12UTC t+12
-6
-4
-2
-1
-0.5
-0.20.2
0.5
1
2
4
6
30°N30°N
40°N 40°N
50°N50°N
60°N 60°N
70°N70°N
100°W
100°W 90°W
90°W 80°W
80°W 70°W
70°W 60°W
60°W 50°W
50°W 40°W
40°W
b) Difference of rms erros for wind at 200 hPa - 20080424 12 UTC T+24
-6
-4
-2
-1
-0.5
-0.20.2
0.5
1
2
4
6
30°N30°N
40°N 40°N
50°N50°N
60°N 60°N
70°N70°N
100°W
100°W 90°W
90°W 80°W
80°W 70°W
70°W 60°W
60°W 50°W
50°W 40°W
40°W
c) Difference of rms errors for wind at 200 hPa - 20080424 12UTC t+36
-6
-4
-2
-1
-0.5
-0.20.2
0.5
1
2
4
6
30°N30°N
40°N 40°N
50°N50°N
60°N 60°N
70°N70°N
100°W
100°W 90°W
90°W 80°W
80°W 70°W
70°W 60°W
60°W 50°W
50°W 40°W
40°W
d) Difference of rms errors for wind at 200 hPa - 20080424 12UTC t+48
-6
-4
-2
-1
-0.5
-0.20.2
0.5
1.0
2
4
6
Impact on the subsequent forecast: Difference of 200-hPa wind rms errors for FC_exp– AN_ref
T+12 T+24
T+36 T+48
RMS:
ref 1.304
exp 1.259
RMS:
ref 2.510
exp 2.416
RMS:
ref 2.025
exp 1.978
RMS:
ref 3.438
exp 3.361
1D+4D-Var assimilation of CloudSat cloud radar reflectivity (Janisková et al. 2011)
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
Experimental 4D-Var assimilation of cloud optical depth from MODIS (1) (Benedetti and Janisková, 2008)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5FG
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
OB
S
Period = 2006040500 to 2006042000Scatterplot of OBS versus FG
125102040751251502002505007501000150020002500
Maximum number per bin = 1908Total number = 2393230
corr. coef. = 0.480RMS = 0.57BIAS (y-x)= 0.22
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5ANA
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
OB
S
Period = 2006040500 to 2006042000Scatterplot of OBS versus ANA
125102040751251502002505007501000150020002500
Maximum number per bin = 2235Total number = 2393205
corr. coef. = 0.672RMS = 0.51BIAS (y-x)= 0.21
Period: 2006040500 - 2006042000
Assimilation of cloud optical depth at 0.55 m from MODIS – fit to observations Scatter-plot of OBS versus FG Scatter-plot of OBS versus
ANA
BIAS = 0.22 RMS = 0.57 corr. coef. = 0.480
BIAS = 0.21 RMS = 0.51
corr. coef. = 0.672
‒ Positive impact on the distribution of the ice water content, particularly in the Tropics.
‒ Impact on 10-day forecast positive for upper level temperature in the Tropics and neutral for the model wind.
‒ ECMWF 4D-Var is approaching a level of the technical maturity necessary for global assimilation of cloud related observations.
Conclusions:
MODIS – Moderate Resolution Imaging Spectroradiometer © ECMWF 2012
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
MLS retrievals: Ice Water Content at 215 hPa
ECMWF model – CNTRL run
CNTRL run – MLS obs
ECMWF model – EXP run
EXP run – MLS obs
MLS = Microwave
Limb Sounder
Courtesy of F. Li, Jet Propulsory Laboratory, CA, USA
IWC [mg/m3]
Experimental 4D-Var assimilation of cloud optical depth from MODIS (2) Comparison with independent cloud observations
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
• Physical parametrizations become important components in current variational
data assimilation systems as they are needed:
‒ to link the model state to the observation quantities
‒ to evolve the model state in time during the assimilation
• Positive impact from including linearized physical parametrization schemes
into the assimilating model has been demonstrated.
• However, there are several problems with including physics in adjoint models:
– development and thorough validation require substantial resources
– computational cost may be very high
– non-linearities and discontinuities in physical processes must be treated with care
• Constraints and requirements when developing new simplified parametrizations
for data assimilation:
– find a compromise between realism, linearity and computational cost
– evaluation in terms of Jacobians (not too noisy in space and time)
– systematic validation against observations
– comparison to the non-linear version used in forecast mode (trajectory)
– numerical tests of tangent-linear and adjoint codes for small perturbations
– validity of the linear hypothesis for perturbations with larger size (typical of analysis increments)
GENERAL CONCLUSIONS
© ECMWF 2012
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
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© ECMWF 2012
Reading, UK Parametrizations and data assimilation
© ECMWF 2012
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